86 Experiments by Fizeau and Hoek seemed to support Fresnel's thesis of at most a partial motion of ether and not Stokes' ideas of total motion. Einstein (1920) was later to say that "the theory of the stationary quasi-rigid ether found strong support in Fizeau's experiment from which one was obliged to infer that such ether (if it existed seemingly) was motionless and takes no part in the movement of bodies" (ie as moving water). But the idea of the stationary ether was also inadequate as an explanation, I believe, and led Einstein to consider other options (which presumably would account for Fizeau as well or better). Certainly, the absolutist position remained in doubt. It is still rather confusing to interpret such results as Fizeau. Does a conclusion of a motionless ether (in running water with light passing through it either with or against the flow) imply there is absolute motion of the bodies used to measure light. If the ether takes 'no part' (an odd way of describing it) in the motion of such a body as flowing water, this seems to be at odds with Michelson's negative result which, before Lorentz's contraction explanation, had to conclude that there was no stationary ether - only a moving form of this - which does take part in the movement of such bodies as the Earth and its attached measuring apparatus as an inertial system such that the classical principle of relativity would apply. But, is the aberration phenomenon (see below) consistent with this view? There seems to have been a number of such contrary findings, anomalies and paradoxes. This was 'the problem' it seems. A new postulate regarding light and the principle of relativity was thus required - one which adapted the latter with regard to its previously unquestioned assumptions (re space and time) and, in terms of the former, needed someone (around the turn of the century) to say, in effect, "Hey, wait a minute; hasn't Maxwell already shown that light's speed is in fact a constant ? Why would we expect it to vary therefore - according to various assumptions concerning the motion of its assumed carrier ? Its speed doesn't remain constant because of any effects of a still or moving ether, but simply because its (always) constant - per se! That someone was of course Einstein, as elaborated further below. But for 25 years, no one else seemed to take Maxwell's discovery and its implications properly 'on board'.
87 But first, in the meantime, we may consider how views on a stationary vs mobile ether was also influenced by findings regarding:
(3) - The Direction of light's path:
When light was viewed as a particle, it allowed an explanation of the apparent deflection of light that reaches the Earth from the stars - ie the aberration phenomenon, something its conception as a longitudinal wave wouldn't allow. How did it fare in this regard when later seen instead as a transverse wave ? It appears that a deflection of the 'wave plane' does not occur. For if the light rays arrive perpendicular to the motion of the observer, the wave planes are parallel to that observer's motion who would perceive them as such. An analysis utilising the relevant Galileo transformation results in the conclusion that the moving observer must see a light wave of exactly the same frequency, velocity and direction as would a stationary observer. How can we account for the well established aberration phenomenon therefore? This is accomplished by treating the light in terms of its 'energy paths' which in effect behave with respect to the laws of relative motion as would light seen as discrete particles. However, it is also possible to account for aberration in terms of light as an unqualified wave phenomenon - by analysing its refraction behaviour in the lenses of the optical instruments involved in its study. In this regard, the motion or otherwise of the ether should prove relevant. Aberration proves consistent with Fresnel's theory of a stationary or partly stationary ether as the conveyor of that transverse wave, but not with the view of a moving ether as advanced by Stokes. The former approach gives a law of refraction of light waves at the surface of moving bodies by which aberration is fully accounted. With the source of the light and the observer moving together (on Earth) no deflection of the light through an ether wind would be expected in this interpretation. The wave conception of light propagating through a stationary ether (also concluded by Fizeau) would however raise other difficulties - in relation to the relativity-absolutivity question - which, with other experimental measures concerning light not readily explicable, took much longer to resolve.
88 As Fresnel's theory again seemed to account exactly for all the facts of aberration and its effect on the apparent direction of light's path, it could, as mentioned, be interpreted in retrospect as support (within mechanics) for a still ether and the principle of relativity as it would apply to optics. Nevertheless, it was accepted that improved methods of optical measurement were still needed - as Maxwell's idea of using Jupiter's moon eclipses (as per Romer). If this showed that the motion of the Solar system relative to a fixed ether had no influence on the velocity of light (apparently not what Maxwell assumed), then the stationary ether theory would be unsupportable. Such a finding would apparently be one of sufficient magnitude and hence not easily argued away with yet more ad hoc hypotheses. The effect of the relative motion of the Earth on the perceived direction of light as a transverse wave had to be consistent with some view as to the motion or other wise of the intervening ether. This focus of the question placed such phenomena within a broader range of such questions about light's behaviour (including its velocity and frequency) relating to this same matter as it pertains to the mechanical model and the conceptions of space and time relevant thereto. Fresnel and Stokes were thus concerned that their respective views on the motion of the ether proved consistent with all such measurements of light - within the mechanical model.
89 But such experiments (as suggested by Maxwell) are apparently too difficult and therefore it became necessary to devise one that could be more certain in its conclusions - ie that could measure the dependence of optical events on the Earth's motion through the generally suspected still ether - up to the level of second order - as the difference sought was known to be such. And if these failed , then the (moving or partially-moving) ether theory would be truly disproved - in a practical rather than theoretical way. This would mean that a mechanically-based principle of relativity for optics would not hold rigorously and thus that Fresnel's partial convection theory was unsupported. Some other theory or principle of relativity, a modification of the classical one, might then be required - one that could hold rigorously. But, if this was not to be associated with either a moving or even partially-moving ether (as apparently it wasn't), the only alternative would seem to be a return to the totally stationary one more consistent with Newton's earlier ideas of absolute space as a base for relativity. This was the situation when Maxwell, Hertz, Michelson and Lorentz progressively entered the stage (ca 1870s-90s) and sought to build on and adapt the theories of Fresnel and Stokes.
For did light - as a transverse wave - still not require a carrier of some kind? Was this not why theories of the ether had originated and persisted - even if having to adapt as the new behaviours, character and properties of light were gradually discovered? Indeed, light could be seen to be that waving ether as it travelled moment to moment from its source - the new, non-elastic ether being a kind of potential light residing in space in a dormant mode until so activated (to vibrate) to become, momentarily, transmitting light energy - like the 'stand-up' phase of a Mexican wave. The ether theory was in fact developed in this very direction (ie returning to the idea of a stationary but non-elastic ether in absolute space) - as the role of electromagnetic phenomena in light became apparent in the last quarter of the century. Various 'ether' concepts of this form were then advanced during the 1880s and eventually coalesced into a single new electromagnetic ether - of stationary character - which gained increasing support - especially as developed by Hertz and Lorentz. (Maxwell had had various thoughts and reservations about the ether, while Michelson took the view that it did exist - as a still medium for light). If the new ether - as a stationary entity - was successful, there would be no place for an idealised principle of relativity devoid of any absolutist basis. Rather, some form of that latter position would seem finally to prevail. But if not successful, possibly some new version of relativity could still prove viable - one not dependent upon ether - of any degree of motion (or non-motion) or elasticity. The final result was a near thing - but decisive. The behaviour of light could then be re-examined to see how it operates - without any hypothesised ether - stationary or otherwise.
91. We may now consider how the 3 characteristics of light discussed above (plus Michelson's study before Lorentz's explanation) gave reason to conclude that light's speed was not dependent on absolute motion and therefore that the principle of relativity did apply although this meant that it's speed should vary...and yet ether shouldn't move (according to the aberration phenomenon); so, one could either deny that it was moving and return to the belief that it was still (as an absolutist principle of mechanics would suggest)...or...find some new interpretation which, for example, says there is no ether, no variation in light's speed, no absolutist principle but, equally, no principle of relativity - at least not one which included unspoken assumptions about space and time. This new interpretation did unfold but only after such as the above was re-considered in light of new conceptions of light and its now non-elastic but still ether-like medium (ie post-Maxwell) - ie still to no avail - but which somehow provided a better platform by which 'the problem' was viewed and in a sense re-defined by Einstein and his theory then advanced to resolve it. Poincare too saw there was a problem but couldn't fully analyse or resolve it.
On the Nature of Light (2)
II. Towards its Electromagnetic Basis - within a Non-elastic Medium (or even No Medium)
92 The fact that certain materials when rubbed with others could produce a weakly attracting 'force' was known from antiquity - as when amber (elektron in Greek) is rubbed with fur. Equally, it was known that certain minerals, as magnetite, would attract small pieces of iron by means of a similar weak force - but without the need for any prior rubbing. But these phenomena were not of particular concern to those such as Galileo or Newton when they were seeking to understand the principles and laws of force and motion generally in nature. [However, Galileo was quite interested in the early account on Magnetism by the English scientist Gilbert.] But shortly after Newton died, Gray (1729) and du Fay (1730) began to investigate such matters more thoroughly. For the rest of that century, many advances were made in understanding these two phenomena - electricity and magnetism - which while showing some similarities were generally treated and studied quite separately. Details of these developments have been given elsewhere (which see). In both areas, the question arose as to how the forces involved, be they those of attraction or repulsion, were transmitted through space (as touched on earlier). Thus, there were increasingly these two additional imponderables to consider - in addition to those of gravity and light - in the overall problem of the relative or absolute motion of all matter or disturbances/waves. Initially, it was assumed that they could only act 'contiguously' - that is, when the materials concerned were in direct or virtually direct contact - causing effects by sequetial contactover space and time. But Newton's theory of the force of gravity gave rise to the concept of forces generally acting-at-a-distance - and apparently instantaneously. This perspective then continued for many decades. But, as with light, they were thought initially to require a medium for their transmission - even if it was instantaneous. Eventually, however, activity through such media were seen by some physicists at least as requiring time. They couldn't transmit instantaneously.
93 Franklin (1747), that amazing polymath, introduced the important concept of electric 'charge' by which a body such as amber is 'charged up' with the unknown electric 'fluid' and through which the associated attracting force was assumed somehow to act. Aepinus (1759) described a qualitative model of the forces that establish such a condition 'at-a-distance'. Quantitative laws to account for this phenomenon of 'electro-statics' were then advanced by Priestley (1767) and Cavendish (1771) and proved more conclusively by Coulomb (1785). The latter's law stated that the force between charged entities (as amber and any small item it attracts) varies as the square root of the distance between them (similar to that of gravity between masses). This provides a means to determine how charges on a body distribute themselves according to the forces set up between themselves - seemingly instantaneously over whatever small distances are involved; time was not seen as a significant feature. The differential equations involved thus pertain to continuous distributions in space, not over time, apparently. Coulomb developed a similar law in respect of the attractions and repulsions of magnetism - the strength of these also varying as the square root of the distances concerned. These early areas of study constituted electrostatics and magnetostatics. Their forces were seen as acting instantaneously over space.
94 Electricity, as a flow of its uncertain fluids or elements - called a current, was soon discovered by Volta in 1792 following observations by Galvani that salty, moist materials in contact with certain metals caused the muscle tissues of frogs (which, conveniently, had provided just those conditions and a built-in measure to demonstrate their actions) to contract. Volta's pile or cell (of alternating metals with damp salty cloths and other arrangements which improved on those used by Galvani) produced electric current which, passing through wires, caused them to heat up. This energy, derived from the chemical processes involved, was thus converted into electrical energy as current and then in turn was dissipated as heat In 1832, Michael Faraday, following work by his mentor Humphrey Davy (1810), and Ohm (1826), discovered the quantitative laws by which the 'intensity or strength' of such electric current could be accurately measured. It was a function of both the electromotive force (ie the difference in extent of opposite charges) engendered between different parts of a circuit and the resistance within its conducting parts. The era of 'electrodynamics' was thus beginning - in the early to mid 19th century.
95 During the early part of the 19th century, less attention was devoted to analysing the basis of magnetism and any comparable dynamic aspects of same. Some relationship between it and electricity seemed likely but no clear quantitative model readily presented itself. But then, in 1820, an extremely important qualitative discovery was made in this regard by Hans Christian Oersted in Denmark. This was that a magnetic needle lying in its usual north-south direction (in a compass lying on a lab bench) turned immediately through 90 degrees - to face east-west - when a current began to flow along a nearby wire - fortuitously also aligned north-south. This discovery of a force which acted between the two fields of electricity and magnetism - each of which had previously been held to possess similar but unrelated forces within their own jurisdictions only - was soon analysed quantitatively - by Biot and Savart - and then formulated by Lapace in terms of action-at-a-distance. While this mode of action usually implied that such effects occurred instantaneously (as if by magic), there must have been some doubt since the equation concerned entailed reference to the velocity of the process - in terms of a constant of proportionality that would later prove of immense importance. But in the meantime, the preferred interpretation seems to have been that of instantaneous action - especially on the continent. However, within a short time, Faraday in England would question this view.
96 This newly discovered magnetic force - induced by a current-carrying wire - differed from any force studied previously. For instead of acting directly between the elements concerned (the wire and the needle point) in a straight line, it appeared to have been set up to operate in a circular manner around the wire in which the current flowed. Thus, the needle is actually pulled to point perpendicular to the current-carrying wire whatever their respective orientations. If free to do so, it would therefore never point directly at the wire (unless, as left by Oersted, the compass was placed on a table beside the wire and thus wasn't free to adopt its perpendicular preference) but always trace out a circle as a tangent perpendicular to the wire. As such, it could in a sense point in any of 360 directions (and those between) if the compass was placed in space around the wire in a succession of circular positions.
97 This discovery turned out to reveal an immensely crucial but unrealised feature of nature - for it represented the first aspect of nature that would not lend itself to the usual direct mechanical analysis. This implies that nature might not, after all, be best or only comprehended in terms of directly acting, mechanically functioning phenomena, with associated rules or laws. Some other, unappreciated 'influence' and/or effects could apparently act in nature and account for (or be accounted by) things in some seemingly 'non-mechanical' way; that is, in ways that followed no known direct, substantive cause and effect sequence. However, in these early days, the character of this 'force' had to be investigated within known mechanical methodology and on this basis proved to have a strength formula similar to those already calculated for gravity (by Newton) and electricity and magnetism (in their static forms) by Coulomb. Thus, as the current of intensity (J) flows along a length (l) of the wire, the strength or intensity of the magnetic force (H) thereby created at a distance (r) from the wire (and, encircling it, perpendicular to it) was found to be proportional to that current strength and the length of that wire, and, just like gravity, inversely proportional to distance r.
. 98 Because this new electrically-induced magnetic force developed (and moved) across space and (in some minds) over time - ie possessed motion - its analysis also fell within a new sphere of enquiry - ie in 'electrodynamics' - rather than electrostatics (or even mechanical dynamics). As it does not act in the direction of the straight line connecting any point on its circular path with the current-carrying wire (from whence the force derives), ie along the radius distance (r ), this formula has a totally different character to those for other forces - even if superficially similar. Rather, it acts - eg on a test magnetic pole - in a direction that is perpendicular to such a straight connecting line. In fact, all three elements - the direction of the current of intensity J (and thus of the electric force underlying that), the direction of the magnetic intensity H and its underlying force, and the direction of the distance (radius) r - are all mutually perpendicular (orthogonal) - occupying all three dimensions of space. The usual (mechanical) analysis of forces - acting directly on substances - couldn't at first imagine the mechanics of this. Some other dynamic seemed to be operating - by its own principles - not yet understood. What was its electrodynamic 'mechanism' or mode of action ?
99 As a current of electricity (ie a flow of electric charges) begins to flow along a circuit wire - due to the immediately prior existence of an electric force somehow arising in response to an imbalance in the levels of (negatively-charged) particles in different parts of that circuit - so a comparable magnetic force is somehow created or activated around the wire of that circuit which, similarly, causes any magnetically-responsive material to move similarly through space, over time - as the compass needle did. Both forces are of a continuous nature but are directional in their effects (and would therefore be later represented graphically by Faraday as 'lines' of force). The electric force assumes a straight line direction where the wire runs straight but could be curved within the bounds of an insulated curved wire. The directional character of the magnetic force set up by the flowing charges (by somehow disturbing or activating the region where the magnetic force occurs) is however circular - around the region of that electric force in the wire - and thus perpendicular to it. If the electric force causes an attraction of charges (the current) to flow from, say, right to left, then the magnetic force set up around the wire concerned would cause any magnetically responsive material to point and/or move in a clockwise direction when viewed along the wire in the direction of that current, and vice versa if the current flowed in the opposite direction. There appears to be no known physical or mechanical model to account for the particular development and orientation of these induced magnetic forces. A new 'electrodynamic' law had therefore to be adopted to account for same - one that apparently follows no known mechanical rules of cause and effect. A disturbed 'field' (ie simply the 'place' in space where all this happens) 'somehow' created ripples of force, through no known mechanism, in a perpendicular circular direction.
100 While the two forces may or may not themselves continue to move in these directions (once established), they possess some property which serves the directional attracting (or repulsing) actions described. Thus, in the case of the magnetic force occurring between the north and south poles of two magnets, it is 'as though' from each pole extends/develops a converse spiralling 'influence' or disturbance which inter-locks with the other thereby pulling (attracting) the free-to-move test poles towards each other and then holding them together. In the case of the electric force, something similar must occur even at the sub-atomic level - as individual charged particles are 'pulled' by more minute vortices or rotational motions of force somehow set up by the imbalance of the opposing charges - each particle so pulled 'bumping' the next along in a torrent of electric current (as a flow of electrically charged particles - eventually to be called 'electrons'). The electrons and the magnetic poles are thus the comparable objects or bodies through which the underlying imponderable forces manifest themselves and their own respective invisible movements - at some immense velocity (like gravity, possibly at the speed of light).
101 Since the strength of this magnetic force (H) is a function of the magnitudes of the current, wire length and distance from that wire, the magnitude of the former can be set in units such that the constant of proportionality concerned is determined by the other quantities - which can all be measured. This implies that the constant represents something about the current (the amount of J) which produces a unit of magnetic force - ie c = Jl/Hr2 and thus
H = Jl/r2 and J = Hr2/l. When expressed in terms of the dimensions concerned,
we find that [H] = [p/lxl] and [J] = [e/t]. From this it follows that [c] = [el/pt] and
because of the identity of the dimensions of the electric charge e and the magnetic pole strength p (Coulomb's laws for the two forces being of the same form), then [c] = [l/t]. This means that c, a constant of proportionality, has the dimensions of a velocity - ie distance (length) per time. Thus, that 'something' about the current turns out to be the velocity of the (underlying) electric force - apparently a constant (and the current caused thereby) - which bears a relationship with the strength of magnetic force so produced. The same would apply to the magnetic force. This constant within the electro-magnetic sphere proves most significant later. [While this velocity may refer to the speed at which a newly induced force develops across some space, it seems likely that it (like gravity?) also refers to the on-going speed at which it continues to act. If the charged particles are swept along like floats in this stream of electric force, they may constitute the electric current but the underlying electric force would appear to be the prior cause of that current; to the extent that the current continues, so that force must also continue to move at that velocity (reflected in the value c).]
102 By determining the values of the factors involved in the production of a magnetic force of a given amount, it was thus possible to calculate the magnitude of c. This was first done by Weber and Kohlrausch in 1856. Its value was a staggering 300,000 km/sec which, moreover, was apparently the same as the velocity of light! They, and many other workers in the new field of electrodynamics, believed that this indicated there must be some unrealised connection between two great realms of science - optics and electromagnetism. But until Faraday's ingenious insights (then just coming to fruition) were developed more quantitatively by Maxwell, over the next decade (see below), this suspected bridge could only be wondered and guessed at. In the meantime, this value pertained to a measure of electric force (velocity) which in turn related to the induction of magnetic force. The analysis of these new inter-acting forces in the mid 19th century proceeded in parallel with, but independent of, that of the transmission of light as an elastic wave propagated through (by?) its suspected ether medium - one which may or may not move. The role of any ether-like medium in the transmission of the new forces (and any problems of relativity vs absolutivity of space and time relevant thereto) was apparently not then an active consideration - ie up to about 1865 or so.
103 In 1837, some years before the value of c was thus determined, and its significance wondered at, Faraday had experimented with an electric circuit in which a simple salty or acidic solution between positive and negative electrodes (as plates of metal) - known to conduct a current - was replaced by more complex substances of uncertain conductivity such as turpentine and petroleum. He found that unlike the salt or acid, they did not dissociate - with their different elements migrating to deposit on opposite electrodes - but that nevertheless there was an effect - on the amount of charge that these electrodes took on when the circuit was connected to a battery - the amount depending on the extent of such an intervening 'non-conductor'. That is, the capacity of the circuit in what became known as a condenser was dependent upon the type and/or amount of such material between the plates. But even when these were non-conductors, there seemed to be some influence acting between the plates - affecting their respective levels of charge.
104 Before this, Faraday and everyone else assumed that the static charges held on the two plates (or the magnetic character on opposite poles) somehow affected each other (set up an intervening force) by virtue of a direct, instantaneous effect across the space between them - ie action-at-a-distance again - with the effects of this on any intervening conducting solution (eg chemical dissociation) following the establishment of such by this instant action. But now, he decided that the intervening space itself was somehow relevant and that such action occurred through and ?involving it - in a slower, contiguous manner - the effect being propagated across this space by successive contact from point to point therein, requiring time, whether through a conductor or non-conductor. He thus imagined that there were invisible 'lines of force' set-up within the non-conductor between its oppositely-charged plates. Such insulators he called 'dielectrics'. The vacuum of space - and any 'ether' therein - was also included in this new category, although Faraday tended increasingly to explain his new insights without recourse to such an ether concept. But he felt that instantaneous action at a distance was an unsupportable idea, with no logical basis. He soon felt that his lines of force, rather than an ether with its magical, instantaneous attributes, should replace it. Force was not substance and thus did not require a substantive medium. It was an important intuitive conviction.
105 In Faraday's new model, the primary concept in electricity became these lines of (electric) force and not the positive or negative charges between which some other such entity 'ran'. The latter had been associated with the electric 'fluids' with their mysterious power to act-at-a-distance. [In these earlier years, workers in the field didn't seem to differentiate 'electricity' into (a) electric force and (b) the moving charges (later electrons) which somehow accounted both for instigating that force and for the consequent current of themselves - by moving to a place of lesser negative charge (ie greater positive charge). Rather, they believed that the charges that acted were the electric force - the electric fluid(s) - which somehow acted instantaneously.] Faraday believed his new contiguous model with its lines of electric force held true for what he described as magnetic lines of force as well. But most of the continental physicists continued to hold to the action-at-a-distance model for forces - with a one- or two-fluid theory of electricity, and something similar for magnetism. (The electron's discovery and molecular structure were some years in the future.) For light, however, a more contiguous model - but with an elastic ether - had been accepted; it being known that while very rapid, it did require time to proceed from its source to any receptor. But for forces, this was as yet uncertain; they appeared to act instantaneously - whatever the distance.
106 The continentals adjusted their force equations in respect of such dielectrics by incorporating a different constant for each such non-conductor which thereby accounted for any reduction in the force arising between opposite charges. For a vacuum, the constant = 1 and for all other (material) dielectrics, it was greater than 1. Hence, Coulomb's force law became: K = 1/d x [e(1) x e(2)]/r2 where d = the dielectric constant and e(1) and (2) are opposite electric charges. For magnetism, a similar constant was required - one which accounted for the varying 'permeability' of whatever medium through which any magnetic force had to pass. Its formula became: K = 1/m x [p(1) x p(2)]/r2 where the permeability constant = m and p(1) and (2) are the respective pole strengths. Thus, the strength of these forces did depend upon the media through which they acted as well as weakening rapidly with distance - as by the inverse square law.
107 The fact that such adjustments appeared to maintain the validity of the instantaneous, action-at-a-distance models indicated that the mathematics used in the analysis were probably representing something close to reality although may not hold generally over all pertinent situations. Thus, Faraday's model when analysed mathematically (long after) turned out effectively to involve the same constants for such media. In the meantime, which view one adopted in the 1840s and'50s seemed almost a matter of preference - based upon one's intuition and general philosophical point of view. Each model built up its physical analogs and the mathematics to best represent these. By the 1860s, however, several scientists on the continent (eg Helmoltz) were beginning to prefer the Faraday-Maxwell interpretation of the mode of action of electromagnetic forces [recall value of c determined in 1856] and by the 1870s - after Maxwell's discovery that light was an electromagnetic wave - were mostly won over to it - even though Maxwell (unlike Faraday) felt there was still a role for an ether - although he seemed ambiguous about its nature. There was a gradual shift from the old to the new interpretation by the 1880s. Some of the technical details are summarised below.
108 In the action-at-a-distance model, the molecular structure of the dielectric between the electrode plates undergoes an electrical displacement whereby the negative charges shift towards the positive plate and conversely for the positive charges. This results in a relative neutralisation of the interior of the dielectric - as negative and positive poles of the molecules align and balance out - and a reduction also in the charge on the two plates as the oppositely-charged ends of each molecule align next to and so neutralise them. This allows the plates scope to take up additional charge (increase its capacity) from a source such as a voltaic cell. Where the intervening medium is a vacuum, the force between the plates distributes itself geometrically as verified by its effect on an electric test body with unit charge. It is apparently not considered as a true dielectric.
109 But in Faraday's contiguous model, both of these intervening entities - the material and the vacuum - constitute a dielectric - each having its characteristic constant. The electrical displacements occur similarly in both. The ether alone (as Maxwell at least saw it) - as in a vacuum - or it and its accompanying solid dielectric (eg turpentine) - can in both cases be imagined as being comprised (before any electric or magnetic force occurs) of randomly distributed electric or magnetic 'molecules' which possess the properties of negative and positive charge or polarity and which are (in this state) randomly distributed in or on themselves - ie are under no tensions - but which, when subjected to the respective electric or magnetic forces, undergo a displacement or re-arrangement such that they become positioned at opposite ends of such 'molecules'. They then align themselves in structured 'chains' (contiguously over time?) and thereby (gradually?) assume the states of tension which Faraday claimed constituted the lines of force of the electric or magnetic 'fields' so created (over time - eg at the speed of light or...?). In Faraday's view, the charges then arising at the surface of the conductor plates (electrodes) or at the poles of the magnet are nothing but the end charges of the aligned chains of these imagined 'molecules'. [Reconcile this view with the reality of the electrons which charge up any electrode.] Internally, there would be a relative neutrality but as a structured tension of the directional lines of force. Where there are both types of dielectric (ie with both real and imagined molecules), the polarisation is stronger within the chains of real molecules and the charges manifest at opposing surface boundaries have greater magnitude than in a pure vacuum - as reflected in the different dielectric constants (being = 1 for a vacuum - the minimum possible - and more than 1 for all others).
110 Because there is no empirical basis for the idea of such 'ether or field molecules', some other analog may be more realistic although such physical models of the unperceived world exist primarily to allow a means of discovering the best possible mathematical relationships between those variables that do manifest themselves. This was Maxwell's intention. Thus, one can imagine instead that the potential field of electric force lines between oppositely chargeable plates - before such charges develop - to be a balance of integrated or superimposed 'blocks' of continuous positive and negative charge density (p) and thus in total electrically neutral. When the plates are charged, a slight shift (displacement) in the distribution of these two theoretical blocks of spatial charge (even in a vacuum - ie no real ether needed?) occurs whereby a thin sheet (of thickness a) of positive charge is revealed on one surface and a similar sheet of negative charge is revealed at the opposite surface. Such electrical displacement D is represented by the surface charge per unit area (pa). Why the ether of the vacuum has its two oppositely-charged 'densities' before the plates are charged, or even afterwards with their displacements, I am presently unaware (ie densities of what? Seemingly, of 'charge'.) Even if this analogy is not accurate, one must assume that there is some such 'charge potential' in the empty space concerned. The direction of the imagined 'shift' (perpendicular to the surface pa) defines the directionality of the 'lines of force' implied.
111 [Ironically, on the day I wrote this summary, it was announced that a possible explanation of why the universe appears to be expanding against any tendency for gravity to prevent such, had recently been discovered. It was thought to be due to the vacuum of (outer) space actually containing billions of minute 'particles' which continually go into and out of existence (changing out of and into energy) which somehow oppose gravitational collapse. It would seem quite feasible that such 'material' could therefore also account for the chargeable nature of the ether of a vacuum (ie space) wherever it is in the universe) and for its displacement from a state of balanced neutrality - when such a 'field' is subjected to electric or magnetic forces - ie the 'tension chains' of Faraday's 'lines of force'). In any case, this would seem as reasonable a model to adopt as any - as one further analyses the nature of the electromagnetic forces that pertain to light. Moreover, it provides some support for Einstein's 1920 suggestion that there may well be an ether of space (or space-time) - an energy reserve without stationary positional attributes - such particles being in constant motion or in their equivalent energy state presumably.]
112 In the action-at-a-distance conception, a 'point charge' e in a dielectric is said to produce a spherical force field E which weakens with distance - ie: E = e/r2 x the (dielectric) constant. In Faraday's model, on the other hand, this field similarly diminishes spherically with distance r but the spherical volume so affected is again imagined to consist initially of a mutually-balancing mixture of positive and negative charge density p (ie possibly now the above described mixture of minute 'particles' and the energy they turn into and out of?) before such a concentrated point charge begins to act. When it does, a displacement of the mixed charge polarities occurs such that the outer face f of a sphere (of whatever radius) acquires a charged surface of thickness a and density p - ie = fap . Any inner sphere selected (displaced comparably) would possess the same charged surface but of opposite sign. Both would be equal in charge to that of the point charge responsible for them - ie e = fap. The total face area (f) of a sphere of radius r - ie f = 4p r2 and thus e = 4p r2 x a p. The formula for the strength of field E thus becomes E = 4pap/e and so E is a function of (is proportional to) ap. By defining displacement D = 4pap then, as E = D/e, so D = e/E. Such a displacement occurs from the central charge e in all radial directions. It applies equally when the charge is not taken to be concentrated at one point but to be distributed continuously throughout the area concerned - with a density p. In such a case, one may write, as per Maxwell, div D = 4pp as the differential equation which sums up the total displacement concerned.
113 The question thus arose (in the 1860s): 'which model better represents the truth - that of the continentals with their action-at-a-distance view or the contiguous action of Faraday and Maxwell? Apparently, if the phenomena considered are restricted to that pertaining to electrostatics and magnetostatics, the two models prove to be equivalent. For Faraday's model as expressed mathematically by Maxwell was arrived at from another direction by the continentals when a theory of 'pseudo-contiguous action' was developed in respect of the spatial continua inherent in those aspects of statics - for which differential equations were appropriate. But this latter theory recognised no finite velocity (distance per time) for the propagation of the force tensions across a dielectric - whether as material or ether (vacuum); they simply 'occurred' - instantly - over some distance. This contrasts with the work of Faraday and Maxwell who accepted that this propagation must entail a series of minute delays as the force developed across any space - ie from point to point (albeit such 'points' being an imagined fiction over the actual spatial continua involved). Such delay(s) reflect in particular the time needed for two phenomena to occur - viz 'a displacement current' and 'a magnetic induction' which were known or assumed to be a part of this transmission of force lines across a field over time. These are discussed next.
114 When a circuit charges the two plates of a condenser, an electric field E is produced between them (as described above). Such a circuit was, before Maxwell's new interpretations, considered an 'open circuit'. That is, the field E was not thought to provide an element of the current flowing around the whole circuit. But Maxwell claimed that the circuit became a complete and closed one (for a time) as the field developed since this entailed the production of a 'displacement current' between the plates - ie through the developing field in the dielectric. Once the plates became completely charged, both this displacement current and the conduction current ceased to flow and again became an open circuit. But while they did so, both would, said Maxwell, produce circular magnetic fields around their brief current flows, as expected from the Oersted/Biot/Savart laws. This was later confirmed by prediction of various relevant findings and more directly by experiment. The strength of this displacement current can be computed from knowing the value of the displacement and electric field strengths and = e/4p x E/t (time) (in the form of a differential equation , I believe). The total current density Jt would be the sum of the two current densities Jd + Jc, the latter being the density of freely moveable 'charges' (particles) and the former that of the displacement current - of a succession of 'charge displacements' within the dielectric (again computed in calculus format). Time was a factor and so such effects could not occur 'instantaneously - at-a-distance.
115 The other phenomenon addressed by Faraday and Maxwell as support for the contiguous theory was that of magnetic induction. This was discovered by Oersted in respect of a conduction current flowing along one wire and by Ampere for current flowing along two parallel wires - causing them to be either mutually attracted or repulsed - depending on the directions of the two currents. These inductions were seen to arise instantly as action-at-a-distance - ie within the mathematical analysis of same made by Biot and Savart, and by Ampere. Whether in fact occurring at-a-distance or via direct contiguous action, it became obvious that magnetism arose and acted by means not of any separate 'magnetic fluid' but by virtue of a flow of electric current. The magnetic force so induced acted exactly like that arising between poles of a magnet within which, therefore, Ampere concluded there must be small electric currents flowing which similarly set up the more permanent magnetic force lines or field.
116 When the currents in two wires so affect one another, the direction of their currents are altered slightly (deflected) and thus the velocities of such currents cease to be entirely constant in direction; they are thus said to have been 'accelerated' (not in rate but in direction of motion). This feature apparently made Faraday ask the question: can the magnetic field similarly alter the direction and/or velocity of a static form of electricity - from one of rest to that of a moving current? That is, can an electric current be induced in a wire by means of some action by a magnetic field - being the converse of the discovery made by Oersted? But what action by a magnetic field? Since magnetism was induced by virtue of a movement of electricity, possibly 'electrism' (electricity) - as current - would be induced similarly by a movement of 'magneticity' (magnetism). In 1831 Faraday had discovered that a static magnetic field did not induce any current but that when that field was moved or changed, it did indeed do so. Such a change occurred when a magnetic field around a flowing current was alternately created and eliminated by turning that current on and off. A current was thus induced (in bursts or pulses) in a second, nearby wire in which, prior to this, there was no current. There seemed to be some relationship between the rapidity of such a changing magnetic field and the strength of the current so induced - one that mirrored that calculated for the converse strength of a magnetic field as induced by currents of (?equally rapidly) varying strengths.
117 Faraday thus formulated a quantitative law of electrical induction for this phenomenon using his concept of lines of force. This was later elaborated by Maxwell and it proved comparable with that of Biot and Savart for the strength of a magnetic force/field induced with a current. It turns out that the induction of an electric field by moving magnetism is a perfect parallel with the induction of the magnetic field - there being both a 'magnetic conduction current' and a 'magnetic displacement current' comparable with these same two currents of the electrical form. And encircling these, a comparable electric field is thus induced which may be manifested in the recruitment of flowing electric charges/particles in a copper wire - if placed within that circular field - but which in any case continues to exist there regardless. The intensity (strength) of the electric field E so induced = I x l/cr2 in which the same constant c occurs as seen previously - being the ratio of the electromagnetic to the electrostatic unit of current (in the order of 1: 300,000) and reflecting both the differences in the respective energies released and the velocity of the currents so induced. It may be recalled that this constant with its velocity relevance - first calculated by Weber and Kohlrausch - turned out to equal the known speed of light. Time was thus again a factor in the induction of such forces across space. While the parallel between these two forces and their means of mutual induction appears to be exact, they do represent different phenomena (otherwise they would of course be the same thing - which they are not (quite). See Lorentz for an explanation of what comes first - the chicken or the egg here - ie the electric field or the magnetic field - or is it that they are really identical and both always present together - perpendicular to each other? [One may recall that Einstein begins his famous paper by referring to an erroneously accepted asymmetry in this area; does this relate to the present subject ?]
118 To Faraday, his conceptions of the lines of force and the fields in which they operate implied no need for a concept of ether in or by means of which such forces were propagated. The electric and magnetic forces arising in response to each other were somehow propagated across space (in the form of waves he suggested) by virtue of the energy released therein. The 'field' (simply where it happened) didn't need to contain a carrier; it was or became the carrier and yet didn't contain an ether of substance or material that obeyed mechanical laws. He was not at that time himself concerned with the propagation of light per se apparently - the origins of which were as yet unknown. If there was an ether in space by which light was propagated, the electric and magnetic forces operated independently of it, although it may have the dielectric relevance mentioned. [The circularity of the lines of magnetic force around a current-carrying wire recalls the motion of planets around the Sun (do electrons move similarly around the nucleus?); thus, does this spatial format arise similarly - due to two balanced forces - one being a straight line back to the current (like gravity) and the other something comparable to the perpendicular inertia of planets (and electrons?). What was the source of the impetus preceding these respective inertias?]
119 Maxwell, on the other hand, continued to believe in the necessity of an ether of some sort although he seems to have been in two minds about it. Because the existing conception of light up to the 1870s assumed the necessity of an ether medium, he seems to have felt it appropriate to adapt this to fulfil a comparable role for his new conception of light (described below) and possibly for its precursors - the electromagnetic forces - also. Before his theoretical predictions about such electro-magnetic waves were confirmed (after he died in 1879), he thus described this new (non-elastic) ether - which he assumed was stationary (I believe) and ways to verify its existence in that form. His views on the contiguous action across his (and Faraday's) electromagnetic field, once accepted by the continentals, thus included enough on the role of an ether (therein?) to maintain this as an important feature in the later evolution of his basic ideas - especially by Helmholtz, Hertz and Lorentz. For this reason, the relevance of this concept not only in regard to its role as a medium but to the problem of space and time - ie absolute vs relative motion - continued after Maxwell's death in 1879 to resonate as an important consideration in the analysis of 'the fundamental problem of light' - as addressed by Hertz, Lorentz and Poincare in the 1890s and eventually re-defined and resolved by Einstein in 1905. [However, Maxwell himself wasn't overly concerned about the possible stillness of the assumed ether apparently nor of its role as a basis for absolute motion.]
120 A beginning was made in the shift from the action-at-a-distance view to that of contiguous action shortly after Coulomb's law was formulated - at least in the spheres of electro- and magneto-statics - with a theory of 'pseudo-contiguous action'. Maxwell realised that the key idea in this conception (as it applied to a continuity over static space) could be integrated with Faraday's ideas on the mutual development of electric and magnetic forces and their dynamic consequences - ie with a continuity of movement (development) - over time also. He took as his starting point the idea that an electric field E (however evoked; see below) is always accompanied by an electric displacement D which = E x e. Such a displacement is a shift of polarity across the area affected. This is the case for either a vacuum (when it accounts totally for the resulting electric field strength) or a material dielectric (when it is only partly converted into such a field - ie of lesser strength). That is, where e = 1 or >1, respectively. This displacement may be visualised as a separation (re-arrangement) of charged molecules (or their spatial equivalents in the ether of a vacuum) which results in oppositely-charged surfaces and a temporary 'displacement current' (of electrons or 'charge') therein until a new balance is completed. A differential law can then be formulated which connects (relates) the charge density p at every 'point' in the space concerned with the 'divergence' (div) of that displacement when expressed as a function of the strength of the electric field E. That is, div eE = 4pp. This is Maxwell's formula for contiguous action as it develops an electric field over time across a dielectric (as in a condenser). [I am uncertain just what it is that 'diverts' in this conception. Seemingly, it's the mutual separation of the polar charges.]
121 The same applies to magnetism and magnetic displacement - with one important exception. While moving magnetic fields (or magnets) can create an electric field (and current), the latter (apparently) don't require such a condition to occur; it will also arise around or between unmoving charged bodies - especially when they differ in polarity of charge. Such bodies are charged initially by.......] No magnetic field or magnet, however, can exist without a moving electric field (and current) preceding it. Thus, a permanent magnet must possess causative internal currents. That is, there are only 'electromagnets' (no other kind of magnetic force can be engendered) whereas there are not only 'magnetoelectrics' (ie electric force/current engendered by virtue of moving magnetic fields/forces - with their underlying electric currents); there are also it seems 'non-magnetoelectrics (ie electric current arising directly through differential charge levels). [This lack of symmetry seems 'awkward' but may be inevitable; a chicken must comes before this particular egg and not vice versa. The 'chicken' appears to be the factor of 'charge' - whatever that is - surely a mystery if ever there was one; we may know what it does (like 'force') but, do we know what they are? And how is a charge instilled or is it only ever transferred (and as a 'relative' phenomenon) from always pre-existing sources?] Apparently, this implies that the induced magnetic lines of force (around a current) never end - being either closed circles or stretching (in theory) to infinity - as noted when a magnetic field is created within a coiled wire when a current flows through it. For in this, it seems, as much 'magnetic displacement' (ie induction) mH continues to enter through one end as exits out the other. This restriction is presumably not the case with an electric field. Therefore, one must set the equivalent divergence for mH to be: div mH = 0 (and not = 4p x p (or whatever). This is the equivalent formula by Maxwell of contiguous action for the development of a magnetic field across an area of known permeability - by a changing (moving) electric field. [Does the idea of 'shift' (vs 'displacement') apply equally in this sphere?]
122 To review: Biot and Savart's law of electromagnetism (following Oersted's discovery) assumed action-at-a-distance. Over the next generation, various continental scientists such as Neumann (1845) Weber (1846) and Reimann (1858) worked on this latter model - gradually adapting it to take account of the velocity of moving charges and the forces set up between them - but still instantaneously. However, these newer versions did not apply the pseudo-contiguous model to such dynamic phenomena. While they accounted for electromotive forces and the induction of current in 'closed' circuits, they did not explain the displacement currents that arise briefly in an 'open' circuit of a condenser (due to the unsuspected 'shift' in its charge polarity). So Maxwell had to apply his ideas to electromagnetism as extensions of the principles he had already applied as above [which seems in any case to deal with the same area??] But even after Maxwell had presented his theory in the 1860s, there was much hesitancy in accepting it - ie until ca 1870-80s - because of the apparent adequacy of the alternative model worked on by the above investigators. But finally, their respected leader - Helmholtz - encouraged experimental tests of these two theories concerning electromagnetism and decided that Maxwell was right. Contiguous, time-requiring action was more realistic. But, first...
123 To convert the action-at-a-distance interpretation of electromagnetism to that of contiguous action (which he felt was the more valid conception), Maxwell had begun by considering - for the case of magnetic induction - a current flowing not along a thin wire but one distributed uniformly across a larger cross-section (or 'face' - f) of some conductor - having a density ( j ) = J/f. This causes a magnetic field around this cross-section which would be at its strongest (most intense) immediately next to the latter (ie at its 'edge') where its momentary direction is everywhere at a tangent to such a circle. The magnitude of this intensity H at this edge radius would, by Biot and Savart's law, be cH = Jl/pr2 for a length l of this section of conductor. Since the cross-section f = pr2, the formula becomes cH/pl = J/pr2 = J/f = j which would hold true for cross-sections no matter how small and length however short (ie a point). This has the form of a differential equation of the magnetic field - the magnetic intensity so represented being proportional to the current density from which it derived. To be complete, however, this equation must consider also the continually changing (circular) direction of the magnetic field created. Its intensity H thus becomes better represented by the concept 'curl H' and the equation becomes: c curl H = 4pj. This states that the strength of a magnetic field that 'curls' around a current is (at any given distance r from that wire) a function of that current's density. It has the same form as the equation (law) for the intensity E - represented by div E - which = eE ie div eE = 4pp which says similarly that the extent of the electrical displacement (mutual polar divergence) in a dielectric space is a function of the charge density (p) throughout that space. The charge density is, in turn, a function of ... (to be determined).
124 The same relationship holds for electric induction - where the rotation is of converse direction (reflected in the opposite sign) - ie: c curl E = - 4p x i. As an electric field develops in a dielectric, the conduction current and the displacement current co-exist. The current densities of these summate to j = (e/4p) x E/t + sE (being a summation of Ohm's and Maxwell's laws pertaining to these, respectively). As a magnetic field develops, there is no conduction current, only a brief displacement current. The formula is thus I = (m/4p) x H/t. If we insert this in the 4 equations above, we get:
3. c curl H = e x E/t + 4psE 4. c curl E = -m x H/t
These are Maxwell's famous 4 equations or laws for electromagnetism and its fields. While they are really precise differential equations (seeking the relevant functions by which these variable are related quantitatively), they serve the non-mathematician as important mnemonics which, according to Born, infer that:
1. Wherever an electric charge occurs, an electric field arises in every volume of which the charge is
exactly compensated by an (?electric) displacement.
2. Through every closed surface just as much magnetic displacement passes out as comes in - there are no
free magnetic charges (only those arising as in 3).
3. All electric currents - both conduction and displacement - are surrounded by a magnetic field.
4. A magnetic displacement current is surrounded by a reversed electric field.
125 These guiding principles concerning electromagnetic behaviour are consistent with the relevant forces propagating across space by contiguous action, which requires time - albeit exceedingly little time. That is, they travel at a very fast but finite velocity - presumably by means of some substantive if 'ethereal' field medium (at least this was the understanding at the time (pre-1900). While the competing theories accepted that forces occur between charged particles (providing a basis for later theories of the electron), they did not (for some time) accept that such forces themselves required time to act - ie that they too had a finite velocity and didn't act (?develop) instantaneously - over whatever distances - ie just 'appearing' throughout any relevant 'field' at the same instant. [Consider how Einstein's reference to the asymmetry problem (and Lorentz's absolute motion of charges) may possibly relate to this area.]
126 Bernstein suggests that after Hertz's confirmation of Maxwell's electromagnetic light waves (1887) that the ongoing interest in an ether medium was further emphasised - in order to maintain the coherence of classical mechanics - still in terms of both its alleged medium (still thought necessary for such waves) and its stillness or absolute positional attributes. Before this, the elastic ether was similarly posited for the generally accepted wave nature of light - ie long before its electromagnetic character was discovered. With the latter's discovery, such a medium was still required however - but without its elastic nature apparently. Yet more hypotheses were required and both the nature and mobility or otherwise of such a medium were still considerations well into the 1890s. [Presumably, Michelson reasoned in the same way. But, although no still ether was revealed, the requirements of the classical principle of relativity are nevertheless not met by the optical principle of relativity in as much as the same paradox arises as described earlier. It is as though Michelson's result somehow represented a 'split decision'. For, on the one hand, with no still ether supported ........... .........while on the other, its speed is not influenced by such as the moving Earth. Thus, it didn't equate in both respects with the classical principle but only in repect of one of these and hence the paradox.]
127 To this point in the analysis of electromagnetic phenomena, Faraday's and Maxwell's researches sought to understand these recently appreciated inter-acting forces and how they might one day be better understood and harnessed to benefit mankind. [Here: Some reference to Maxwell's equations serving to collate and integrate within one mutually consistent model of electromagnetics the four earlier 'laws' or principles advanced by......(to be completed). Just as he saw before others the overall picture so indicated, so Einstein would later gather together clues advanced by several workers such as Bradley, Doppler, Maxwell, Fizeau, Lorentz, Voigt, Abraham, and Poincare and integrate them into a new conception not previously realized.] Meanwhile, as touched on earlier, other areas of physics were also advancing independently at this time, including optics. But except for Faraday's remark in the 1830s that he suspected that light, like the new electric and magnetic forces, travelled as undulations, there was (I believe) no particular focus of attention upon any possible relationship between light and these 'new' forces - eg through the 1840s and'50s. Light was believed to require a medium - the ether - in which it was propagated as a transverse wave but discovering a medium, if any, for the propagation and mutual actions of electric and magnetic forces (even if also propagated in the form of waves) and their manifestations in electric current and magnetism, did not appear to be a major concern. Nor, initially, were there any suspicions that these two apparently unrelated fields might have some mutual relevance.
128. However, the very concept of 'the field' to which Maxwell's equations of electromagnetism pertained, seems to have implied in Maxwell's mind at least that it must operate by means of a substantive medium. Because the traditional concept of light's medium, the ether, was generally accepted as existing throughout space, something like it, therefore, was assumed to comprise 'the field' - even if, later (with a new conception of light), it was thought unlikely to be of an elastic nature. But its existence, as a substantive quality, if exceedingly tenuous, continued to be assumed since, to this point in science, there were only substantive or mechanistic conceptions of how anything functioned (whether light, electricity or magnetism); there were no other known 'ways' for waves or forces to generate, propagate or interact. Thus, Einstein (1920) said that "for Maxwell, the new ether still had mechanical properties - if of a complicated kind - compared to the old elastic ether. While his laws of electromagnetism by which forces were generated were clear and simple, his mechanical explanation of the (?ether-like) field as a propagating medium for these phenomena (eventually including a new conception of light as well) was, he felt, too complex and inconsistent. [Note: Maxwell's 1878 article on the ether may address this to some extent; see below.] From this time on, therefore, some physicists (eg Hertz and Poincare) began to accept that the old mechanical principles may not fully account for the new electromagnetic phenomena (which Einstein later described as constituting new 'fundamental irreducibles' not explicable or reducible in (old) mechanical terms to simpler particles and forces). Another unwelcome dualism was thus gradually presenting itself to science (ca 1880/90s) - of which Maxwell's uncertainty and complications of just a few years earlier was probably a foreshadowing - and for which some resolution was increasingly required. Lorentz tried but didn't quite make it while Poincare saw that a new but still 'mechanical' model was probably needed but couldn't quite elaborate it himself. [Note: Some of the foregoing anticipates later developments as per parags 150+.]
129. Nor was the speed of light yet discussed as an invariable constant, it would appear. Like the speed of anything, including sound, it was generally assumed this would still vary depending on what speed, if any, any source, carrier or receiver was moving at when it was measured - relative to an observer. While electromagnetic waves were found by the 1860s to have travelled at the same immense speed as light, there was no suggestion then that nevertheless, this speed wouldn't be varied - as was everything else - if it or its source was boosted or retarded by appropriate means. And later, when Maxwell concluded (implicitly?) that this immense basic speed was apparently a 'constant' - just as there were many constants in physics - it was not appreciated that for the velocity of anything to be a true constant was actually a most significant finding - with unimagined consequences, compared to all other physical constants which pertain to non-velocity phenomena. Even later, when Maxwell became interested in light and concluded it to be an electromagnetic phenomenon which nevertheless still required an ether medium (whose existence might be confirmed by the use of light's speed), this apparent or possible constancy did not appear to be considered a crucial aspect. Indeed, they actually seemed to rely on it not (?always) being so as the basis of verifying the ether! Nevertheless, it seems implicit in the contiguous model with its necessary medium, that motion (speed) considerations of both forces and light must have relevance to matters of space and time and their relative or absolute natures - if still within a mechanical model.
130. There were however two items of interest that bore on the (early) idea that there may be a connection between light and the newly investigated electric and magnetic forces. Firstly, in 1834, Faraday noted that the plane of a beam of polarised light was turned 90 degrees when it was passed through a transparent material that was being magnetised - if the light was parallel with the lines of force of the magnetic field applied to that material. He apparently concluded that if there was any ether carrier involved, it would seem to be utilised by both the light and the magnetic force similarly and that therefore it probably wasn't of an elastic nature (on which so much research effort had and was still to be invested). Equally, he seemed to feel that if the latter force didn't really require an ether carrier at all, then light - even as an undulation - may not either. But Faraday did not have the mathematical expertise to resolve this question further. Secondly, as touched on earlier, Weber and Kohlrausch had, in 1856, noted that the value of (c) calculated as a constant of proportionality between the strength of an electric current and that of the magnetic field created thereby, with its velocity character, happened to exactly equal that value already determined for the speed of light (300,000 km/sec) - an exceeding large and unusual number. This particular ratio was soon related to the velocity of the forces concerned as well since it was through the interaction of these phenomena that such forces and waves emerged (and continued) - at that speed.
131 So, electromagnetic force and light travelled at this same immense speed. What did this signify? This caused considerable interest amongst contemporary physicists who felt this could not be just a coincidence but little was done about it at the time (late 1850s). But then, in 1868, Maxwell, who did possess mathematical skills, made the revolutionary discovery alluded to above which, by identifying the missing link, resolved this mystery and so discovered this recently suspected 'bridge' between Optics and Electromagnetics. Light, while not an electro-magnetic force, was an electromagnetic wave of energy that arose by virtue of certain interactions arising between such forces and, like them, travelled at that same immense speed (c). Attention was naturally focused on the similarity (indeed total equality) of the speeds of these two sets of phenomena rather than on the constancy of that identical speed - which was further revealed by Maxwell's equations. And while constants in physics were certainly nothing new, the implications that there was one, albeit 'hidden' within a constant of proportionality, which pertained specifically to the speed (of anything) seems not to have been fully appreciated. It may have been superficially accepted by some, but its full implications apparently were not; until Einstein, that is. What were those implications? This will be discussed later. Meanwhile...
132. If the electromagnetic forces didn't require an elastic medium for their propagation/development across their fields, but still took a finite (if exceedingly small) time to move (or develop) from a to b (seemingly as waves), what kind of medium, if any, might they require? And would the complex electromagnetic waves emerging - as light - from an interaction of such forces (under the right circumstances) not also depend on this same new, non-elastic medium for their transmission - even at their enormous speed? What did Maxwell's field equations tell him about this? When arising in a vacuum which has no conductivity (ie s = 0) and no true charges (ie not between the plates of a condenser where the balanced neutrality is shifted to reveal some charge) - that is, when p = 0 and its dielectric and permeability constants (e and m) both = 1, then the intensity of the diverted (displaced) electric and magnetic fields produced both = 0. That is, the first two field equations tell us that div E = 0 and div H = 0. This implies that all lines of force therein are closed (or run off into infinity). And the other two field equations become: - c curl E = h/t and c curl H = e/t (where the small case letters to the right signify that these are the differential equivalents of the large case properties (E and H) concerned). Thus e/t represents a rate of change (alteration) of a tiny portion (e) of an electric field in a very small amount of time (t). When such an electric field arises, the equation for c curl H tells us that a magnetic field immediately develops around the former - with a strength proportional to this rate of change (e/t). The greater this rate (on average), the greater the intensity of the magnetic field H created. But a 'rate of change' in the strength of an electric field implies exactly that - change and such change is reflected in a comparable change in the (strength of the) magnetic field evoked by that change. This latter change equals a minute amount of field strength (h) per small interval of time (t) and the magnitude of this rate of change - by virtue of the equation (- c curl E) - determines similarly the strength of the ensuing electric field E, etc.
133. In the ensuing small intervals of time a sequence of such rapidly alternating fields of magnetic and electric force, each perpendicular to the other, will arise (in all directions from its point of initiation). These mutually-evoking actions - while analysed here as if occurring discretely after very small intervals of time - actually recur continuously; it is the fact that they are both changing - continuously - that accounts for their subsequent actions on their perpendicular and ever-present 'stable mates' - the strength of each depending upon the rate of that continuous change. A chainlike process of a continuous complex wave motion having mutually perpendicular elements thus continues and spreads out with its constant finite velocity (rather than infinite because of the effects of inertia between 'successive' (if continuous) mutual inductions). It is as though the strength of the two mutually provoking (inducing) forces (which would normally weaken rapidly with distance) somehow have their energy converted into that complex wave which, while now being without the power of force, nevertheless has the capacity (energy) to travel (devoid of any mass) at its immense but constant speed, undiminished over great distances. It would seem reasonable to assume that the rate at which these mutually effecting changes can occur (and move forward) represents the ultimate upper limit on the speed of anything. In one sense, one could imagine that its speed is so constant because its 'field' is always absolutely still and can never move - with or against it.. This seems very akin to Newton's concept of absolutely stationary space.
1. Re-considering the Elastic Ether - as a basis for a new Electromagnetic Medium for Light
134. How do such mutual actions and the ensuing propagation compare with that previously worked out for light - conceived as a transverse wave travelling as a succession of vertical vibrations in an ether-like elastic medium? In 1829, Cauchy had applied mechanical laws worked out for elastic waves generally to the field of optics (assuming this field was a part of mechanics) - although he seems to have limited his analysis to the action-at-a-distance assumption (thus ignoring or over-looking any brief time delays implicit in any medium involved.) The differential equations developed (?pseudo-contiguous) were similar to those developed subsequently for the contiguous model but, crucially, did not include a term for inertia with its time implications. That is, it was not appreciated or accepted that the force which displaced earlier 'particles' of the elastic medium was not transferred into comparable motion of neighbouring particles (with which they are in continuity) until the inertia of the latter, each in its sequence, was first overcome. The succession of such short delays would likely account for the finite time taken for the transmission of the elastic wave. If such particles are imagined to become smaller and smaller in size and mass, with a corresponding increase in their number (so that the total mass concerned remains a constant), they would eventually constitute a (virtual) continuum of the medium concerned - although the wave motion within this may be more readily analysed as though they remained very small particles. Maxwell adapted Cauchy's model along these lines - if not for light alone as originally conceived, then for all the electro-magnetic phenomena (generally) that he soon discovered it to be one form of. [See resume of his 1878 article below.]
135. Thus, in a series of such particles, a displacement (u) of a first particle (P) - due to the application of some force - has an effect on its immediate neighbouring particle (Q) with which it is in continuity. The extent of the consequent 'deformation' (d) depends on the ratio of that displacement to the distance between such particles (a) - ie d = u/a. The force (K) needed to restore this is proportional to that deformation - ie K = p d - where p = the 'elasticity' constant. If the deformation is set to a unit = 1, then the restoring force = p - the elasticity constant. But the next particle (R ) also has an opposing influence on Q - ie a force = K' which = p (u'/a). This works to oppose force K. The net force remaining will affect particle Q to the extent of: K - K' = p d - p d' = p (d-d') - that is, it will be less than the elasticity constant p x 1 - (as it will now = p x less than 1). This force on Q, like any force = mass x acceleration - ie m x b . Thus, the particle concerned undergoes an acceleration (a change in its velocity) due to the effective net force acting on its small mass. This velocity change implies a motion over the displacement distance in time t. The inertia of that particle's mass thus requires time to overcome and move - from a zero velocity up to some maximum. So the displacement of particle P is not followed by any reaction by Q until after a short time lag. Equally, therefore, it can't act to influence a more distant particle - as it is said to do in the action-at-a-distance models without some time lag. If each particle had no mass and so mass density p = 0, there would be no inertia to overcome and such instantaneous action across a medium could then in theory transpire.
136. As the particle size and mass decreases towards the continuum limit (and their number increase accordingly) so the mass per unit length - ie m/a - provides a measure of the mass density (a linear quantity) p. The effective force acting over the distance a (however small) becomes = p x b which, from above, is seen to be a function of the deformation per distance a - ie dependent on the elasticity constant p. The foregoing formulae may be compared to those for velocity and acceleration. Thus: where instantaneous velocity v = u/t so very small deformation d = u/a. Similarly, where a change in velocity b = v-v'/t = w/t so a deformation change (?frequency) f = d-d'/a. In each case, these values remain real no matter how short t or a become (towards the limit of a continuum but, crucially, never getting there - otherwise no real mass, inertia or time would be involved). The values for v and d are thus 1st order differential coefficients and those for b and f are 2nd order ones. The equation of contiguous motion of a wave across a continuous medium is a 2nd order coefficient -
in respect to its change of position in (linear) space over time. For a square area, an additional term would be required and where the wave spreads throughout a volume - as in an expanding sphere - two additional terms are needed. This is the form of such equations for whatever type of wave is of concern - be it sound, water or light. A form of this differential equation can apply to the field of electrostatics - where there is no dynamic transmission of any waves (of force or light, say) across a medium - ie where p = 0 - in which case the instantaneous 'spread' (ie occurrence) of a charged state is called 'pseudo-contiguous action'. Some space but no time seems to be involved. This type of differential equation was developed first (?1840s by Cauchy) and seems to have been a basis later for Maxwell's more comprehensive and valid analysis of the 1860s. [But Einstein was to point out that Maxwell's conception of ether was becoming too complicated when compared with the simplicity and robustness of his equations about e-m phenomena; it was probably incorrect, he concluded. Such mechanical explanations may have to give way to more 'electrodynamic' ones eventually.]
137. In the meantimw, the contiguous differential equations appeared to reveal the essential qualities needed in an elastic medium - ie one that should possess both mass density (mass per length, area or volume) and elasticity. Any one of the 4 variables concerned could be determined if the other 3 were known. Thus, if we write b = p/p x f, then for a wave of a given frequency (degree of deformation), the acceleration b becomes greater as the elastic responsivity (rigidity) p increases and/or the inertial resistance due to mass density p decreases. The velocity of a wave - such as light (c ) - would thus be greater in a highly 'elastic' but low mass medium - ie it would depend upon the ratio p/p. What medium maximises this ratio?
138. This 'velocity of wave motion' - V (wave) = p/p - as a 'law' - can be derived from basic geometric considerations: Each 'point' in a medium executes a simple periodic motion as a series of deflections from a mean resting position to that of maximum deflection (along an axis) and back again depending on the magnitude of the force initiating same and the 'restoring force' which exactly equals that (due to the medium's elasticity). This can be reproduced with the 'point' represented by a spherical mass attached to the free end of a metal band of spring fixed at its other end which can move in either the vertical or horizontal direction. When the mass is pulled some distance from its resting mid-position and then released, it will move back to its starting position starting with zero velocity, gaining speed as it accelerates to the starting position and will then continue past this point (at which its speed will have reached a maximum) - gradually decelerating down to a zero velocity at the other extreme position. Where its velocity is at its maximum, its acceleration becomes minimal and vice versa. It will then reverse the process.
139. The velocity changes of this mass may be represented and more graphically revealed by depicting a point (P) transcribing a circle of radius (a) at constant velocity v - 1 revolution (2 pi a) taking time T - and then projecting its position at various points around this circle as positions (A) over time on an axis bisecting the circle. This constant velocity V(P) then = 2 pi a x 1/T or 2 pi a times v and as a differential coefficient, as: s/t - while the varying velocity v of the point (A) as projected onto the mid-line axes (X and Y) - at various positions displaced from a central resting position (except at Y where the deflection = 0) - ie V(A) = s/t x Y/a = 2 pi times vY. That is, the velocity is a varying proportion (as per vY) of that represented by the constant velocity of point P. Similarly, the varying acceleration (b) can be calculated to equal velocity changes (v-v') - or
140. That is, the velocity (c) of a wave in any elastic medium = p/p. However, the type of medium will affect the form of such waves - being only transverse in a solid-type elastic medium but a mixture of transverse and longitudinal in gaseous and liquid elastic media. The value of c will thus depend on the medium and form of the waves therein. Transverse waves would be fastest in a medium with high elasticity and low mass density (which the 'field' in a vacuum would be assumed to be) and slower in such as water or glass. The assumed particles' respective accelerations (b) were thus a function of the elasticity (p) and deformation (f) of the medium - ie pb = rf . Because p/p = c times c , we find that b = (c times c) f. That is, that the particle acceleration b (the 2nd order differential coefficient with respect to time) is determined by the deformation of the medium f (the 2nd order differential coefficient with respect to space) multiplied by the enormous value of c2 - being the square of the velocity of elastic waves.
2. Electromagnetic Phenomena transmitted in the assumed New Ether.
141. The foregoing analysis of the contiguous transmission of light as a mechanical wave motion (in or of an elastic-like ether) may now be considered with respect to electromagnetic forces and then to light as an electrodynamic (not mechanical) wave motion in or of a non-elastic ether/field. The case is nearly the same but instead of there being only the one factor - viz 'displacement' - that depends on both time and space, there are now two factors so dependent - namely, the intensity of, respectively, the electric and magnetic fields - E and H. That is, momentary changes of the electric field ('E'/t) sets up the magnetic field H around it. But this then undergoes comparable changes so that similar momentary changes in the latter field ('H'/t) in turn adds to the electric field E at a neighbouring point. It is the rate of such changes that determines the consequent intensity (and speed?) of the chain-like sequence of interlocking electric and magnetic fields - each perpendicular to the other. We recall that 'E'/t is a 1st order differential equation with respect to time, while curl H is the same - with respect to space (as the magnetic field curls around the electric field). The same applies to 'H'/t and curl E. Thus, both the electric and magnetic fields depend upon factors of both time and space.
142. In the earlier mechanical interpretation of light , we had p b = p f - the equation for the motion of a wave as contiguous action across an elastic medium. This is a differential equation of the 2nd order with respect to both time (since b = v-v'/t) and space (due to f = d-d'/a). And, since p/p = c2, then b = c2f. In the electromagnetic sphere, we may arrive at similar 2nd order equations thus: The 1st order differential coefficient with respect to time is e/t . The 2nd order equivalent (for E and time) is analogous to the left side of the above derived b = c2f - which is now called b(E). The 1st order differential coefficient with respect to space is -c curl E. The 2nd order equivalent (for E and space) is analogous to f on the right side of the same equation - now called f (E) so that the 2nd order equation (implying changes in both displacement velocity over time and deformation amplitude over space) for the motion of electric waves - with velocity c of that changing deformation - is: b(E) = c2f(E) - which is in complete analogy with that above for elastic waves (eg of light). The right side of this equation entails the removal of two 'mixed' 2nd order coefficients (for time and space) which cancel out.
143. By like reasoning, it is possible to derive a comparable 2nd order equation for the magnetic field H which is: b(H) = c2f(H) - which likewise describes the motion of magnetic waves - also with velocity c - which occur in association with the electric ones - each driving the other on. If either transpired without the involvement of time, no propagation of electric force waves (nor of the magnetic ones) would occur. The necessary changes in the electric field to initiate this sequence and joint propagation depend upon Maxwell's 'displacement current' - the greater the rate of this change (via e/t), the stronger the ensuing force waves generated.
144. The foregoing provides a theoretical analysis of the propagation of electromagnetic waves in some kind of medium - whether elastic or of some less certain constitution. This can be compared with a consideration of such propagation as would be expected to occur in an actual situation. If two metal spheres possess large and equal but opposite charges (e+ and e-), a strong electric field E would exist between them. If near enough, a spark should occur across the intervening space (representing an electric current) which would neutralise their charge difference. The field would then decline in intensity very quickly - at a rate of change represented by the differential coefficient e/t. That change in the electric field is immediately reflected in the creation of a magnetic field which itself changes - thus initiating a sequence of alternating electric and magnetic fields - each compose of their own 'force lines' (in the form of waves seemingly). These respective forces are always perpendicular to one another and to a line running perpendicular to the direction of the spark (current) about which they radiate symmetrically. The electric field thus becomes an electromagnetic one almost immediately and expands in all directions with velocity c in the form of complex transverse waves. That is, the deformation pattern progresses in the direction of propagation across (transverse to) the direction of displacements of the medium which themselves do not move in the direction of propagation but perpendicular to it. It does so as two interlocking waves moving at right angles to each other.
145. When the attractive force of the initial electric field exceeds the threshold of the forces restraining the release of the particles of negative charge (e-), the latter begin their flow towards the positively charged sphere. Until they begin to reach that sphere, the field strength will not have begun its initial changes and so the magnetic field will not have begun to develop around that flow or current. While such a stream of charged particles would rip through one's finger if placed in their path - causing some tissue damage or pain - there would at this extremely early and brief stage be no accompanying observed spark - ie as an intensely illuminated and hot flash. This would only develop after the first particles reached the positive sphere and so started the change (reduction) in the electric field strength which, in turn, would set up the first waves of enveloping magnetic force and the ensuing sequence of alternating but interlocking electric and magnetic waves - ie a complex electromagnetic wave. At this point, the electric spark (with invisible magnetic field around it) now becomes obvious - as a flash of light. The strength of the mutually orthogonal lines of force weaken quickly as they spread out from their source but an electromagnetic wave continues - as light at a constant speed (c).
146. Transverse electromagnetic waves with a velocity equal to the constant c - which was shown in 1856 to equal the known speed of light - allowed Maxwell in 1868 to conclude that light must consist of such waves. This proves consistent with the above analysis of why a spark produces light. However, Maxwell came to his conclusion by purely theoretical means without such empirical evidence. But interestingly, it was by the use of sparks that in 1887/88, Heinrich Hertz finally confirmed Maxwell's theoretical prediction by showing that sparks produced between two spheres at one end of a long room was followed by the induction of a current in an incomplete loop of wire at the other end - as manifested in the production of sparks across the gap of that distant loop. The only conclusion was that the initial sparks did indeed set up electromagnetic waves which crossed the room - presumably at the speed of light. Such waves were partly light but mainly other forms of the same general phenomena - ie radio waves which have that same velocity of c = 300,000 km/sec. They could be reflected and made to interfere and so their wave lengths could be measured. By knowing the frequency of the oscillations, he could calculate their velocity. When this proved to be that of light - ie = c, he had confirmed Maxwell's radical theoretical conclusions. But it seems unlikely that there was any concern at that time as to whether such a speed, albeit enormous and ostensibly a constant, should not vary (as everything else did) if its source or target moved very fast (as in Michelson's recent experiments). But Maxwell's equations apparently implied a true and absolute constancy for the speed of light (and the other e-m waves); but this aspect seems initially to have been overlooked or at least not properly addressed. [One may reasonably enquire why such a constancy is so invariably the case when such light, etc is measured with respect to (ie 'by') any observer no matter at what speed that person may themselves be moving (in relation to anything else). The answer to that simple question equates to understanding the theory of (special) relativity.]
147. The immense constant speed of e-m waves are somehow a function (a product?) of the balance (ratio) of electrostatic and electromagnetic forces (in a ratio of 1:300,000 in km/sec). A vibrating charge must somehow entail these two forces interacting in their constant proportion - thus producing energy which moves the resulting waves at the constant speed of light (in 'quantum' packets - or wave-like particles) and other electro-magnetic 'waves'. One may also enquire as to the 'mechanics' (or, rather, 'electrodynamics?)- not just of their propagation, but of their prior instigation, production and elaboration. Just what happens when the Sun burns, one strikes a match, causes a spark or lights a candle?
148. The concept of Maxwell's field entailed the idea that it is has a chargeable nature. Certainly, any conductor of electricity contains molecules and atoms on which charged poles can be so arranged that while neutral centrally, there is a preponderance of one charge at one periphery and the opposite charge at the other (ie a displacement or divergence of polarity). Between these, an electric 'field' will exist with its directional lines of attractive force by which negative charges will flow as electric current. As they do, the electric field changes and thus sets up an equally changing magnetic field around itself. However, such electric (and magnetic) lines of force will also exist across an apparent vacuum - and while they may also do so in the (?vacuous, ether-filled) space around such molecules, there appears to be no equivalent 'ether-molecules' to account for any displacement (re-arrangement) of charges in a pure vacuum - the changing nature of which might be expected to account for the creation of the fields concerned. And yet the laws (equations) worked out by Maxwell appear to account correctly for the passage of forces (and light) across such vacuums - ie as though there were some such rapid changing arrangement of charge ratios across same. What were the mechanisms and forces at work here - in the new ether that was assumed must exist to account for such phenomena? Einstein's remarks about the difficulty Maxwell had in interpreting how the new ether functioned (in mechanical terms) is again relevant. Nevertheless, before Maxwell, we knew much about what light did while after him, we knew much more about what it was. But, it would not be until the role or otherwise of the ether was finally resolved that light's true nature was revealed.
149. As mentioned above (in 131), that the speed of anything could ever be a true constant seemed to go against 'common sense'. But any such difficulties were seemingly not addressed for some time. If they were, there would have to be some explanation as to how, for example, a bullet of lead fired from a gun might travel at, say, 500 mph when fired from a standing position but do so at (about*) 600mph if fired from a train going at 100 mph (ie in its same direction) - in both cases assuming such speeds in this 'thought experiment' were through a vacuum offering no air resistance - while a 'bullet' of light 'fired' from a suitable source in the same circumstances would apparently, and for unknown reasons, not travel in that second 'boosted' situation at that additional 100mph (approximately*). Why not? How could it remain at its one constant speed ? Such speeds would of course be relative to some selected stationary markers - as timed between them. But if these were afixed to the Earth, they would of course be themselves already travelling at a considerable speed - relative to the Sun (say). Could we make the comparison in respect of two truly (absolutely) stationary markers - set as it were somewhere in fixed space and the respective speeds timed by some absolute timing mechanism? Then, we would have real and known speeds to compare and maybe be more certain in our conclusions. Or, as discussed above, is this ideal really necessary? Isn't a set of smoothly moving markers (as on the Earth), common or relative to all measurements - combined with some relative timing system, totally sufficient? Probably. And conveniently so if in fact there was no such thing as absolute distances or timings. That is, doesn't the principle of relativity apply as usual? [*The need for these qualifications, which is part of the explanation, is addressed later.]
150. But if such a result could indeed be arrived at (ie in a practical sense), the unexpected resistance of light to be enhanced in its speed (from some fast-moving source) may well be viewed sceptically by many who would therefore, in effect, be denying Maxwell's conclusions (including even Maxwell himself possibly; see below). Rather, they may try to account for such an unexpected result by positing various ideas concerning the variously assumed 'media' for light - ie 'the ether' in one of its forms (even in an assumed vacuum) which somehow neutralised (opposed) that extra 100mph. And what if the light was sent through other transparent media which flowed - either in the same direction as the burst of light or in the opposite direction? Would light's speed not be affected there either ? Apparently not very much if at all. And if the light was sent out from a fast-moving source through a stationary medium of that special kind used by light (so that the latter in effect was like the wind one feels if putting a hand out a car window at speed), would it not be thus slowed? Again no, seemingly. Moreover, it may be appreciated that to establish the truth or otherwise of the suggested constancy of the velocity of something that travels as fast as light - in any practical sense - would be very difficult to arrange or measure whatever moving sources, targets or media were involved. Any differences found from an expectation that it would vary in speed accordingly, would likely be so minute that they would most likely be explained away - one way or another - in terms of all the necessary variables and error terms involved.
152. But first, Maxwell's new theory of light as an electromagnetic phenomenon (with an assumed new ether) did provide answers to various other difficulties - concerning optical laws of refraction, reflection, polarisation, etc - which the previous theory with its elastic ether had found impossible to resolve. In particular, it explained - without having to invent special properties for the ether - why longitudinal waves of light appeared when light crossed from one medium to another. Earlier, MacCullagh had further adapted such theories (with his rotational forces) to account for this problem - seemingly with a new ether - one without the elastic properties long assumed - and in so doing had in effect stumbled upon an interpretation which proved surprisingly consistent with Maxwell's later e-m model. But MacCullagh's was an ad hoc theory which could now be accounted for on a more rational basis within Maxwell's more general theory. There was now no doubt that light materialised out of and was under the influence of electromagnetism and that the carrier was not quite the elastic ether medium long assumed - but rather 'the field' - a kind of non-elastic, electromagnetic 'ether of sorts' - which would became the accepted medium for light (ie by about 1875 or so).
153. It was soon accepted that all electric, magnetic and optical waves were probably carried by their newly-conceived ether-like medium (the electromagnetic field) for which the long analysed elastic constitution did not now fully apply. It behaved instead according to Maxwell's 4 equations (laws) - which apparently were not consistent with the elasticity hypothesis - but the constitution of a 'new' ether (still believed to be necessary) was not yet properly determined; only that it wasn't of an elastic nature. While it was eventually referred to as the 'electromagnetic field', just what it was in or of that field that executed or allowed the waves concerned to propagate (or how) was unknown. What is it that vibrates (is displaced) and, requiring time, deforms itself - into the form of a rapidly moving wave? As mentioned above, Einstein noted that while Maxwell's equations proved simple and robust, his conception of an ether-like medium for the transmission of electromagnetic waves thus explained was more complicated and uncertain. In 1878, Maxwell gave his views on this latest form of ether in a review article entitled 'Ether' written for the Encyclopaedia Britannica - 9th Edition (1878) - Vol 8 (p 568-572). It is of value in any analysis of the evolution of the theory of relativity in that it was written at a time when ideas on light and its assumed medium were subject to increasing attention and development. Maxwell was naturally influenced by the views of those who came just before him - just as those to follow would be similarly by his own thoughts and discoveries. As such, it provides an excellent reference point in the development of our subject.
154. Maxwell begins by noting that the origin of the term 'ether' or 'aether' comes from the Greek meaning 'I burn' (being invisible like air or oxygen?) although Plato apparently derived its name from its assumed perpetual motion (which must be of interest in view of later hypotheses as to its presumed stillness). Maxwell then describes it as a material substance of a kind more subtle than visible bodies and supposed to exist in those parts of space which appear empty, even in a vacuum. He points out that many earlier scientists including Descartes attempted to account for various phenomena in terms of a number of different ethers - until all of space would he said have been filled three or four times over with all the various kinds of ether! There was then a reaction against this approach during the 18th century when much less was heard about it. However, Newton had suggested that gravity may be accounted for by differences of pressure in an ether but did not publish this theory "because he was not able from experiment and observation to give a satisfactory account of this medium and the manner of its operation in producing the chief phenomena of nature" (as light and gravity seemingly). How wise! (But then he was, of course.)
155. The main type of ether to survive from the many that preceded it was that suggested by Huygens to explain the propagation of light. Maxwell points out that 'evidence for the existence of a luminiferous ether has accumulated as additional phenomena of light and other radiations have been discovered...'. Moreover, its properties as deduced from this increasing understanding of light turn out 'to be precisely those required to explain electromagnetic phenomena'. Evidence supporting the wave theory of light is quoted by Maxwell as support for the the existence of the ether. Thus, 'interference phenomena' indicates that only waves of light - a half a wavelength apart - neutralise one another and show that light must be a wave process (not a substance) but which takes place in a substance - ie in the ether.
156. Interestingly, Maxwell then points out that 'light is known to be propagated with a certain velocity' - ie at about 3 x 1010 centimeters per sec in vacuum - without mentioning that this is a constant. He then states that "If, therefore, we suppose a movable point to travel along the ray with this velocity, we shall find the same process going on at every point of the ray as the moving point reaches it". This is difficult to analyse. For how could the travelling point 'find' (ie observe) the 'same processes' going on 'at every point' (ie on 'reaching a succession of such points) of the light ray - as it travels along with it, if its only travelling at that same speed? One could well imagine young Albert Einstein a few years later, aged about 16, reading a translation of this article by Maxwell and then formulating in his mind his famous 'thought experiment' concerning how a wave of light might appear if one (as a ?point) could travel along with it - at its speed. Would it appear as a frozen (unchanging) wave or ??. In any case, Maxwell goes on to describe the time 'light takes to travel one wave length' (or undulation) - being the time between identical phases of the wave (eg from the bottom of one 'trough' to the bottom of the next) as such a wave passes a given point). The nature of the process is unknown (as eg a 'positive to negative' displacement, a disturbance, a rotation, etc of something ether-like) - only that it comprises positive and negative (ie equal but opposite) components which, if occuring together half a wave length apart, will neutralise the converse of whatever that process is - as then manifest by the other.
157. He represents the quantitative geometrical aspects of this unknown process mathematically by:
in which u is the phase of the process - at a point p whose distance measured from a fixed point along the beam of light is x - at the time t. At any given point along the stream of passing waves, the process is called a 'vibration', the constant A is the 'amplitude', the time between the same point in a wave = 2p/n - called the 'period' while the 'phase' = nt - px = a. The overall configuration at a given instant is called a 'wave' and the wave-length = 2p/p. The propagation velocity of such waves = n/p. Whatever the actual physical process in nature, such precise representation mathematically can provide a more valid and accurate conception of the underlying reality than anything else.
158. Whatever the physical nature of this propagation process, the substantive medium in which it is assume to occur was assumed to undulate in response - and at that immense velocity. Certain aspects of the actual process are suggested by studies using polarized light. Parallel planes of such light can result in interference - with alternating bands of dark and light appearing on a test screen. But if the planes become perpendicular, this disappears and the illumination becomes uniform on the screen. The physical process of propagation is thus a directed quantity or vector capable of having its direction reversed - with the vector at right angles to the beam of light - either in the plane of polarization or perpendicular to it. Fresnel supposed it to be a displacement of the medium perpendicular to the plane of polarization whereas MacCullagh and Neumann considered it to be a displacement in the plane of polarization. The resolution of these conflicting theories rerquired experiments with 'dense media' (see later; also Lorentz's theory about it).
159. But Maxwell suggests that the actual process (in its media substance) may be 'an electromagnetic one' - where the electric and magnetic disturbances are perpendicular to each other - so that either may be supposed to be in the plane of polarization. All this would apply equally to non-visual forms of radiation (ie of electromagnetic waves). The foregoing addressed primarily the geometric character of the process of light's propagation. Maxwell then considers further the substantive medium in which it takes place. (Note; he doesn't say 'in which it is assumed' to take place). He uses the term 'ether' to denote this medium - 'whatever it may be'. The first quality to note about the ether is that it is capable of transmitting energy (eg even through a vacuum). [It is interesting to consider that if and when the ether per se is later deemed not to exist, that the energy of light is accepted as travelling through a vacuum nevertheless and that it is virtually this possession and transmission of energy per se that now constitutes (or best characterises) the mysterious non-substantive 'field' in or by which it is so propagated.] The second characteristic is that this energy is not transmitted instantaneously but exists for a time 'in the medium' as it so transmits.
160. According to Fresnel and MacCullough, half of such energy is in the form of potential energy held within distortions of the ether and half is kinetic - expressed as its motion. From this it follows that the ether has elasticity and density. Using a number of assumptions, Maxwell estimates the density of ether to be greater than that of interplanetary space but much less than that of solid matter such as the planets themselves. That light travels through some medium much less dense than air (ie the ether) is indicated by the fact that the vibrations of air travel a million times slower than does light in its medium and in any case they are not the transverse vibrations by which light is transmitted. Solid transparent bodies such as glass can transmit transverse vibrations but these are still much slower than those of light passing through same. As Maxwell states, "we are therfore obliged to suppose that the medium through which light is propagated is distinct from the transparent media known to us (as air, water or glass), though it inter-penetrates all transparent bodies, and probably opaque bodies too".
161. The fact that the velocity of light does differ in different transparent bodies suggested that the latter must take some part in the light propagation process such that their particles also vibrate to some extent - as do those of the ether therein. However, the energy of vibration of the transparent particles would be much less than that of the ether since so little of the incident light is reflected when light passes from a vacuum to some transparent material or vice versa. Because of this, it was concluded that the ether within dense bodies must be 'somewhat loosely connected' with such bodies. But how 'loosely'? If such a body is in motion - whether through the thin air of space or even through a vacuum and thus through 'the great 'ocean' of ether - is the ether they (apparently) contain carried along with them and if so, is this association complete (as per Stokes' theory) or, as Fresnel found, only slight...or, does it completely pass through them - as the (relatively still) water of the sea passes through the mesh of a moving fishing net pulled by a boat? In fact, it would of course be the net that actually moved - through the still sea - although such movement is really relative and either description is equally valid.
162. It was apparently the posing of this question that led Maxwell to go on to propose methods to determine the stillness or otherwise of the ether - relative to the moving Earth. That is, did it move - both within and as an envelope around the Earth - or was it perfectly still - like that stationary sea - through which the moving Earth sails? Sadly, having accepted that the ether may be only 'loosely connected' with dense bodies, the need as he sees it for further research concerning the ether is expressed as a rather limited goal - ie (therefore) '...we have next to inquire whether, when dense bodies (eg as the Earth) are in motion through the ether, do they carry their own ether along with (and immediately around) them or does it (as a still ether) pass passively through them (as still water through a moving net, etc) as they move through it? He appears to make no attempt to relate the relevance of finding the answer to this question to anything about the propagation or nature of light. But his Encyclopaedia article and his letter to D.P. Todd (see below) both imply clearly that he is basically interested in establishing the velocity of the Earth and/or of the Sun relative to eg a still ether so that he may determine what if any may be the effects of that ether and/or of the moving Earth and/or Sun relative to that ether on the velocity of light - presumably as an electromagnetic disturbance.
162b. If this is indeed his goal, then it follows that he had not, by that point, convinced himself that the velocity of light was a true constant - in all circumstances; rather, it could be affected by various relevant factors. He may also have been seeking evidence as to the mode of transmission of light in its ether, but does not appear himself to have considered the possibility that light travelled by means of any non-mechanical construct (if that conception had even crossed his mind). Also, while we have discussed above the implications of a constant velocity of light, this property had not been verified (or even put to the test) by this date (ie ca 1870-80). It was but a mathematical conception. albeit an internally consistent one. Interest in the role and constitution of the ether seems not to have been premised on concerns in that regard but rather simply as a means of verifying Fresnel's earlier hypotheses regarding the motion of the ether - ie as just another stepping stone in understanding the wave theory of light and how it could be shown to be consistent with any anomalies such as aberration.
But Maxwell seems also to have sought to determine if the velocity of light was affected by any motion of the ether. As far as I am aware, this wasn't motivated by any prior questioning by others about the possible role of light's accepted medium on the velocity of light or by any anomalous observations in that regard. Quite possibly, Maxwell was curious to know if there was any such effect in view of his earlier conclusion that the velocity of light was supposed to be a constant but didn't wish to be too dogmatic about this?
163. His suggested method to determine the motion of the ether terrestrially was an indirect one which relied on determining any difference in the time taken by light as measured firstly in the same direction as the Earth's orbit and then in the opposite direction. But any increase in the time taken by light due to the opposition of a still ether (if it be there, still or not) - ie as though moving against it (equal to the relative velocity of the Earth in the opposite direction) would be so slight he concludes - being but a hundred millionth part slower than the time of light's transmission between measuring stations - that no method was available, as he believed, to discern it. Such a minute difference would, he claimed, be 'insensible' (ie beyond our senses, or that of our devices). But, in any case, it seems most odd that to determine something about the ether - with no reference to the relevance of the outcome to the more basic one about the transmission or speed of light, he suggests actually using the latter to resolve the former - as though it were in some totally independent sphere of nature; but, on the contrary, it would appear to be intimately associated with the very phenomenon he is investigating. How could one distinguish cause from effect? What are the dependent and independent variables here, the latter ideally varied one at a time? Does he want to learn something about what affects the velocity of light (as the dependent variable) or is light the independent variable used to determine some effect on a different dependent variable - namely, the stillness or otherwise of the assumed ether? Whatever the answer, it seems that someone felt that such a minute difference could be made 'sensible' and do so using an elaboration of the method suggested by Maxwell. Within a short time, Albert Michelson (1881) made his first attempt to determine the motion, if any, of the ether. Hopefully, we may discover more about the ultimate significance of determining same in the forward of his article.
164. But, still in 1878, Maxwell points out that while any motion of the ether might affect the phenomenon of the aberration of light (although there was as yet no useful theory about the ether to help predict what that might be), it again would likely be so slight (eg according to Stokes) that this too could not be accurately measured. A method was however suggested by Maxwell for determining more directly (but still indirectly?) the relative velocity (or stillness?) of the ether - relative to the solar system (ie the Sun). This was again by comparing the times taken for light to travel in the two opposite directions relative to the assumed ether - as deduced by means of the eclipses of Jupiter's moons (as per Romer's method) - at opposite points of the ecliptic. (See his letter to D.P. Todd for more about this below.)
165. He then refers to a 4th method (proposed by Arago) in which the deviation of starlight passing through a prism would be expected to differ according to whether the light entered the prism with or against the motion of the ether (assumed to pass through the prism) - with the latter's (apparent) direction - against or with the starlight - determined by the motion of the Earth towards or away from the relevant star (and its light). Maxwell arranged an experiment based on Arago's idea but by means of a more practical method. But he obtained only negative results. He seems to have concluded that this didn't necessarily mean that the ether near the earth was carried along with it as it moves in its orbit (and so neutralise any changes in the deviations expected otherwise) - quoting Stokes and Fresnel that any apparent motion of the ether through the prism would again be too slight (due to refraction limitations) to be measurable by Arago's method. This appears to imply that any positive results that might have occurred would have supported the view that the ether was still and it was the motion of the Earth (with the prism attached) through it which would result in an apparent (ie relative) motion and any effect this may have on the dependent variables observed. We may assume that Maxwell's other references to testing 'the motion of the ether' implied this same rather roundabout way of expressing the hypothesis that the ether was in fact 'still'. Again, we know not why, in any direct sense, he wishes to establish this - other than simply to further consolidate Fresnel's theory of the basically still ether as light's medium (and so possibly strengthen the idea that the medium by which electromagnetic phenomena are transmitted (or in which they are engendered) is this same ether by which (possibly) some verification of the theoretically concluded constant velocity of light (at its understood velopcity )c) could be more reliably obtained).
166. Maxwell refers next to experiments performed by Fizeau around 1860 one of which appeared to support the idea that light's velocity is greater when it passes through water running in its same direction than the converse although not as great as might be expected due to the increased speed of the water. This seemed to imply that the mainly still ether in the water reduced the effect. Moreover, it didn't occur similarly when the stream was of moving air. In both cases, therefore, Fizeau's results seem to have supported Fresnel's theory - of only partial convection (ie motion) at most of the ether in moving bodies - and approaching stillness in air (whether moving with or against the direction of light or as still air). But Maxwell sums up by saying that the motion (ie the 'state') of the ether near the Earth and its 'connection' with matter is far from being settled by experiment. Only the celestial Jupiter method, he felt, might eventually establish this. Its a pity that nowhere in his article does Maxwell make clear what relevance either a still or a moving ether (whether partial or complete), as light's medium', may have to our understanding of the nature and propagation of light, nor of the magnitude or constancy of its velocity. If it was unquestionably still (or conversely, moving), what would that signify regarding light per se - other than some interest in how the velocity of light might be affected ? But it would be a generation later before Einstein took the bull by the horns and, unlike Maxwell himself (despite he being the one whose equations popinted to it being a constant), proclaimed that nothing affected the magnitude nor the constancy of the velocity of light. I can see no concern either on the part of Maxwell (ie up to 1880) on matters pertaining to the principle of relativity, the absolutism-relativity topic or the mechanical vs non-mechanical model of physics.
167. But Maxwell then leaves the subject of the possible motion/stillness of the ether and does address next the matter of the function of the ether in 'electromagnetic phenomena' - ie initially in the electric and magnetic forces that at least subserve light. He notes that Faraday, who said the "if there be an ether, it should have other uses than simply the conveyance of radiation...", suggested that this same medium may serve a similar role with electromagnetic phenomena - specifically with the transmission of electric and magnetic forces. Subsequent investigations have, says Maxwell, served only to strengthen this view. He points out that 'electrical energy' is of two kinds - electrostatic and electrokinetic. The former depends upon a property of the medium (ether) through which it is transmitted and in which an electric displacement elicits an electromotive force in the opposite direction - having an inverse relationship with the specific inductive capacity of the ether. [This is a bit technical; these variables and mutual interactions need clearer definition.] The electrokinetic energy is simply the energy of motion set up in the medium by electric currents and magnets and it is not confined to the wires and magnets concerned but exists wherever such forces occur - ie in their surrounding 'fields' (then a very ether-like concept.
168. The foregoing discussion leads into Maxwell's 'Electromagnetic theory of light' (published some years before, I believe). He notes that the properties of the two ethers (for light and for electromagnetic forces) seem very similar. The extent of this similarity may be assessed by comparing the velocity which such forces are transmitted through their assumed medium with that of light through its. If they are the same (ie = c), there is strong reason to believe that the two media occupy the same space and are (therefore) one and the same thing (as indicated above). Calculations based on experiments in which electrostatic and electromagnetic systems of units are compared provide evidence to show that in air the velocity of such electromagnetic disturbances (forces) and of light are equal within acceptable errors of measurement. He contrasts the former undulatory theory of light, with its assumption of motion via an elastic ether, with the electromagnetic theory in terms of three difficulties. Firstly, the former theory indicates the possibility of vibrations normal to the surface of the wave. But that would mean that certain optical phenomena should arise thereby and the fact that they don't is only explainable by accepting that the the medium is incompressible; ie not elastic. Secondly, the phenomena of reflection and double refraction require inconsistent planes for the associated vibrations. Thirdly, one can't account for the identity of velocity of light in principal planes and when polarized in such planes in a doubly refracting crystal unless highly artificial relations are assumed among the coefficients of elasticity. On the other hand, the electromagnetic theory of light with its non-elastic ether (but an ether nevertheless) satisfies all these requirements by a single hypothesis (ie that offered by Lorentz (1875) - that the electric displacement is perpendicular to the plane of polarization. [Some of the explanation of these relations is rather complex and will have to be accepted for now. See below for more on the electromagnetic basis of light and the independence of the crucial ratio underlying its resultant constancy.]
169. Finally, he discusses the constitution of this new ether by which light and the electromagnetic phenomena are transmitted. Is it molecular or continuous? If molecular (by this, he seems to mean atomic or particulate), it would have to be of a very stable configuration and not like a gas - with its continuous random motion of constituent 'molecules' - since the otherwise undiminished energy of light and these forces would soon be dissipated. Such a stable but molecular-like constitution is suggested by Maxwell if it can display a kind of homogeneity (of its minute 'bits') in respect of its density but a heterogeneity in respect of its motion (being possibly rotational around the axes of each minute portion of the medium - as in Sir Wm Thomson's vortex hypothesis). These 'molecular vortices' (like spinning electrons?) appear to be self perpetuating and use up no energy as they convey their light or forces. But Maxwell concedes that (as of 1878) there is as yet no satisfactory theory to account for this absence of any dissipation of energy as light is conveyed by the (?rotary) motion of such miniscule portions of ether. However, he doesn't concede that, therefore, light must propagate by means of some non-substantive process alone - rather than via some theoretical substance which, miraculously, offers no resistance and dissipates no energy. He concludes by expressing his view that the vast interplanetary spaces are 'no doubt' not empty but filled with some such uniform material 'substance' or 'isotropic matter' - which must be that substance which his article addresses - ie 'the ether'. The general tenor of his paper certainly indicates that he believes that one of its functions is the propagation of the processes of light and equally of the electromagnetic forces which underlie and produce it.
170. In his article, Maxwell refers to recent articles on the constitution of the ether written by S. Tolver Preston in 1877 (in Phil. Mag.). While his ideas had not yet been the basis for any experimentation, he felt they offered a basis for theorising as to the probable particulate constitution of the ether (whatever its state of motion). This included the idea that where such particles didn't interfere with each other, they could allow the unhindered propagation of light by means of their local rotation about an axis. Preston wrote further on this topic ('On a Mode of Explaining the Transverse Vibrations of Light') shortly after Maxwell's death - in Nature (1880) - in which (in the Jan 15th edition) he agreed essentially with Maxwell's development of his theory of a constitution for ether (as like a gas consisting of exceedingly minute 'atoms' of ether in motion) which allowed the propagation of light in a straight line (as transverse vibrations) without having to resort to the discredited hypothesis of 'action-at-a-distance'. The 'atoms' thus act upon each other across the spaces between them. He then elaborates further on the role of ether in gravity and proposes that the distinction between ponderable and imponderable matter disappears as a consequence. The same ether medium ('this magnificent physical agent' as he describes it) accounts for the phenomena of both light's motion and gravity's action. In a reply to some criticism of these ideas a fortnight later (Feb 19th) he pointed out that his theory was not advanced in opposition to some existing theory - on the constitution of the ether as the medium for the propagation of light - 'as no other theory or clear conception of ether's constitution in this regard appears to exist' to so oppose. This provides a convenient benchmark - as of 1880 - for our subsequent discussions.
171. The year 1880 can also serve a useful fulcrum point in respect of the other (ie non-medium) property of the ether addressed by Maxwell - namely its possible stillness or motion. On Jan 29 1880, Nature reported (p 314) on matters discussed by Prof Stokes at a meeting of the Royal Society held on Jan 6th that year. Stokes had previously written to the Society - on 19th March 1879 - to inform them that D.P. Todd, Director of a Naval Office in Washington, D.C. had sent him a copy of an unpublished paper he had received from the late Prof J. Clerk Maxwell (who, sadly, had died in November 1879). Todd had written "I regard the communication as one of extraordinary importance...". Stokes noted that as the method "referred to by Maxwell in his Encyclopaedia Britannica article on the ether was very brief, being confined to a single sentence, and as the subject is one of great interest, I have thought it best to communicate this letter to the Royal Society". It was presumably communicated in turn to Nature magazine following the Society's meeting of Jan 6 1880 and somehow then became entitled 'On a Possible Mode of detecting a Motion of the Solar System through the Luminiferous Ether'. It elaborated on the method discussed above utilising the satellites of Jupiter - seemingly as the only practical way of establishing the (relative) stillness or motion of the ether (with its relevance to the propagation and velocity of light). In his letter to Prof Stokes, D.P. Todd admitted that 'it may be a long time before we have sufficiently accurate measures of the satellites to put the matter to the test'. He was apparently an expert in this latter aspect and hence why Maxwell had written to him - seemingly in late 1878 or early 1879 - as follows:
To D.P. Todd, Esq. - "Sir, I have received with much pleasure the tables of the satellites of Jupiter which you have been so kind to send me, and I am encouraged by your interest in the Jovial system to ask if you have made any special study of the apparent retardation of the eclipses as affected by the geocentric position of Jupiter?
I am told that observations of this kind have been somewhat put out of fashion by other methods of determining quantities related to the velocity of light, but they afford the only method, as far as I know, of getting any estimate of the direction and magnitude of the velocity of the Sun with respect to the luminiferous medium. Even if we were sure of the theory of aberration, we can only get differences of positions of stars, and in the terrestrial methods of determining the velocity of light, the light comes back along the same path again, so that 'the velocity of the Earth with respect to the ether would alter the time of the double passage by a quantity which depends on the square of the ratio of the Earth's velocity to that of light, and this is quite too small to be observed'. [It was this latter comment that motivated Michelson apparently.]
[Maxwell then describes mathematical analyses relevant to calculating various pertinent quantities, including V - the velocity of light (the symbol c having not yet entered the scene). He then continues: 'But no method can be made available without good tables of the motion of the satellites, and as I am not an astronomer..., [I (Maxwell) would not know if other such tables would be useful to calculate an important value in this connection]. 'I have therefore taken the liberty of writing to you, as the matter is beyond the reach of anyone who has not made a special study of these satellites'.
"In the article on the ether in the 9th edition of the Encyclopaedia Britannica, I have collected all the facts I know about the relative motion of the ether and the bodies which move in it, and have shown that nothing can be inferred about this relative motion from any phenomena hitherto observed, except the eclipses...of the satellites of a planet, the more distant the better.
If you know of any work done in this direction, either by yourself or others, I should esteem it a favour to be told about it. Believe me,
Yours faithfully," (signed: J. Clerk Maxwell).
172. We may note that in his letter Maxwell refers to the methods he describes as '...methods of determining (quantities related to) the velocity of light...' but then goes on to say that the best of these methods - utilising the eclipses of Jupiter's satellites - '... affords the only method as far as I know (not of directly determining the velocity of light but) of 'getting an estimate of the direction and magnitude of the velocity of the Sun with respect to the (ether)'. One must assume that it was these latter 'quantities' that were so relevant to determining thereby the velocity of light - that clearly being his primary interest. This is supported by his remark later that "...the determination of V, the velocity of light, by this (Jupiter) method"...depends on differences in the Jupiter to Earth distance (on different occasions)...etc. He also says that if one tried instead to use the terrestrial method of determining 'the velocity of light' (ie still his major interest), 'the light comes back along the same path...so that the velocity of the Earth with respect to the ether would alter the time of the double passage by...(too small a quantity to observe)'. In both cases therefore, he really seeks to establish not the motion of the solar system per se but the stillness or otherwise of light's assumed medium, relative to such moving celestial bodies, in order to see if it affects his previous theoretical conclusions regarding the velocity of light or even its constancy.
[Note: Maxwell died aged only 48 on Nov 5th, 1879 (of stomach cancer).]
If it was found to be still (or indeed moving), what, we may ask, would either of those outcomes imply? Was he interested in the propagation and/or velocity of light per se (whether as per Fresnel's ideas or his own as its ?predicted constancy) or simply as a means (a tool) by which some measure of the ether (per se) might be assessed? This would imply a readiness to accept that the velocity of light may not be truly constant in all circumstances - something that his own equations apparently denied. Had he not taken that 'reality' fully 'on board' - just as no one else seems to have (ca 1875-98) - until Einstein? The answer may arise through the work of two researchers active during the 1880s - Michelson and Hertz - who approached the matter from these contrasting points of view. We will consider the work of Michelson first but before that a general summary of the position arrived at by this point (with some discussion about difficulties of research in this area) may prove useful:
173. During the first half or so of the 19th century, considerable research and theorizing took place concerning the nature of light and its assumed medium the ether. We may accept that this interest was aimed at at better understanding of these phenomena per se and not as part of some grand design to lead to some overall understanding of the natural universe. During this period the velocity of light was discovered - both across the vacuum of space and in various transparent media such as air, water and glass, where it was somewhat slower (depending on their indecies of refraction). The motion and constitution of light's assumed carrier - the ether - was also investigated and theorized about - as by Fresnel and Stokes. Because of the intimate interaction assumed between light and this carrier, studies about either at the time necessarily had relevance to the other. Then, in 1868, Maxwell concluded, on theoretical grounds, that as electric and magnetic forces travelled at the same speed as light, it (still as a wave phenomenon) may well have an 'electro-magnetic' character itself. This was later confirmed by Hertz (1887/88). As such, it was generally believed a the time that it required an ether medium that was not of an elastic constitution. But, otherwise, these two interacting features of nature - light and the ether - continued to be investigated as before. Two properties in particular could continue to be addressed:
1. 'Was the ether essentially 'at rest' or did it move (in association with moving bodies)'? and
174. Because of the belief in the intimate association of light and the presumed ether, it was difficult to arrange experimental tests of these two questions. But for the first question, one could begin with an hypothesis such as 'If the ether is at rest, we would expect (as confirmation) that the velocity of light passing through it would be slowed (compared to any neutral comparison). If it wasn't slowed, we may conclude that the ether did not remain still but actually moved - ie with the light - thus not affecting its velocity. (Or, as light's speed didn't vary (ie wasn't slowed), as expected, it must have remained constant.) The hypothesis could of course have been framed in terms of the converse: 'If the ether moves...etc'. For the second question, the latter conclusion could itself be the primary objective to be tested - the comparable hypothesis being: 'If the velocity of light is constant (whatever the motion of its source, media or target), we would expect (as confirmation) that the ether through which the light passes must remain still regardless of any moving source or target. But, if it didn't remain still, we may conclude that light's speed wasn't constant but varied - ie with that moving ether. (Or, as the ether moved, against expectations, it must not remain at rest.) Again, such an hypothesis may have been framed as: 'If the velocity of light varies...etc'. It was clearly not an easy area to investigate.
175. However, it seems as though it was primarily the first question that was of prime interest during the following decades (1870s-90s). That is, that an already assumed variability in the velocity of light under various circumstances (eg as noted with different media), was used to establish the much more uncertain (and controversial) motion or otherwise of the ether - rather than an already assumed stillness (or mobility) of that medium being used to establish the constancy or otherwise of the velocity of light (in a given medium) - this apparently being of little concern or doubt at that time. It seems it was generally assumed that, as with everything else in the universe, light's speed relative to any neutral 'third party' frame of reference would depend on the speed of its own immediate frame (as a fast-moving source of that light, say) - ie would, additively, equal its own speed plus that of the reference frame. That is, the principle of relativity would apply to it - as it did to everything in mechanics. One problem with this assertion however is that the often confused description of the objectives of experiments in this sphere (possibly due to the intimate association of the variables concerned - as light, ether and such as the moving Earth, Jupiter, etc) allows of the possibility that the researcher (or reviewer) may actually perceive a different (or more implicit) objective than appears to be the more explicit case described. Where neither of the independent variables (each serving as dependent variable to the other in different studies) have been previously confirmed as valid and reliable, the reliability and validity of the conclusions must remain suspect. Its a bit like stealing from Peter to pay Paul. In any case, this reviewer will tend to perceive most studies, where possible, as seeking ultimately information/ confirmation on the (theortetically concluded constancy, or otherwise) of the velocity of light, even if indirectly. Maxwell himself may have fallen in this camp. But its not easy to be certain of ultimate goals in this area of research.
176. Some of the inter-relationships of variables involved in studies in this sphere may be visualised in terms of a fairly simple analogy (which likely includes various inconsistencies). Thus, we may imagine measuring the speed of a sound wave produced in the carriage of a moving train. At the back end of the carriage, a bell rings and its sound travels to the front end where it is detected and its journey time recorded. As it is a closed carriage, the air through which the waves travel is moving with the carriage at its speed. The time and speed for the sound's journey from one end of the carriage to the other would thus be exactly the same as it would be if the carriage was stationary, or if the same distance was travelled and measured outside the carriage near the station platform - on a still day. Of course, the distance travelled by the sound, and its speed, would be greater for the sound travelling in the moving carriage if these values were measured instead in relation to the stationary platform - ie by amounts accounted for by the speed of the moving train. If we then repeat this 'experiment' but imagine now that the carriage walls are composed of chicken wire so that the air outside can (relatively) now rush through the moving train at will, the sound waves would now have to 'battle' their way against this opposing handicap. Their time would thus be slowed compared to that in the stationary or enclosed carriage. We have assumed it was a still day; if there was actually a strong wind blowing against the direction of the chicken-wired train, the sound would of course have been slowed even more or vice versa.
177. If we now repeat all this but use light rather than sound, we can ask whether we would get similar results. When we do so, we find that the speed of the light waves in the intact carriage is no faster than they would be in the imagined chicken wire carriage. This is soon explained by the fact that, unlike sound, light doesn't need the medium of air (whether still ot opposing) in which to travel. After all, it travels from the Sun through millions of miles of the apparent vacuum of outer space. It allegedly travels by means of its own special medium, the ether, which while still a substance (as generally assumed), is barely confirmable within that (seeming) vacuum of space or between the molecules of any material including air or water. In fact, its assumed particles are so small and subtle that, to it, the carriage walls are already like chicken wire; as far as light is concerned, the train passes right through it (and vice versa) so that it appears (again relatively) to flow unhindered through the moving carriage - just as we imagined the air did when the sound's chicken wire (moving) carriage was the case. If it was possible to make the additional comparison - of the light's expected increased speed as measured in the moving train compared to that in a stationary carriage, or even outside beside the platform, we should probably find, rather surprisingly, that it was no faster (just as it was no slower when measured as it travelled through an ether 'wind' flowing through the very porous carriage - there being no possible enclosed carriage of ether, moving with the carriage, in which a faster speed of the light could have been found). But this disagreement with the principle of relativity - indicating some odd invariability in the speed of light whatever comparisons are made - was not determined by such imagined experiments - as the speed of light is so immense that such tests in reality were not practicable. Rather, it was necessary to utilise the greater speed of the Earth (or even Jupiter) moving through or with the ether and sophisticated instuments involving mirrors, interference waves and double jouneys for the light in order to put such questions to this test. And, even then (as explained), interest was focused initially on whether the assumed ether was in fact still or in motion - and sought to do so by actually utilising any variation noted in the velocity of light - such variation (and its assumed possibility) obviously being taken as a convenient and available given in 'such' tests (via ether's motion or not of light's speed) - ie it being the convenient independent variable. We may now return to the studies of Michelson.
178. The celestial method involving the satellites of Jupiter seemed to Maxwell the only reliable way forward, but it required more accurate background data than then available before it could proceed, while the challenge of the terrestrial method - thought by him to be impractical as the differences sought would be too slight to measure with any accurance - was nevertheless taken up, in America, within the year. In the same decade as Hertz was seeking to build on Maxwell in terms of Stokes' theory of a mobile ether (designed it seems to show that the velocity of light could and should vary and be compatible with a moving ether); see below), Albert Michelson (a Polish-born American of German (?Jewish) descent) attempted (in 1881) to put the idea of Fresnel's fixed ether to the test - as a test pertaining to Maxwell's interest (whether implicit or explicit) in the effect of such a still ether on light's speed (as I understand it).
Thus, in the first of his two articles, entitled 'The Relative Motion of the Earth and the Luminiferous Ether' (Amer. J. Sci, 22, 120-129 (1881), Michelson begins by stating that 'the undulatory (ie wave) theory of light assumes the existence of a medium called the ether 'whose vibrations produce the phenomenon of light' and which is supposed to fill all space'. Quoting evidence by Fresnel, he concludes that we may assume that this ether is at rest (possibly in some absolute sense?) and that therefore the time required for light to travel from one point to another over the Earth's surface (which, given equal distances, equate to a statement about the velocity of light) would depend on the direction the light travels relative to that of the Earth. In one direction, it would move with the Earth - with the light given a moving start or 'boost' as it were Thus accepting that its velocity could indeed vary) but the receiving station moving away from it thus increasing the distance and time for the journey. This could be balanced by also measuring it in the opposite direction. But, if Fresnel was right, it would also be slowed by having to travel through (ie against) a still ether which, in one direction at least, would in effect serve as an opposing 'wind'). The difference (D) in the net speed of the light after the various distance and direction variables were taken into account, should establish the existence or not of the hypothesised still ether and, if so determined, would indicate that the velocity of light had been so affected by same. Michelson quotes Maxwell's letter (to D.P. Todd) in Nature (of 1880) in which he indicated that the difference D as might be determined by the terrestrial method would however be so slight - at a hundred millionth part of the whole time of light's transmission (being the square of the ratio of the Earth's calculated velocity to that of light) - as to be 'quite too small to be observed' (measured). This seems to have been due to the need to re-trace the light's path in each of the opposing directions (possibly to equate the dfferences in distance travelled...or ?).
179. However, Michelson asserted with confidence that, on the contrary, there is a time quantity which - if the predicted effect of the still ether exists - can be "easily measured" ! This would be an indirect measure of this effect of the ether on the times taken by the light and hence on its velocity (where distances travelled were effectively equalised). In fact, it would seem to be a doubly indirect measure of such an effect - obtained by means of (a) a different time-difference measure (one that presumably still accurately represents the original difference (D) sought and (b) determining that new difference in terms of interference bands arising from the discrepancy in the phases of the respective light waves arriving at a common end point. Thus the measure pertaining to (a) was to be the difference between the total time taken over both directions of the light's passages and that taken over an equivalent distance at right angles to the former (when no influence of the ether wind should be expected) as judged by any interfernce effects. That is, for (b), the difference would be manifested by a spatial displacement of interference bands of the light arriving from these perpendicular paths and this spatial difference could be transposed into a velocity difference. Michelson's method was thus designed to determine the influence of the Earth's assumed motion (vis a vis an assumed (tested for) fixed ether encircling it) on the speed of light in such a way that the predicted (?slowing) effect of the suspected (still) ether would be verified. Its confirmed stillness would of course also imply its very existence and so support the mechanical model of physics (in terms of one or other of the two (mechanically-relevant) considerations - light's substantive means of propagation and/or a fixed reference system for the principle of relativity). One has to assume that Michelson was also interested in the matter of any variation in the velocity of light per se due to such a still ether as he doesn't make that explicit nor allude to what any such variation might signify. Equally, like Hertz, he treats light as a phenomenon which requires a substantive ether for it transmission but, unlike Hertz, without considering its possible electromagnetic character - something only later confirmed - by Hertz ca 1887/8.
Because of the great difference in the speeds of the Earth and light - as represented by the ratio b at 1/10,000 described earlier - the sought after effect was known to be of a very small order - probably nearer the level of b . The technique and instrument used would thus have to be precise enough to find this - ie over and above errors of measurement. Michelson's interferometer was thought to be such an instrument. Following Maxwell's recent suggestions, Michelson's technique relied on measuring the difference in times taken for a beam of light to travel back and forth between a source and a mirror over the distance d of two arms of his apparatus set at 90 degrees (one being parallel to the Earth's motion) - and noting any difference in time as being due to that motion through the assumed still ether (and light's medium) effectively serving as an opposing force (like a 'wind' experienced when putting one's head out the window of a fast moving car on an otherwise still day). If compared to the value it would be if the Earth was actually at rest relative to that ether (ie if both were moving in tandem or both were absolutely stationary), the difference is only of the second order in b. This time is shown by t = d{1/c=v = 1/c-v} = 2dc/c2=v2. This can also be written as t = 2d/c x 1/1-b2. If this time could be so accurately measured that the fraction 1/1-b2 could be distinguished from 1/1 - ie from 1, it would be possible to prove (or support) the existence of the still ether - through which the Earth moves - thus giving instruments attached to it a sense of being subjected in effect to that opposing ether wind moving at about 10,000 kms an hour.
However, there is no way to directly measure speeds of light and such minute second order differences. Rather it was necessary to take advantage of the very slight discrepancies in over-lapping light waves which can augment or neutralise (ie interfere with) themselves depending on their times of arrival at a common receiver. This technique (as mentioned above) entailed a comparison between light sent on paths along the interferometer's arms that were (a) parallel to the Earth's motion and (b) of the same distance but perpendicular to this. [I believe that account must be taken for the longer zig-zag path of the light sent initially at 90 degrees to the Earth but received back at its source at an angle slightly less than this (for each round trip).]
181. The difference between the two times is equal to 2d/c {1/1-b2 - 1/sq root of 1-b2}. The terms in the brackets may be written as 1+ b and 1+b2/2, respectively, if we ignore values of b4 which occur when such near equivalents are obtained by necessary algebraic re-arrangements. The difference in times then approximates (extremely closely) d/c x b2. This means that the retardation of the light that would be expected by any 'ether wind' present (representing in fact the existence of the assumed stationary ether) would be of a magnitude of second order. By turning the interferometer through 90 degrees, the interference fringes obtained are displaced in the opposite direction thus doubling the perceivable difference - to 2 x d/c x b2. When account is taken of slight differences in path lengths and of the wave lengths of the light used, the crucial ratio becomes 2db2 over the wave length. This is a measure of the extent of displacement of the interference fringes from their distance apart before the apparatus is turned 90 degrees to that after the turn. It should amount to over one third (ie 0.37) of that original distance. Michelson was confidant that the apparatus could discern as little as one hundreth of that distance (ie just 0.01) - well within the minute second order effect sought.
However, the results obtained were negative; there was no significant effect on the speed of light due to the hypothesised still ether acting as an opposing 'wind' moving effectively at the velocity of the Earth. The velocity of light was apparently quite unaffected. Moreover, the explanation of the phenomenon of aberration which assumed a still ether was also not supported.
182. Apparently, Michelson initially concluded that therefore the surrounding ether must move with the Earth in its orbit - as Stokes had suggested - and that Fresnel's view of a still or even relatively still ether to explain aberration or as an influence to vary the velocity of light as Maxwell apparently assumed - was not supported. So Michelson reviewed earlier tests of this hypothesis - in particular that of Fizeau (1851; 1859). He decided to repeat that latter test, with certain improvements, and reported his results in 1886. In this paper, Michelson begins by noting that '..the only work of any consequence on the influence of the motion (or otherwise) of the ether..on the velocity of light - is the experiment of Fizeau'. This was first reported in 1851 in the J.pr.Ch.,1,319 (Rammelsberg; Mineral Chemie) and, possibly more fully, in 1859, in Ann.de Ch. et de Ph., III, lvii, p 385. He had found that light moved through rapidly moving water (in its direction) with only a slight increase in it speed (depending on the index of refraction of that transparent medium); in moving air, it didn't increase at all. These results agreed with those calculated theoretically by Fresnel previously and most satisfactorily demonstrated by Eisenlohr (Verdet: Conference de Physique, ii, 687, ?year). Fresnel concluded that the ether in a moving body (as water) remained essentially still except for a small portion which may surround the molecules of water as a small condensed atmosphere of the (?assumedly) much more minute ether 'particles'. Michelson suggests therefore that the bulk of "..the ether is entirely unaffected by the motion of the matter which it permeates"; that is, that it is essentially stationary, as assumed in his 1881 study - which had sought further confirmation of this.
182b. But previously, to confirm his findings, Fizeau had developed, with ingenuity said Michelson, a most remarkable contrivance which relied on an examination of any displacement of interference fringes due to the effect (if any) on the speed of light in the paths of the light compared. Despite this ingenuity and precision, there was apparently some doubt later expressed about the Fresnel-supporting results obtained (ie of a still ether) and/or in their interpretation. [Note: some years later Einstein would quote Fizeau's work - as interpreted by himself - to support his analysis of 'the problem with light' (as later recognised) which led him (independently from the line of investigation and analysis following on from Michelson's experiments) to his theory of relativity - as discussed more fully below.] Thus, Michelson mentions these experimental problems, some supportive, some perplexing - 'together with the fundamental importance of the work', as justificatio for a repetition of his own 1881 study. He might have mentioned also the fact that his own earlier test of the still ether had not found the result he expected and he may have wanted some other supporting evidence before he tried again - but with an improved method - to yet obtain that result. For his replication of Fizeau's experiment had utilised improved methodology. His results fully supported Fizeau's and in his conclusion he states: "the luminiferous ether is entirely unaffected by the motion of the matter which it permeates" - be it air or water. It thus appeared to him that light must moves through a stationary, unaffected ether with its usual velocity.
One can imagine that Michelson, having obtaining his confirmation of Fizeau, would conclude that if the ether didn't move with moving bodies of matter (as eg with the Earth or flowing water) but invariably remained still, then the velocity of light travelling through it from a source attached to the moving Earth (so that the ether served in effect as an opposing 'wind') should indeed be affected (ie slowed) after all. But why, he asked himself, had he not found it so in 1881 therefore ?
182c. Because of this confirmation of Fizeau and Fresnel and because of one or two criticisms of his 1881 study, Michelson did indeed decide to repeat the latter experiment - but with improved methods. If the otherwise still ether could in effect be made to move (as if it were a wind), surely the (paradoxical) still ether actually underlying this would serve to slow the velocity of light - as a reflection of that basic condition of the ether. This 'ultimate' test of Fresnel and Fizeau took place in 1887. While Maxwell had died before any of Michelson experiments of the 1880s, he would likely have found any such confirmation of the still ether useful as the assumed non-elastic medium for his electromagnetic conception of light (something, as mentioned, not addressed by Michelson), although what Maxwell would have made of its seeming effects on its velocity we can only surmise. Equally, we cannot say whether either would find it of any relevance with respect to the matter of the assumed fixed reference system (comparable to absolute space) - as a means of confirming the ultimate basis of Newton's mechanics generally - with its classical (Galileian principle of relativity - and any absolutivity vs relativity implications. Apparently this was not then (in the 1870/80s) a particular focus of attention; Michelson's very thesis implied a belief that light (as everything else) would move at its usual speed relative to its immediate or relevant frame of reference but could be slower or faster relative to observations from other frames depending on the speed of that frame where the light was sourced. But, paradoxically, any negative finding by Michelson might well stimulate explanations which could bring those absolutist considerations back into the fore.
183a. In his 1887 paper with Edward Morley entitled 'On the Relative Motion of the Earth and the Luminiferous Ether' (Amer J Science XXXIV, 203 p 333-345), Michelson begins by pointing out that while the emission theory of light failed to account for aberration, the wave theory (which initially appeared to fully account for it) also had a problem after Airy (1871) found that the extent of the aberration didn't as expected increase by about a third when it was measured by means of a telescope filled with water - which slows light's velocity (from that as measured in a vacuum) by about this proportion. But Fresnel's theory and Fizeau's results appear to account for this unchanged aberration by virtue of the partial (if slight) motion of the ether in moving water. According to Fresnel, stated Michelson & Morley, the ether in the wave theory of light is assumed to be stationary relative to the moving Earth (relative to the Sun) - described here as his 1st hypothesis - except in moving transparent media when it moves slightly - but with a velocity much less than the velocity of that media, according to the latters' indices of refraction (the 2nd hypothesis). Thus, it barely moves at all in moving (or still) air and moves to a slight extent only (eg about 10%?) in moving water.
183b. These two hypotheses, say the authors, "give a complete and satisfactory explanation of aberration. The 2nd one must be considered fully proved by the celebrated experiments of Fizeau (1851; 1853 and 1859) and by the ample confirmation of those in our own study (of 1886)". It is thus the 1st hypothesis that is the subject of the present paper. They quote Lorentz (in French) who said (earlier in 1886) that we mustn't accept one hypothesis or the other (about the ether) merely by their apparent probability or simplicity but by establishing by actual experience (ie experiment) "de repos ou de mouvement dans lequel se trouve l'ether a la surface terrestre" ie their relative movement. As in the 1881 study, any variation in the velocity of light will be used to establish that the ether is either 'at rest' at the surface of the moving Earth and thus can effectively act as an opposing 'wind' (eg to any instruments attached to the Earth) as the Earth moves through it, or otherwise. We may note that this basis of establishing his results utilises the possibility of a variation in the speed of light that is at variance with (later) assumptions by Einstein and others that the speed of light was indeed the true constant that Maxwell's equations seem to have implied (even if not fully appreciated then by most and possibly not even by Maxwell himself, nor by Lorentz or Michelson seemingly - with their shared belief in the role of an ether in light's propagation and in its speed, if it offered any opposition.
184. But after the 1881 study, someone (M.A. Poitier of Paris) had pointed out to Michelson that he had overlooked a possible effect of the motion of the Earth through the ether on the path of the rays that traveled at right angles to this motion. Lorentz took up this aspect also which, with Michelson's 1881 experiment generally, was the subject of a searching analysis by Lorentz (1886). This included the view that the overlooked effect should by no means be disregarded. Had it been considered, the difference sought would likely have been twice as large and hence would have exceeded any experimental errors more clearly.
However, despite a more sophisticated methodology used by Micheslson in 1887 (with Morley), the expected evidence to indicate that the velocity of light varied according to the relative motion of a fixed ether (ie that the ether around the Earth was at rest relative to its motion) was again not forthcoming. The difficulty first pointed out by Maxwell (regarding light having to re-trace its path) seems to be have been a major problem. Michelson suggested methods by which this may yet be overcome - apparently still convinced that the ether (a) did exist and (b) that it was, as Fresnel proclaimed, at rest relative to the Earth (and, one might add, that it had a role in the propagation of light the consequent velocity of which under the arrangements applied should have been affected).
Thus, the measurement of light's speed had remained stubbornly constant whatever the circumstances. But the latter attribute per se was apparently still not the focus of attention as to the basis of the failure - ie by any suggestion that it was somehow a true constant and did not therefore obey the usual, if implied, principle of relativity. If any consequences of that as yet unmentioned explanation might prove awkward for the long held mechanical model of nature, they weren't then proferred by Michelson as the basis for maintaining his faith in one day finding the still ether. Nor was it mentioned by such as Lorentz or Poincare at that point.
185. In 1889, two years after Michelson's 2nd paper on seeking the elusive still ether (with its suspected influence on the velocity of light), the highly respected professor of physics in Dublin - George Fitzgerald - suggested a possible explanation which, again, didn't question light's capacity to vary in velocity (within any given transparent medium - as a vacuum or air, say). Fitzgerald sent off his suggestion to Science magazine in America that year but later reported that he was not aware if it in fact had ever been published. However, it was known that he discussd it on various occasions with his students in lectures in Dublin (ca 1890-92) and, in America, Lodge made reference to it (probably having noted it in Science where it had indeed been published) in an article entitled 'Aberration Problems' later published in Phil. Trans. R.S., 184 A, 1893. At about that same time (1893), Lorentz suggested a very similar explanation himself (apparently independently) which he too had reported - in Zittingsverslagen de Akad v. Wer te Amsterdam (1892-93), p 74).
In both cases, the effect of such an explanation, if valid, would be to resurrect (or continue) Fresnel's and Fizeau's conception of light's propagation by means of a still ether medium and one influence on its velocity. During the later 1890s, this explanation, integrated within a developing electron theory by Lorentz, represented a continuation of the fundamental ideas about light of Fresnel, through Maxwell (but now as an electromagnetic disturbance) and Michelson to Lorentz and Poincare. In this, the classical principle of relativity (recalled by Poincare in about 1900) was effectively maintained and with it a role for a still, substantive ether, a flexible velocity for light (seemingly) and the maintenance of the mechanical model as the ultimate explanation of nature. We may conveniently think of this orientation as 'the traditional line of enquiry' which continued to be pursued until at least 1910, I believe.
Meanwhile, around 1896, apparently with no knowledge about Michelson's results in the 1880s, nor Lorentz's explanations of same, Einstein (still a teenager) began considering aspects of Maxwell's original ideas (and the studies of Fizeau) and, without knowing that others were concerned with similar topics, realised on his own that something didn't quite make sense. Eventually, he sorted out the difficulty (by focusing on the actual (but over-looked) constancy of the velocity of light) and, having done so, would have predicted that an experiment such as Michelson's (of which he eventually heard) should have had its particular negative result - but not because of any belief in the moving ether of Stokes, nor for the post-hoc reasons later suggested by Fitzgerald and Lorentz, and pursued by others during the 1890s. For these (despite being very close) would fail in the end as they were based on a false premise (of the ether). Rather, such a result was eventually explained by Einstein by a similar but crucially different reason - one which didn't so fail. We might describe this as 'the radical line of enquiry' which ran in parallel with the traditional one latterly although not in the public domain until 1905-10. (One would like to know exactly when it began? Probably around 1903.)
186. In his excellent text on these matters, Born describes the foregoing situation thus (paraphrased): 'The ether has been treated as a substance (a body) that obeyed the laws of mechanics. As such, the classical principle of relativity should hold for it. From this it follows that the velocity of light must appear different in different inertial systems so that its different velocities would reflect (and be explained by) any variations in the motion of this substantive medium as the Earth moved through it in the direction of such measured light or in the opposite direction. But, all tests of this type have led to negative results. The velocity of light appears to be independent of the relative motion of the (celestial) body on which the observations are carried out - ie vis a vis the supposedly still ether. (See also parag 75 (11) where this is touched on similarly). There were, according to Born, two possible explanations or points of view concerning this matter:
1. The negative results were due to some secondary, half-accidental causes that neutralised the small finding sought by virtue of some kind of mutually-compensating actions operating in opposite directions. Hypotheses about these actions were helped by the fact that belief in the role of the ether continued, especially as regards the degree or not of its motion. At the lower level of accuracy (1st order), Fresnel's theory could account for much of light's behaviour in terms of his partial convection theory of ether. That is, light's apparent constancy of motion could be denied. A sufficiently accurate method of terrestrial measurement of light's velocity allowing precision beyond 2nd order quantities (or equally accurate measurements made using the eclipses of the satellites of Jupiter), if ever perfected, would however show Fresnel's ether theory to be unsupported. Lorentz sought to overcome this setback by sticking to the traditional methods of mechanics - albeit with some necessary and awkward post hoc adjustments. Or...
2. In this second explanation, a fundamentally new assumption would have to be made - that light somehow behaved differently from all other material bodies - as far as measurement of its velocity was concerned. If measurements of light are deemed sufficiently accurate (and such as the above nil results apply), this point of view seems inescapable (rather than seeking mutually neutralising causes relating to the nature or motion of the assumed ether). It was this more radical path that was eventually pursued by Einstein - which he found (in the style of Hertz) benefited from avoiding all speculations about the nature of light or its means of propagation - whether via ether or otherwise. But, however it acted, it didn't appear to operate through the usual mechanics. However, as pointed out elsewhere, Einstein didn't adopt this route of enquiry simply to explain Michelson's result (of which he was then apparently unaware). Rather, there must have been other comparable experiments in which the velocity of light similarly 'did not vary when it was expected to' which comparably motivated his attention. [Fizeau's studies and Bradley's aberration findings were probably rlevant here.] Otherwise, his main motivation appears to have been the conflict in his own mind concerning the contrary predictions that Newton's mechanics and Maxwell's electrodynamics (with the constancy of light's velocity inherent therein) would imply in regard to his imagined experiment of travelling beside a light wave at its speed. Would it appear 'frozen' or not? And, was there really an ether, or not ?
187. Before considering Lorentz's earlier line of enquiry - which was in response to Michelson - (or the relatively independent approach of Einstein later), we may first describe the work of Hertz - who was also active in the 1880s, about the same time as Michelson. [His ideas, combined with the concurrent work of Michelson and later correspondence with Poincare, likely fed into Lorentz's more traditional lines of enquiry and eventual theory.] Following the prediction that light was an electromagnetic process of vibration, it was concluded by Maxwell that its carrier was identical with the (non-elastic) medium that transmits electric and magnetic forces. The ether as this carrier was thereby given additional support. It also, said Born, 'came to be identified with' the traditional Newtonian space of mechanics - assumed to be absolutely 'at rest'. It would seem that Born was referring to the influential ideas advanced by Lorentz in this regard - from about 1892. But, before this, we may consider the views of Hertz in the late 1880s:
188. While Lorentz soon became aware of Michelson's studies as performed and reported in America in the 1880s, neither Hertz seemingly nor, later, Einstein had. Hertz became intrigued by Maxwell's theoretical conclusions about the relationship between electric and magnetic phenomena (ie their respective forces) and the waves they were predicted to initiate in the right circumstances which travelled at the same speed as light. Maxwell felt that light and similar wave phenomena were the very same thing as these predicted electromagnetic waves and that they travelled by means of an identical (non-elastic) medium - the ether. From about 1875, several mechanistic theories of the new electromagnetic ether were put forward, including that by Maxwell himself (1878). The latter's had similarities to MacCullagh's - with magnetic forces having a rotational character in relation to the more linear nature of the electric field. William Thomson and Bjerkes also contributed useful ideas in this sphere.
But, following Helmholtz, Heinrich Hertz in particular eventually and deliberately turned away from all such mechanistic speculations. He simply accepted that all bodies (with their assumed internal ether) and free ether itself (considered a substantive body) - can have a state of rest disturbed both electrically and magnetically by various arrangements of perceivable bodies (vibrating charges) and that we simply do not know the nature or form of these disturbed internal states of the ether - be they mechanical or whatever. We can only know the observable phenomena before and after any such applied arrangements. The microscopic nature of such things seemed to operate by different laws (ie new 'electromagnetic' ones possibly) which may only reveal themselves in time. Whether it was still 'mechanistic' or something else seems to have been left an open question (ca 1885-95) by Hertz but possibly some new thinking was thus stimulated. Hertz's attitude thus served an important bridge between mechanics and an eventual electrodynamics but, in the meantime, he apparently kept a foot in both camps. Einstein later pointed out that nevertheless the awkward dualism in science continued with Hertz's belief in a substantive ether medium for light (whether still or, as he believed, with Stokes, moving) even after he had confirmed that Maxwell's prediction was correct when in 1888 he reported on having produced light as a consequence of the interaction of electric and magnetic forces. That is, importantly, he confirmed Maxwell's ideas that light was an electromagnetic wave.
189. Thus, as conceived by Hertz, the apparent carrier of such electro-magnetic waves was still the ether whose state/condition/constitution (whatever it was) was sufficiently described in terms of two perpendicularly-directed magnitudes (ie vectors) - the electric and magnetic strengths of Maxwell's perpendicular 'fields' - 'E' and 'H'. Inter-dependent changes of these across space and time (ie by moving 'bodies') could be validly interpreted in terms of Maxwell's field equations (whatever was 'actually' going on). This contrasted with light when thought to be transmitted via the former elastic ether in which such a 'strength' parameter was apparently not relevant. The effects of these changes should then be observed by means of various mechanical, thermal and chemical activity in macroscopic matter. The place where these effects occur in the ether carrier was increasingly called 'the field'. For a time (the 1890s), the two terms appeared to be inter-changeable. Whatever the exact nature of the assumed ether carrier of electromagnetic waves, including light, the question of how the velocity of same may be affected by the relative movements of the various 'bodies' of relevance to light - as its source, target or that 'new' but still substantive medium itself, was still an important consideration. Did light still obey the principle of relativity ('still' in the sense that it had always been assumed to so obey)? That is, what were light's mechanics - over time and space - in regard to its frequency, velocity and direction? Many of the conclusions reached in the earlier analyses appeared at least to have remained valid in this comparable area of 'the electromagnetics of moving bodies' - ie in terms of these three geo-dynamic characteristics of light - now seen as an electromagnetic process occurring in a substantive electromagnetic ether 'field'. But did they? And did any of those then interested in this area actually ask such questions, especially in respect of the principle of relativity per se, or are these simply retrospective, rhetorical questions posed by those (eg Born) many years later when trying to analyse the thinking, rather than actual publications, of the time?
190. Prior to the emergence of the electromagnetic theory of light, the principle of relativity as it pertained to optics appears to have been sufficiently valid and acceptable - within the limits of the order of measurement accuracy (in b = v/c) then possible (assuming again that it was being so considered at the time). That principle, if so considered, would imply that 'optical events depend only on the relative movement of those 'bodies' that emit, transmit and receive the light. In a system of reference moving with constant velocity relative to the apparently stationary ether (the latter being one of these 'bodies'), all optical events therein would occur as though it were at rest. There was seemingly therefore no recognition that the motion of the relevant frame of reference did not affect the speed of light, nor that distance and time measures were in any way affected. The same measures were thus used to calculate the varying speeds of light. It would be assumed that as an electromagnetic phenomenon light would still function in accord with such accepted mechanical rules to which the principle of relativity would apply even if, as Hertz stressed, we don't know exactly how any medium concerned may operate at its level. [Note: this paragraph seems to imply that the principle of relativity would be (or may have been) a consideration - ie by Hertz - around 1888-92, as though the appreciation of its role in mechanics from the time of Galileo and of Newton, and through the 1800s, was an unbroken one upto and beyond 1887. However, it is usually stated that it was only Poincare who 'recalled' its long-dormant relevence - from ca 1892. In 1904, he further formalised its application to the concerns which Lorentz and Einstein were then addressing aound. ]
191. As mentioned earlier, two theories had been proposed to account for the apparent and (effectively accepted) relativist position in respect of light's transmission in the elastic ether (the optics of moving bodies) - even if it wasn't yet discussed in these terms. That of Stokes (ca 1850) assumed that the luminiferous ether inside matter (including planets) was carried along with them - completely, whereas Fresnel (1840s) assumed that such 'conveying' of the ether was only slight at most and more generally was independent and 'at rest' - eg in outer space. The latter idea seemed to agree better with most experimental findings pertaining to the behaviour of light treated as a wave within a presumed elastic ether. When later applied to the electromagnetic theory, the same two stances were thus further considered. Do observations of electromagnetic phenomena (which includes light) - arising now instead from relevant arrangements of electric and magnetic apparatus and the fields so arising - provide more support for one or other of these two hypotheses? Hertz concluded that the Stokes theory of total ether conveyance (despite some difficulties when applied to earlier conceptions of light's medium) had an attractive simplicity to which his own ideas of the new electromagnetic phenomena - as per Maxwell's field equations - could be the more validly applied. This would seem to require acceptance that it was the fields themselves (as the new ether) that had to move along within the bodies concerned - as with moving train or rocket ship examples in which the internal air moves with those vehicles, or with the Earth in its orbit.
192. Particularly with respect to the behaviour of the induction of electric and magnetic fields by the action of moving conductors, Hertz's ideas supported Stokes' version of the applicability of the relativity principle - ie to Maxwell's electro-magnetic phenomena. However, when tested in terms of moving insulators, they were not so confirmed. Partly in response to this failure, Hendrik Lorentz would seek instead to apply Fresnel's ideas to the new electromagnetic phenomena - to see if such a partial convection approach might prove to account better for the relativist position regarding those major dimensions of light - viz its velocity, frequency and direction - in respect of its assumed ether-like field carrier. But, because Hertz's investigations (especially that of 1888) provide insights into the behaviour of electro-magnetic phenomena and certain conclusions to which later researchers like Lorentz and Einstein addressed themselves as they attempted to resolve similar issues, it is useful to detail his work - even where it failed. [It also allows us to become more familiar with the manipulation of the variables involved in Maxwell's equations. We may also consider Einstein's later focus on the false asymmetry generally accepted as between the effects of moving magnets and conductors.] This (on Hertz) follows below, before a similar account of Lorentz's variation of Fresnel's solution (incorporating his adjustments to account for Michelson's results) - eventually in terms of a relativist point of view. Finally, Einstein addressed the same underlying difficulties. [But, again, I'm uncertain if those workers before Einstein elaborated their positions with any regard to the principle of relativity directly at the time. One will also want to consider the very relevant ideas of Poincare at this aame period.]
193. Hertz's theory (following on from Maxwell) may be examined in terms of the four categories: Conductors and insulators moving, respectively, within electric and magnetic fields. Thus, when a conductor is placed in an electric field, it acquires charges on its surface which remain with it if that conductor is moved in that field - and are thus displaced relative to its assumed ether. Biot and Savart's law says that such moving charges, which should constitute a current, should produce a surrounding magnetic field. Such a field should be of the same strength as one produced by an actual current of the same magnitude flowing through that conductor when at rest. Maxwell's laws can be applied to predict the exact quantitative values concerned. The predicted values were confirmed in Helmholtz's laboratory by Rowland in 1875. This somehow supported Stokes' (and Hertz's) contention of a completely mobile ether-like field within the displaced conductor. To Hertz, one of the 'moving bodies' in his 'electromagnetics of moving bodies' (in contrast to Einstein's later elaborations) was thus the substantive ether-like field. Hence, any adjusted principle of relativity' that it might support would still be one with an assumed mechanical basis. [See Einstein (1920).]
194. If the conductor is moved instead within a magnetic field, an electric field is induced within it - which provokes a flow of electric current therein (as discovered by Faraday). Again, the strength of this current should prove to be the same as that which occurs in a conductor subject to a comparable electric field associated with an electromotive force between oppositely-charged bodies. This too has been amply confirmed - by the many electric applications of the induction law whereby energy of motion is transformed into electromagnetic energy. In this case, Faraday's own laws and equations concerning cutting his lines of force (later adapted by Maxwell) provide the quantitative analysis. We may again assume that this is consistent with the idea of a completely moving ether within the bodies concerned. [Does Einstein's comment regarding the asymmetry of this and its converse process apply here ?]
195. If between two plates of a condenser a disc of a non-conducting material is placed, an electric field will arise within it when the condenser is charged. This is associated with a displacement of charge within the non-conductor which produces a surface of charges of opposite polarity next to those of the condenser's plates which is proportional to the extent of that displacement (due to the induced field). As described earlier, such displacement is considered to have two components: that due to a displacement or re-arrangement of charge within the molecules of the matter of the insulator and that due to a comparable displacement within the assumed ether therein. If the disc is now moved parallel to the plates then, according to the Stokes-Hertz model, the ether-like field within the insulator should move along with it completely, as should the opposite charges on its two surfaces. The latter should therefore induce magnetic fields in their vicinities. Rontgen showed (1885) that a magnetic needle was deflected towards such a predicted field. However, the deflection was much weaker than predicted by Hertz's theory. Only the surface charge density expected from the displacement accounted for by the insulator matter alone was apparently available (moving with the latter) with which to induce a magnetic field. No ether appears to have moved with the insulator. (Is there no comparable displacement in a vacuum?)
196. If a (non-magnetizable) insulator material is placed instead between the poles of a magnet and moved in one direction, any charges arising on its metal-coated lateral sides may be ascertained with the aid of sliding contacts connected to an electrometer. This is analogous to the movement of the conductor in a magnetic field described above. In this case, an electric field is induced across the insulator (between the superficial metal side-plates) which should show surface densities of opposite charges - which would cause a deflection of the electrometer needle. This experiment was carried out by Wilson in 1905. As with Rontgen, it produced a weak deflection only due entirely to the effect of the moving matter of the insulator - and not to any moving ether allegedly therein. The Stokes-Hertz theory failed.
197. In all four cases tested by Hertz, the only motion which shows any measurable effects is that of the field-producing bodies - relative to the conductor or insulator investigated. Instead of moving these, they could have been held motionless and the rest of the apparatus moved in the opposite directions; the results would have been identical. For Hertz's theory recognises only relative motion of the bodies concerned - the ether being reckoned as one such movable body. And where any system moves with a constant velocity, everything happens, according to Hertz and the original principle of relativity, as if it were at rest. That is, the classical principle of relativity holds in Hertz's theory of electromagnetic activity just as it was assumed to hold by those who had applied it in earlier optical (elastic ether) interpretations. It would therefore predict that light's speed should indeed vary (under appropriate circumstances) and if any test did not support this, a reason would be sought to explain it. But, if its constancy is admitted, then the requirements of the principle of relativity as applied to electromagnetic phenomena are not met and it would need to be re-stated in terms of a more complete relativity principle - one without its former absolutist under-pinnings/assumptions - whose requirements only then could be met.
198. Einstein (1920) later pointed out (as mentioned above) that the awkward dualism of the mechanical and electromagnetic interpretations of the transmission of light "still confronted science within Hertz's theory - where matter appears not only as a bearer of motion, velocities, energy and mechanical pressure but also - in the form of a substantive ether - as a moving bearer of electromagnetic fields. Matter (including ether) is thus treated as having both mechanical and electromagnetic states - with both moving together. But this was at variance with, for example, Bradley's and Fizeau's earlier findings (and of Michelson's 1886 repetition of the latter). Hertz's version of an 'electromagnetic principle of relativity' - in its original form (in what year was this published vis a vis Poincare's earliest reference to that principle?) - was thus inconsistent with the experimental evidence. How was this to be resolved? It was attempted by Lorentz - who would also seek to build on Maxwell's ideas, but more in line with Fresnel regarding the essential immobility of the ether - after making due allowance for Michelson's 'unexpected' results of 1881 and 1887 (seemingly not an influence on Hertz however). [NB Did Hertz formulate his ideas in terms of such a principle at the time or is this Born's much later interpretation of what, in effect, he was doing??]
199. Two years after Michelson's 2nd failed attempt to verify the still ether, George Fitzgerald, the professor of physics at Dublin, proffered a different explanation (as touched on above) - ie in 1889. This was not that the ether moved with the Earth (as Stokes suggested) but that the arm of the interferometer pointing in the direction of the Earth's motion (vs when it was at 90 degrees to same) had contracted by a minute amount that exactly accounted for the lack of measured effect on the speed of light that would have supported the concept of an opposing fixed ether (and seemingly a variation in the speed of light upon which this apparently relied). If it was yet a consideration, the requirements of the principle of relativity would presumably be met by light thereby - as an electromagnetic wave in such a fixed ether field. [NB. This was one of those 'post hoc hypotheses' alluded to by Born which introduced a compensating effect which, rather conveniently, neutralises the unexpected effect that had actually occurred and so was masked.] As such, light's speed should vary according to the presence or not of that fixed ether resistance when its source moves through it. The moving source of the light (ie the Earth) should result in an increased speed of the light and the opposing ether should have the opposite effect with a net result which verified the still ether and an expected altered velocity of light (now allegedly masked by that contraction; or was it only ether's behaviour that was so masked ? ).
199b. As also mentioned above, Lorentz came up (in about 1893) with a very similar idea to that of Fitzgerald (independently). The basis of the interferometer contraction had been initially described by Fitzgerald in terms of physical pressure due to the ether's resistance on the gross parallel dimensions of the arm. Lorentz too believed such a contraction occurred (if not, in his later elaborations on this, in such a direct physical manner) but initially could give no clearer explanation; it was almost, said one critic, as though it was simply 'an act of God'. But, by 1895, he gave a more considered explanation (described below) - within the context of his then new electron theory based on the ideas of Maxwell. But this had also to address another problem - as revealed within Hertz's equally recent views. This is described first. As Michelson's results were published (1887) in an American journal, it is possible that Hertz was not made aware of it before advancing his Stokes-based theory (ca 1888-90) - later adapted by Lorentz (who was aware of Michelson) - but in terms rather of Fresnel's ideas of a fixed ether. In any case, all these adjustments sought to maintain the primacy of the traditional mechanical model as this was still the only accepted logic of physical science. Otherwise, such phenomena would have to remain unexplained in mechanical terms and this was generally unacceptable (before Einstein realised it was necessary to be more radical and 'break that classical mechanical mold'). But with what?
200. We may recall that in the four cases tested by Hertz, the only motion which showed any measurable effects was that of the field-producing bodies - relative to the conductor or insulator investigated. Instead of moving these, they could have been held motionless and the rest of the apparatus moved in the opposite directions; the results would have been identical. For Hertz's theory recognised only relative motion of the bodies concerned - the ether being reckoned as one such movable body. And where any system moves with a constant velocity, everything happens, according to Hertz, as if it were at rest. As mentioned, the usual principle of relativity holds in Hertz's theory of electromagnetic theory but this was inconsistent with the experimental evidence. How was this to be resolved? [Note: This latter reference to the principle of relativity appears to be more convincing than the previous ones and may well suggest that they were also the case at the time!?]
201. Attempts to resolve both difficulties (arising in the works of Hertz and of Michelson) were then advanced by Lorentz (from 1893 and 1895). He tackled Hertz's difficulties by adapting Fresnel's partial ether movement theory. He did so by taking exactly the opposite point of view to Stokes and Hertz with regard to their preference in the relativity-absolutivity debate - suggesting that 'the ether is at rest in absolute space'. If he too addressed the problem as one concerned with the electromagnetics of moving bodies, the ether at least was not now to be one of these moving or movable bodies - even partially it seems. Only the (other) bodies moved - in and through it. But, it was still there - as a body - if now unmoving (as per Fizeau's results). This allowed a mechanical analysis to be thought still appropriate. The role of the ether in Lorentz's theory apparently followed from his conception of the material basis of the electric current. Following the reasoning of Helmholtz that Faraday's laws of electrolysis were intelligible only if the electric charge was conceived not as a continuous 'fluid' but as discrete or indivisible entities, Lorentz proposed that such entities - now called 'electrons and protons' (after their verification by Thomson and Lenard; see below) - were now seen as the determining factors in all electromagnetic phenomena.
201b. As Einstein expressed it, " Lorentz addressed the difficulty left by Hertz (and the dualism problem therein) by taking away from the ether (most of) its mechanical qualities (only its 'immobility' remaining) and leaving it as the seat of the electromagnetic field - and away from matter (most of) its electromagnetic qualities (only its carriage of electric charge remaining). By this means, he was able to bring theory into better harmony with reality and reduce all electromagnetic phenomena to Maxwell's field equations (ie as in free space) - but still retaining a suspect immobility element of light's medium (and that medium's existance in any case), as well as potentially suspect hypotheses which kept the behaviour of light within the mechanical model with that still ether. [Poincare was to accept most of this as well, but added that a way was now needed - a 'new mechanics' (but still mechanics) - by which the principle of relativity, as he then re-stated it, could be more fully interpreted or 'explained'. [Had the others actually used this relativity concept prior to this?] This would have to be compatible with the findings of Michelson - as accounted for by Lorentz - ie with its ultimately substantive, electromagnetically active ether but also with some suspect constants added to deal with certain awkwardness in the quantitaive analysis of the elements of velocity - ie distance and, especially, time (for which, unlike distance, Lorentz still had no plausible explanation). All laws should fall within this better explained principle of relativity, said Poincare - as they were always assumed to do. He appears to have been so very near to a final solution by about 1904. Maybe it was just a matter of wording...or was there still some crucial difference in substance here? What were his views then on the constancy or otherwise of the speed of light, and on the ether?? Did light's speed fall within his concept of "all laws" ? Could its velocity be boosted by a fast source - vis a vis an observer on a another reference frame ? Would the correct solution have to fall somewhere beyond mechanics? One suspects that Poincare realised that some other explanation was indeed needed to account more realistically for the alterations in space and time that Lorentz's equations were based on. [He would not have to wait very long for such an explantion; it would be available by the autumn of 1905.]
202. Lorentz's analysis further developed in conjunction with his new electron theory. The growing understanding of the nature of the simplest atom of matter - that of hydrogen - was due mostly to the work of Sir J.J. Thomson and P.L. Lenard on cathode rays. These were concluded to be a stream of negative electric charge - now called electrons - which had a mass about 1/1800 of that of the hydrogen nucleus - the proton - in which resided an immobile 'positive' charge of similar value to that of the negative charge held on a single electron - but of opposite sign. Elements of more complex atomic structure had more protons and electrons - generally balanced to be electrically neutral. They also contain some electrically neutral particles called neutrons to make up the weight. While the negatively-charged electrons were often free to move, positive charge always remained within the proton. In poor conductors, the electrons are more tightly bound to the protons of that material and while not easily freed, they could be slightly 'displaced' within the orbit of their atom so as to constitute a 'dipole' structure. But in good conductors such as copper, the electrons moved about more freely - sometimes colliding with their atomic protons and neutrons. In electrolyte liquids and in conducting gases some of the constituent atoms may have a slight excess or deficit of electrons and are thus able to move under the influence of varying electric fields - as ions - carrying both electric charge and associated matter (as proton and neutron mass) with them. Electrons have some mass which moves similarly with their associated negative charge.
203. When the electrons in certain materials - mostly metals such as copper, iron, cobalt and nickel - are free to move and do so in closed orbits which constitute 'molecular currents', a magnetic field is set up thereby and the material as a whole can act as a magnet. Similarly, when the electrons in a conductor such as copper are relatively free to move about, they will contribute to a flow of current if that conductor is placed appropriately within an electric field. - as created between centres of oppositely-charged material. In either case, the electron theory of Lorentz accepts that such electrons (or their negative charge?) and their counterpart positive charges in protons exist within a stationary 'sea' of the new electromagnetic ether (or field) which occupies all space - even within and between the electrons, protons and neutrons of all matter. Their behaviour therein transpires in accordance with Maxwell's equations concerning the electromagnetic forces so engendered. But as this all-encompassing environment, while not an absolute vacuum (since it is filled with the ether-like 'field), still requires values of 'e' and 'u' set to = 1 and an 'electron convection current' 'p'v which replaces the density of the conduction current in the 4 equations. These now become as per Lorentz:
and obey the laws of Coulomb, Biot and Savart, and Faraday in the usual way. From this, it follows that: 'all electromagnetic events consist fundamentally of the motions of electrons and the force fields associated with (?accounting for) them'. Moreover, in Lorentz's theory, all matter, and its properties, also depend on these same motions of electrons - with respect to their associated atoms. Such matter will thus have a conductivity (s), a dielectric constant e and a permeablity m, such that Maxwell's original equations should be derivable from the above more fundamental laws for the individual electron and proton. Lorentz showed this derivation was possible - giving Maxwell's laws in the simplest case and accounting for many physical facts that were previously inexplicable in the areas of optics, colour dispersion, magnetic rotation of the plane of polarization and other interactions between light and electric and magnetic fields. [Einstein would later show that all these explanations and others were better accounted for within the sphere of relativity - but without the need for a concept of the ether.]
204. But our main question here stll concerns the part that the alleged ether may play in this conception of matter and force. While the electrons and protons are in motion, is the background field in which they so move (the state of which is apparently determined by that movement) still or also moving? As stated, Lorentz's initial answer was to proclaim that 'the ether is at rest in absolute space'. Space is no vacuum but is something filled with an ether-like field with definite properties whose state is described with the help of the two quantities - the electric field E and the magnetic field H. Even where these may have a zero value, their potential must exist. This absolute motionless field state of space with its electric and magnetic potentials is called the ether. But when active, the fields therein do each have directional attributes. It would thus appear in Lorentz's conception, to remain as a substance with positional attributes and utility. Otherwise it would seem arbitrary which term was used - 'ether' or 'field'.
205. This definition or assumption differs slightly from the earlier one of Fresnel who regarded the knowable ether of outer space to be at rest in a special inertial system which, while it may or may not itself be moving in respect of some theoretical absolutely stationary space, it could be regarded (like any inertial system) as being the complete equivalent of a such a system. However, he felt that the ether within moving material bodies 'down here' (including the Earth) was not totally at rest in this sense, but was partly carried along with them. With this model, Fresnel found many optical phenomena were accurately accounted for (possibly within the less rigourous 1st order level) within the current relativist framework. But Lorentz dispensed with the complex partial convection aspects of Fresnel and found that with some simple adjustments of the ether field (in his electron theory), he could arrive at essentially the same results (but again possibly only valid within a 1st order level) - within a framework of a stationary ether - seemingly with both relativist and absolutist characteristics (see below).
206. This can be demonstrated in the following example: As described earlier, a non-conducting dielectric between the plates of a condenser acquires an electric field perpendicular to the plates when the latter are charged. The atomic structure of the dielectric while not favouring the actual conduction of a current of electrons, does undergo a displacement of the electrons which align themselves to face towards the oppositely-charged plate so that the atoms concerned form dipoles - their more positive 'poles' (left as such by default as the electrons migrate to the other side of the atoms (on average) aligned conversely to face the negatively charged plate. There is in addition a comparable displacement (according to Maxwell) within the ether/space/field portion of the dielectric (which is much greater in extent than that occupied by the material atoms and electrons) with a dielectric constant e = 1. The total displacement = eE - ie 1 x E = E. That due to the electronic displacement is thus = eE - E = (e - 1)E = E - E = 0. [But was there no displacement left?] From Rontgen's experiment, we see that only this (electronic) part of the displacement takes part in the motion of an insulator between charged plates and so induces a weaker than expected magnetic field. Lorentz's theory would predict just this outcome - without the need to hypothesize that ether was carried along with the moving insulator. Lorentz claims that it remains absolutely still - whether inside matter or elsewhere (as in outer space).
207. Similarly, it can be shown that Lorentz's interpretation shows that the convection of light (vs that of electric or magnetic fields per se) also comes out in exact agreement with Fresnel's formula - ie:
As in Wilson's experiment, a transparent dielectric body moves with velocity v while a light ray moves within it in the same direction - along an x axis. Within this ray, one may imagine that it comprises two alternating waves or vibrations; an electric one E moving parallel to the y axis and a magnetic one H doing so parallel to the x axis. His experiment showed that as the vibration of the magnetic field moves along the x axis, it induces a corresponding displacement and field in the y axis (ie perpendicular to itself) of the value = (e - 1) v/c (H). If we divide by e, we get a total electric field
208. If the convection were considered total, as in the Stokes-Hertz model, one would have only e rather than e-1 - leading to a total field: E(total) = E+v/c (H). But in the alternative formula, v is replaced with e - 1/e x v. Thus, this value should equal the absolute velocity of the ether within matter (as per Fresnel); that is, should equal the convection coefficient j of optics. This turns out to be exactly so, for according to Maxwell's electromagnetic theory, the dielectric constant e is equal to the square of the index of refraction n (ie e = n2). If this value is inserted in the above, we get :
which is Fresnel's famous convection formula. But Fresnel's theory encountered difficulties with colour dispersion. The refractive index n depends on the colour (frequency) of the light and thus so will the convection coefficient j. But the ether can only be carried along in one way for light generally, not differently for every co-existing frequency. This difficulty vanishes in Lorentz's electron theory since the ether remains at rest while it is the electrons in matter that are carried along or move randomly; colour dispersion is explained by their being forced into vibration by light energy and so reacting in turn on the latter's velocity. [Recall: frequency x wave length is a constant velocity.]
209. In summary, Lorentz assumed the existence of a still, field-like electromagnetic ether - as a medium to mediate electric and magnetic forces and carry resultant electromagnetic waves (including light) - one which is at rest in some absolute sense (in contrast to Hertz's and Stokes' moving ether). Nevertheless, all such electromagnetic phenomena including light's velocity, frequency and direction depend only on the relative motions of material bodies - so far as terms of first order (b) are concerned. It thus accounts thereby for all the known phenomena - such as the fact that the absolute motion of the Earth through the still ether can not be demonstrated by experiments on the Earth involving only quantities of first order. This is an affirmation of the classical principle of relativity which thus again assumes that light's speed may well vary depending on the speed of its source or medium. However, the result of one experiment of first order is not explained any more by Lorentz than by other theories thus far. This is the failure to find an absolute motion of the whole solar system (in relation to an ubiquitous fixed ether in which it was assumed to reside) by means of Romer's method - as suggested by Maxwell (or of the Earth viv a vis such an ether - by Michelson's; see next paragraph).
210. By not accounting for this failure, it would seem unlikely that Lorentz's theory could account for other tests which can provide even more sensitive differences - ie those of second order in b (ie b2) on which its ultimate acceptance of failure would be decided. For such experiments (eg Michelson's) should make it possible to establish the absolute motion of the Earth through the ether - which, by definition, would itself have to (a) exist and (b) be absolutely still. That is, it should confirm the existence of such stationary ether - as the assumed necessary carrier of electromagnetic waves of light. And, it should cause light to be slowed (ie varied - as with Hertz) which the spatial contraction hypothesis (if correct) would then mask. Lorentz's theory was premised on the existence of such an ether (as, I believe, was Maxwell's also). Despite the apparent failure of the theory in respect of the above mentioned first order test, some hoped that it would nevertheless still pass this more rigorous test (seeming to imply that the former, as a test, had some unsuspected fundamental flaw, or the effects were at the less apparent 2nd order level?) arose when it was seen that it did at least achieve the distinction of providing an electromagnetic interpretation of that most fundamental of physical concepts - inertia. This is detailed next - before the more rigorous test referred to is more fully considered.
211. The discovery that light was an electromagnetic wave and that its carrier was therefore no longer considered to be of an elastic constitution meant that the original mechanical explanations for light and its carrier were now less appropriate. But Lorentz's theory in particular with its belief in an ether at rest in the same absolute space in which Newton's mechanics validly operated meant that the electromagnetic and mechanical spheres overlapped in terms of their joint reliance upon that absolute space. It seemed reasonable that these two realms of physics should be reconcilable within the same model of nature - ideally, one being subsumed within the other. The theories of Stokes, Fresnel and Hertz tried to account for electrodynamics within the mechanical model but failed. It was time (during the 1890s) to consider the converse approach. Poincare and Lorentz appeared to lean in this direction but may not have given the real constancy of light due weight. If it was the case that the classical principle of relativity (based on Newton's conception of an ultimate absolute space and time underlying the law of inertia) was largely replaced by a form of that principle based on an inertia associated more with the idea of equivalent inertial systems (but with continued belief in absolute time and space as background realities; one such system was assumed to be absolutely at rest), it would seem that the belief in a role for a still ether for the transmission of light waves (ie ca 1890s) shifted the emphasis back towards Newton's conception or at least re-opened the earlier duality of views.
212. If this could be shown, it would mean that the theoretical absolute space of Newton could be identified with the more plausible reality of Lorentz's ether. Newton's inertial resistances and the absolute centrifugal forces could be interpreted as physical actions of the ether - as electromagnetic fields of some relevant form. A principle of relativity with no absolutist assumptions for both mechanical and electrodynamic phenomena would then be accepted as not totally valid - but rather only approximately so - ie for quantities of first order in b only. A continued acceptance of an absolutist model would thus remain. Lorentz's theory seems initially at least to have denied a new principle of relativity (with no absolutist underpinnings) and to continue to promote that based on Newton's (effective) absolutivity with its fixed ether/space. But did he adapt this as new data accrued? However, it seems that while electrodynamics did prove to be the more fundamental conception and to subsume mechanics, it wasn't so on the basis of any reliance on an ether absolutely at rest. Rather, the still faulty principle of relativity, while not fully valid as suggested, was eventually to prove the more appropriate approach - once (after 1900) it was adapted to newly appreciated realities. This 'new principle of relativity' was initially unproven - being advanced in the form of a hypothesis or theory. Following some hints by Poincare, its subsequent formulation by Einstein is discussed later. It too entailed an attempt to subsume mechanics within electrodynamics - but one that succeeded. Its predictions would be consistently verified.
213. The primacy of the electromagnetic phenomena (initially within Lorentz's ether model but later in ether-free terms) is demonstrated thus: The propagation of elastic waves in a presumed elastic ether occurs, in the mechanical interpretation, with finite velocity due to the delays arising from the inertial resistance between neighbouring points of the continuous medium. This is represented by the formula rb = rf . Since c2 = r/p then b = c2f. In this case, b refers to the acceleration of the particles of the ether and is a 2nd order coefficient with respect to time, while f is the same with respect to space. It is seen that the acceleration is massively greater than the value of f - due to the enormous value of c2. Now, in the case of the electromagnetic phenomena, the situation is almost the same. But instead of only the elastic displacement of the ether being dependent on space and time, we now have both E and H being so dependent. The propagation of electromagnetic waves arises through the mutual action of these latter fields which produce an effect analogous to that of mechanical inertia. Once generated, the spread of such fields show a persistence similar to that of matter (mass) in motion. To generate the field, some work had to be done and when the field is resolved, this work potential re-appears (ie as energy). An example of this is seen in the behaviour of a Marconi wireless transmitter. A condenser is charged until a spark jumps a gap in the open circuit - which discharges the condenser. This allows the condenser to build up its two sets of charges again - but of opposite sign to before - until another spark occurs. It is thus similar to the mechanics of a pendulum where gravity takes the bob beyond the neutral centre point and it re-bounds (oscillates) thus until the energy is dissipated as heat. The similar oscillations of electricity proves the inertial property of the field.
214. J.J. Thomson inferred from this that the inertia of a body would be increased when an electrical charge is given to it. A greater force is indeed required to impart motion to a charged body than an uncharged one and to move or accelerate that charged body requires even more force than otherwise - there being both an electric and magnetic field associated with the latter which incurs an inertial 'cost' - to be overcome by some greater applied force. Because a force K acting for a brief instant 't' gives rise to an impulse J = K't' which will impart a change of velocity w in a mass m - ie J = mw - then for a charged mass the value of w will be less (ie it will remain nearer the original velocity v) but will now generate a magnetic field. The value of mw will now = J - J' (where J' = the part of the impulse needed to generate the magnetic field) and so give the smaller value of mw due to the reduced value of w. As w increases, so J' must be greater to provide the stronger magnetic field and it is approximately proportional to w. If we call this factor of proportionality m' (which is not a constant as it varies according to the initial value of v before the increase in same), we can set J' = m'w, so mw = J - m'w and thus J = (m+m')w.
215. It is thus as if the mass m were augmented by an amount m' - which may be calculated from Maxwell's field equations (and depends on initial velocity). While the value of m' for a given velocity may depend also on the distribution of electric charge over the moving body (and thus its field inertia) its limiting value for velocities that are small compared with that of light c (ie for small values of b) may be obtained without knowing such distributions as: m' = 4/3 x S/c2 where S = the electrostatic energy of the charges on the body.
216. Because the mass of the electron is 2000 times smaller than that of the proton, it was wondered if its mass may be nothing but that of a particle of electric charge - ie composed only of what might be seen as a small compaction of 'electromagnetic mass'. From Coulomb's law, the electrostatic energy of an electron with a radius a and charge e is S = 1/2 x e2/a. From this and the above equation for the value of the factor of proportionality m' = 4/3 x S/c2, the value of the assumed electromagnetic mass m(em) may be calculated: m (e-m) = 2/3 x e2/ac2. This in turn allows a calculation of the radius of an electron - which is found to be about 100,000 times smaller than the atom (and hence much denser, as its mass is proportionally much less small). But is the mass of this minute entity completely electromagnetic in character? Does it consist of some kind of 'stuff' - albeit 'charged stuff' ? Can it turn into 'pure energy' ?
217. Because there was evidence that the mass of the electron depended on its velocity, it was taken as support that it was indeed of this latter character. This conclusion seems to rest on the fact that the increased velocity (due to an application of more energy) caused an increase in the inertia of its increasing electromagnetic field - taken to equate to an increase in mass apparently - as per a theory of M. Abraham (1903). This in turn relates inertia (at least of electrons) to the modification of the ether in which such electromagnetic fields were assumed to exist. [Compare these conclusions with those reported by Einstein in late 1905.] Might therefore the mass of protons - as carriers of the positive charge - also be of this form? If so, then inertial persistence (of a body) would cease to be conceived as a function of mass per se (as in Newton's mechanics) - as the fundamental or primary concept of physics - but rather would become a secondary consequence of the inertial actions of the electromagnetic ether (or field) acting on both electrons and protons (and presumably neutrons) - ie on all matter in motion. Newton's abstract or theoretical absolute space as required by his mechanical law of inertia would thereby, in Lorentz's electron theory, be subsumed within the concept of an absolute and still ether - with known electromagnetic properties. Whether or not this view was to be upheld by later findings, it is the case that the relationship between mass and electromagnetic energy at least (rather than inertia per se) - discovered within this context - proved to be a fundamental discovery of profound significance. But would the still ether be replaced by yet another construct - a 'field' of uncertain substance (if any)?
218. But at the turn of the century, Lorentz's theory appeared to provide the best coherent picture of the world of physics in which all forms of energy, including the former mechanical inertia, were explicable in terms of an electromagnetic field in/of a stationary ether. It was thus still a mechanical 'world view' essentially - stretched to its absolute limit according to Poincare - who felt, however, that it still relied too much on post-hoc hypotheses such as spatial contraction and local times to account for certain awkward results. But with some improved 'explanation' of how the the principle of relativity should apply now (to all laws) and a 'new mechanics' to better account for these almost accidental anomalies of space and time, he felt the difficulties could be resolved. He was so very close yet missed the crucial and more fundamental point - finally revealed in 1905 by Einstein. [But see Lorentz's later version of his theory - published in 1904 (apparently not seen by Einstein however before he submitted his main 1905 paper on June 30 1905. (But what about Poincare's 'Note' of June 1905?).]
219. As mentioned (in par. 199), Lorentz had also to resolve Michelson's seeming negative result in a way that would prove consistent with his new and, during the mid-1890s, still developing theory of the electron. At first, Michelson's results seemed to indicate that any ether around the Earth was not motionless but possibly carried along as a blanket or envelope with the moving Earth - as had been suggested by Stokes in his theory of the elastic ether, and by Hertz in his later electromagnetic (non-elastic) ether theory. [That the Earth itself might not actually move through space at all, with or without ether, was discounted entirely; Copernicus was never questioned.] But various experiments, both in optics and electrodynamics, as well as the aberration phenomenon, had established the likelihood of only a partial motion at most of such ether. With no apparent still ether (and thus no absolute motion of the interferometer arm), Lorentz's theory would have been in difficulty had he (and Fitzgerald) not met this finding (and others) with a new interpretation - which said there was a still ether field (in keeping with Fresnel) and that it did slow light but that (to maintain the integrity of a mechanical orientation) this was completely (and rather conveniently) masked - by a contraction due to the real (absolute) motion of the parallel arm of the measuring apparatus moving through the still(?ish) ether - rather as per Newton.
220a. Lorentz had first suggested his hypothesis to explain Michelson's apparently negative result in 1892 (not then knowing that in Dublin Fitzgerald had already produced a similar explanation in 1889, 3 years earlier). By 1895, Lorentz had developed his idea further and published same in a short section entitled (in its English translation) 'Michelson's Interference Experiment' which was included within his book 'Versuch einer Theorie der electrichen und optichen Erscheinungen in bewegten Korpern' (Leiden, 1895. pp 89-92). In this, he sums up succinctly the situation addressed by Michelson, as it was then understood, as follows [witn my paraphrasing in brackets]: " As Maxwell first remarked, and as follows from a simple calculation, the time required by a ray of light to travel from point A to B and back to A must vary when the two points together [as aligned in the direction of the Earth's motion] undergo a displacement [due to that motion] - without carrying the ether with them. The difference [in time] is, certainly, [of very small magnitude] but [nevertheless was thought] sufficient to be detected by a sensitive interference method. This experiment was carried out by Michelson in 1881 [see American Journal of Science, 22, 1881, p 120]. His apparatus, a kind of interferometer, had two horizontal arms, P and Q, of equal length set at right angles to each other. [Rays of light were sent at the same time along each arm and back such that at their returns, their waves would interfere with each other if their journey times were not identical. The apparatus could be rotated so that each arm in turn could be the one that faced the direction of the Earth's motion and the other at right angles to same. On the basis of Fresnel's theory, it was anticipated that when revolved from one position to the other, there would be a phase shift and displacement of the interference fringes.] But no such displacements - due to any difference in the propagation times for the light rays' journeys - was found. Michelson concluded that the ether must have moved with the Earth rather than remaining still as generally assumed."
220b. Michelson's results had apparently perplexed several of Einstein's (slightly older) contemporaries. The mechanistic basis of the ether interpretation of Maxwell's equations (which Michelson seems to have sought to verify) was, on the face of it, worryingly compromised. Some new theory or speculation was required - one which would account for the miniscule time difference found for the two different directions over which the light's speed had to be measured as observed from the moving Earth. Amazingly, Fitzgerald had calculated that a minute contraction of one arm of the interferometer of just 1/200th of a micron (a hundred millionth of a meter!) would adequately account for this. But how to explain such a miniscule but seemingly crucial contraction? He suggested that it might result from the force or pressure of the opposing ether 'wind' (but seems to have considered that such an effect would be more apparent nearer the speed of light). But Lorentz, who had been working on his theory of electromagnetic forces to supplement Maxwell's theory of the field, still within the mechanical model, eventually published his alternative view.
220c. As mentioned, his later idea (ca 1895) was based on the fact that electrically charged matter was the source of Maxwell's fields - which existed in the empty spaces between all particles of matter. Charged particles then interacted with each other by means of their fields which causes such particles to move according to Newtonian (mechanical) laws of motion. Under conditions of stability, such particles assume a particular position relative to one another but when such matter moves (seemingly in absolute terms) in one direction, localised electromagnetic forces evoked by that motion (vis a vis the still ether) must pull their particles slightly closer. The gross matter of the arm thus contracts and this would be much greater along its length (ie in the direction of motion) than across its narrow width. The forces involved would be propagated by means of the intervening ether in the same way as any electromagnetic force - which he pointed out were themselves known to be modified when their sources are in motion. Seemingly, Lorentz felt such motion must be absolute (whereas Einstein would realise it need be only relative; indeed, he would later point out that, in his view, that was the only kind there was).
220d. Because Michelson had taken the phase difference which the theory would predict at twice its proper value (as later pointed out by Poitier), the conclusion of a moving ether was brought into question. When the figures were re-calculated, it was found that these smaller expected displacements would now be within the usual range of experimental error. That is, the expected effect may well have occurred (and the ether thereby concluded to be still, etc) but being so slight could have been thus obscured. So Michelson repeated his experiment (with Morley) with an even more sensitive apparatus [see American Journal of Science, 34, 1887, p133] which would be expected to find a displacement of 0.4 of the distance between the interference fringes. However, all that was found were displacements of only 0.02 of this distance, which could well be ascribed to errors of observation and in fact be essentially equal to zero. This result again did not support Maxwell's ideas based on the theory of Fresnel. It was however more in keeping with that of Stokes and his theory of aberration. But Lorentz saw too many difficulties in that latter theory to find support there for Michelson's negative result and so said "I would rather try to remove the contradiction between Fresnel's theory and Micheslson's result. An hypothesis which I brought forward some time ago [1892-93, as above], which had also occurred to Fitzgerald [in 1889], enables us to do this." To simplify matters he explained this hypothesis in terms of Michelson's first apparatus - with the arm P laying exactly in the direction of the motion of the Earth. He let v be the velocity of the Earth [relative to the Sun?], L the length of either arm and hence 2L the length of the path traversed by the light rays. According to the theory as described by Lorentz in an article in Arch. Neerl, 2, 1887, pp168-176., the turning of the apparatus through 90 degrees should cause the return journey of the light ray to be longer than otherwise by t = Lv2/c2 (in seconds?)." [Note: the 2s here represent squaring. Also, Lorentz's equation actually shows the value of c in the denominator not to be squared but cubed; this is an enormous number and would seem to be an error.]
220e. Lorentz then points out that if there were no effects arising when the arm is turned into the direction of the Earth's motion, this same time difference could still appear - providing one arm was longer than the other by just half this value (ie some portion of a micron). The phase differences expected could thereby be fully neutralized by appropriate changes in the arm lengths. As such, Michelson's seemingly negative result could be fully explained. He suggest that such a contaction in the arm's length could be imagined on theoretical grounds by virtue of some 'influence' being exerted on any such body when moving through the still ether. He suggests that such an influence could be the attractive forces set up within the molecular structure of any body when it moves through the ether quite comparable to the attractive forces transmitted through the ether between charged particles. In regard to the outcome of actual experiments, he notes that any such effects as contraction would amount in the case of the arm set in the direction of the Earth's motion to about one two-hundredth of a micron only. But, rather too precisely, this slight degree of contraction would exactly remove the evidence of the phase shift predicted for the Maxwell-Michelson displacement. By reference to other calcualtions Lorentz had made, he shows that the extent of such a contraction is in the proportion of 1 to the sq rt of 1 - v2/c2. Thus, the magnitude of the contraction would be as suggested = 1/2.v2/c2.
220f. So, Lorentz's 'answer' to the difficulty thrown up by Michelson's result was (in 1895) the assertion that 'every body which has an absolute velocity v with respect to the still ether contracts in the direction of motion by the proportion sq root of 1-b2 (or sq root of 1 - v2/c2)'. If this were the case, then Michelson's experiment would have to give its (negative) result (exactly) - for the interferometer arm would contract by exactly the amount that the predicted slower light* would require to manifest that slowing. This hypothesis was at first viewed rather sceptically since it seemed rather too perfect and there was no way of verifying it by an observer on the Earth. For any means of confirming such a contraction (ie using some form of 'measuring rod') would itself be contracted equally, if used on the moving Earth, so show no difference. If one could observe it from beyond the Earth - from a position at rest in the assumed still ether - such a contraction in theory might then be observable (if it existed) since the entire Earth itself would be slightly flattened (contracted) by its absolute motion relative to a still ether (by about 6.5 cms apparently) - and everything on it would be seen by such an unaffected distant observer to be proportionally shortened likewise. But this again relies on the assumed existence of such an ether. [* Was the prediction that light would be slower or just that it would take longer - as it would if the distance was greater ? Was it ?]
221. An early difficulty in acceptance of the Fitzgerald-Lorentz contraction hypothesis was the fact that it appeared to arise (in Lorentz's initial conception at least) simply as an unexplained 'companion circumstance' to absolute motion through the ether - rather as a 'gift of God' - and not through any physical pressure due to the 'opposing ether wind' say (as Fitzgerald had briefly suggested) or otherwise 'physically' caused in terms of precise sub-atomic detail. Despite these early misgivings by others, Lorentz eventually integrated this new view successfully into his later electron theory, giving it a more rational explanation which also seemed to account for the earlier Michelson results. For he suggested that such absolute movement produced forces via the ether field which acted between atomic sub-particles (of the body so moving) which caused them to become narrower (and/or closer together) and so reduce the dimension of the material - in the direction of its motion through the ether. This suggested there was still a kind of physical basis for his contraction hypothesis - one not due directly to any gross physical action of a substantive ether pressure but to electrodynamic force effects at an inter-atomic level that real movement per se (of charges) had on the electrical forces so arising within any atomic system of such charges (ie on the electrons and protons) of that moving material (measuring arm).
222. Absolute movement (only possible through an absolutely still environment as assumed for the ether) thus caused such forces to establish a new equilibrium within matter, said Lorentz, so that it necessarily contracted in the direction of motion - by the sq root of 1-b2. This seemed a reasonable hypothesis and of course still fell within the mechanical model; certainly moving charges set up magnetic fields and vice versa and these could well influence the arrangements and even sizes of the sub-components of matter. The still ether (ie the field) was seemingly the means by which such electromagnetic forces operated and thus remained a basic feature in Lorentz's explanation; the motion of such charges was thus seen as real or absolute. [Note that Einstein would later point out that such charge- and magnetic-inducing motions (of their respective sources) need only be mutually relative (not absolute) - as they had always been. Lorentz may have accepted that this might also apply - if at a lower degree of certainty.
223. As more sophisticated techniques sought to reveal any minute second order differences arising due to the motion of the Earth through any still ether, their consistent failure was however proffered by Lorentz as yet further support for the contraction hypothesis. Just as one couldn't establish that a train was moving by observing normal mechanical actions performed thereon, so no movement of the Earth through an ether (or otherwise) could be discerned while an observer moved along with the Earth because of the ubiquity of such contractions (or by other mechanical measures). The classical principle of relativity thus appeared to hold good for both mechanical and electromagnetic phenomena, thanks to the contraction hypothesis. But when Lorentz attempted to account for the classical principle of relativity in terms of his basis for the contraction processes, he was not so successful. It could apparently be interpreted with equal logic either to support or infirm that principle!
224. Lornetz's ideas appeared a most reasonable hypothesis (first published about 1892-3, with later modifications in 1895, 1899, 1904 and 1906). Thus, in his paper 'Electromagnetic phenomena in a system moving with any velocity less than that of light.' which appeared in an English translation of the Proceedings of the Academy of Sciences of Amsterdam, 6, 1904, he sought to better develop his initial theory (after the earlier versions). While this entails considerable calculus manipulations of Maxwell's equations (and related matters), its more verbal introductory and concluding remarks may, for us non-mathematicians at least, throw further light on his general thesis. We can then compare and contrast these ideas with those of Einstein - which were to appear only a year later - although Lorentz's 1904 paper had not been read by Einstein before he sent off his own paper in late June 1905. (But what about the 'Note' by Poincare published in early June that year ??)
Lorentz's 1904 Theory.
Lorentz begins his 1904 paper by noting that by virtue of the Earth's annual motion around the Sun (and so through the still ether?), electric and optic phenomena (eg light)undergoes an effective 'translation' (that is, the motion and velocity of light can be analysed with respect to either or both the Earth's surface as its source and/or an allegedly surrounding still ether through which the Earth and light source (and light) - the ether serving effectively as an opposing 'wind' or resistance. The velocity v of the light source relative to that ether may be considered as a ratio with respect to the velocity of light c, ie v/c. He describes this ratio as being of the 1st power (order of magnitude). When such 'an influence' (on a body moving through a still ether) is of a more subtle degree - ie of a 2nd order (as v2/c2) - but still potentially perceptible - it may, he notes, prove more difficult to analyse: "The first example of this latter kind (examining such subtle effects of this 'translation') was Michelson's interference experiment (1887) - the negative result of which led Fitzgerald (1889) and myself (1892) to the conclusion that the dimensions of solid bodies are slightly altered by their motion through the ether'.
[Note: To describe the topic of concern as 'electric and optic phenomema' (rather than simply as light and its speed) undergoing an 'effective translation' and/or 'this influence' strikes me as unnecessarily abstruse and vague; Michelson didn't describe the objective of his experiment thus, I believe.] In any case, some new experiments, in which a 2nd order effect was again sought, had more recently been published: In 1902, Rayleigh examined the question of whether the Earth's motion may cause a body to become doubly refracting. If such motion did indeed effect any body's dimensions, such an effect could be expected. However, his result was also negative. This experiment was repeated by Brace in 1904, but again failed to show this effect. Between these experiments, Trouton and Noble attempted in 1903 to detect a turning couple acting on a charged condenser, the plates of which make a certain angle with the direction of translation. Such a couple should occur according to the present theory of the electron (as matter moves through the ether). In the apparatus of Trouton and Noble, the condenser was fixed to the beam of a torsion balance sufficiently sensitive to be deflected by the 2nd order of magnitude of the terms representing the inevitable 'electromagnetic momentum' arising from such an electostatic system moving with velocity v as the condenser moves through the ether (functioning as the dielectric). However, no such effect was observed.
The seeming failure of these 4 experiments suggested that a new examination of the problems connected with the motion of the Earth through the assumed ether was desirable. Moreover, Poincare (in Paris, 1900) had objected to the need for introducing new hypotheses in order to explain such failures as Michelson's experiment (as eg the 'contraction' hypothesis). Inventing new hypotheses for each new experiment was really too artificial. Lorentz thus admits (in his 1904 theory) that "...it would be more satisfactory if it were possible to show by means of certain fundamental assumptions, and without neglecting terms of one order of magnitude or another, that many electromagnetic actions (why doesn't he refer more explicitly to the the velocity of light and its possible constancy?) are entirely independent of the motion of the system." [Such 'independence' appears to imply that most or all other moving bodies are not thus independent but rather are dependent upon (ie 'relative to') - the motions involved (at least in their initially measured outcomes) and that these were previously taken account of by the application of the traditional (Galilean) transformations (in order to determine the net values assumed under the originbal principle of reltivity not to be affected by such (uniform) motion .] Lorentz then refers to his earlier (1899) attempt to frame just such a theory and thus his present attempt to elaborate and improve on that earlier version. The only restriction being that the system (as the moving Earth with the light measuring apparatus or??) must move with a velocity less that that of light. [On what did he base this resriction?
Possibly his calculations based on Michelson's finding indicated that at the speed of the Earth a particular degree of contraction (and dilation of time??) neutralised the expectation of the speed of light and that pro-rata this meant that the relevant ratio would exceed unity beyond that value for light.] He apparently seeks to explain that not only light but other phenomena in the electromagnetic sphere may prove not to be adequately accounted for by the usual Galilian transformations when analysed from a differently moving frame of reference - being (apparently) independent of the motion of the system. Thus, not only Michelson's result but those of the other studies mentioned were bound to 'fail' as the effects expected by their moving systems (eg - of increasing the speed of light by the amount of that system) were masked by the deformations of the moving apparatus. [Was the 'independence' only apparent therefore? And did this independence imply (amongst other things) that the velocity of light was not affected by any such movement (of 'systems') - ie that it was a universal constant...or?? Lorentz had thus concluded (?deduced) on the basis of the apparent effect of an assumed still ether that the velocity of light was a constant (or..'must appear as a constant'?). This contrasts with Einstein whose basic postulate and starting point was that the velocity of light was a constant - with no need for any ether from which to deduce (as coming about as a consequence) that fact. It was a law of nature and as such should accord with a generalised principle of relativity.]
He sets out his new theory in terms of an elaboration of Maxwell's equations, being concerned as he is with the electromagnetic (contraction) effects on sub-atomic processes by the ubiquitous ether, which are manifested in the deformation of electrons, molecules and the larger bodies they comprise, as they move through that fixed ether - the greater the velocity (v), then greater the degree of contraction of the body concerned and all its constituent parts. He suggests that a body contracts in the direction of its motion by an amount b (beta) which when squared = c2/c2-v2 and is thus very slightly greater than unity. [How did he conclude the equation (value of) beta ? Presumably this was implied within Maxwell's equations? Or was the extent of Michelson's failure for the body moving at 30 kmph utilised at all?] It also contracts by a generally lesser amount (l) perpendicular to that direction. What appear to represent the measures of the coordinates in a system any body may move after a translation - viz: x', y', z' and t' - are described as independent. t' is referred to as the 'local time' (on the moving system - of the Earth). In order to allow the unexpected constant velocity of light to be accounted for despite its attempted 'boost' by the moving system, Lorentz derived his famous transformations (later named after him by Poincare) to remove exactly the correct amounts of the distance and time elements of the velocity concerned. These were thus given by:
That is, the values of the variables in the moving system (the Earth) are a particular function of those in the stationary system (the Ether), as shown - the ratio of v to c being crucial. The transformations were consistent with the equations:
so that the behaviour of light was seen as the same in all systems (moving and not) related by the transformations. [Lorentz's conclusions here may be contrasted with the similar ones by Einstein but without any role for an ether or any 'real' contractions or time dilations; see later.] Lorentz's main assumption is that such a translation results in the dimensions of bodies becoming b.l times smaller in the direction of motion and l times smaller (ie unchanged) in the perpendicular direction. For most (low) values of v, b.1 is essentially = 1. The derivation of all the logical steps in his analysis is much too complex for my understanding. But the general drift seems to be that the various experiments he referred to above - which relied on finding 2nd order effects - could not do so because actual physical deformations of exactly those magnitudes, arising by the interactions between the elements of all moving bodies and the still ether, would always mask or neutralize same. Such effects would be a function of the velocity (of translation?) with which they moved through the ether - being much less at slower velocities - when v/c is a very small value (fraction) but becomes maximum as the value of v approaches the speed of light and thus v/c approaches 1. But how was that exact function arrived at? The masses of such bodies would be comparably affected due to increased charge values at faster speeds.
[We may point out here that whereas Lorentz associates his coordinate vaues of x, y, z, and t with an (?absolutely) stationary system represented by the still Ether, and his values of x', y', z' and t' with a (consequently ?absolutely) moving system represented by the Earth, Einstein more typically uses the latter values for his moving system (as a moving train) and the former ones for his relatively stationaty system - the Earth or embankment (rather than the Ether). Moreover, while Einstein points out that the mathementics and conclusions are equivalent if the stationary and moving systems are reversed (as their mutual motions are relative and equal), Lorentz's analysis must retain the one and only relationship which is thus not symmetric. The typical different variables which, say, x' or t' represents in their respective analyses, can thus prove somwwhat confusing.
To confirm that the measured net velocity of light, despite the influence of moving against the ether 'wind', was actually as his hypothesis now stated (ie 'independent' of such actions; but due to what?), Lorentz applied a new (non-Galilean) transformation (but adapted from same?) as had emerged from his analysis. This showed that the net value for light's speed (before confronting (ie aiding or opposing) it) was indeed unchanged when that effect (influence) was removed by means of the transformations. For the new transformations took account of the hypothesized contraction and time effects of bodies moving at, say, the speed of the Earth. The extent of so 'taking account' was seemingly based on the results of Michelson's experiment in which the velocity of the Earth relative to the assumed fixed ether (at 30 k per hour) provided one objective value and the velocity of light provide by Maxwell' equations (I believe) provided another. But, unlike Einstein's analysis, the constancy of the speed of light doesn't seem to be directly considered by Lorentz; nor does the phrase 'principle of relativity' appear in his paper - despite Poincare, with whom he was in correspondence, having pointed out its relevance in 1899 and again in 1902 with respect to the very matter addressed by Lorentz. It seems that Maxwell's differential equations on which Lorentz based his derivations considered both space and time as having local significance as coordinates for local measurement rather than as universal (Newtonian) parameters. As such, his equations would later prove consistent with Einstein's relativity principle (not an explicit part of Lorentz's theory at that point).]
Apparently when later considered by his peers, the basis for his suggested variation for the ether-affected length dimension of any body was granted some support but that for the variation (?slowing) of local time (not yet mentioned here) appeared to be much less acceptable. [Einstein had his own comparable explanations for the 'mechanism' he believed responsible for these equivalent effects (see later). Lorentz explained his actual physical contractions (and time dilations?) as being due to an electrodynamic effect of the still ether on the sub-atomic structure of matter moving through it - this being his explanatory 'mechanism' (at least with respect to contraction) - ie as though the ether was effectively moving against and influencing that structure, whereas Einstein explained his non-physical effects on space and time as being due to an inevitable 'lag' in the receipt of the perceptual information about them - this being his explanatory 'mechanism'. Lorentz's conception was based upon the combination of an assumed still ether and the results of Michelson's experiment about it while Einstein's was based on the combination of the postulated constancy of the speed of light and a generalised principle of relativity which was required to prove compatible with that constancy (or 'independence'). Both interpretations led to the same transformations which showed that the net velocity of moving bodies, including light, were consistent with the laws governing them - as conceived by these two theorists]
With respect to Lorentz's questioned 'mechanisms', Poincare (1904) for one, felt that Lorentz's defence of the mechanical interpretation of Maxwell's electrodynamics still relied too much on such post hoc hypotheses (Lorentz's assumptions) - especially as it implied that the resulting adjustments, while still within the mechanical model, would apparently only hold true 'up to the speed of light' - which was thus inconsistent with Newton's mechanics (which Lorentz was lafgely attempting to support). Also, Michelson had already attempted to put Lorentz's idea (by comparing different interferometer arm materials) to the test but (ca 1900) this too failed. Hence Poincare's opinion that if Lorentz's (1904) ideas had any merit, a 'new mechanics' (but still a 'mechanics' seemingly) must be required - one which he felt must exist (to properly account for recent findings) but which contemporary physicists could as yet barely glimpse. But within the year, someone else also not fully convinced of Lorentz's overall theory to explain those recent results (and if not Lorentz's then those of other contemporary workers) was about to glimpse an alternative 'non-mechanics' as a way out of the dilemma - and do so with greater clarity. Poincare himself was also about to glimpse (albeit only a part of) this that same year.
225. But, the still ether would be retained by Lorentz until about 1908 in order that his conception remained consistent with the only known world view of how nature worked - ie the mechanical model. Michelson was convinced and (as mentioned above) attempted a test of this idea - comparing arms made of different materials. It too failed and the absolute motion of the Earth in relation to a still ether was again not found. By 1909 and 1915, however, Lorentz, in later versions of his ideas, would show increasing acceptance of Einstein's theory as first propounded in 1905. But he still saw it as that 'new mechanics', as demanded by Poincare, which also entailed an actual contraction of length (and a comparable dilation of time). However, the rationale for this was based on quite different reasoning and was not required to account for Michelson's result (as Fitzgarald and Lorentz thought it did - at least to maintain the mechanical world view - which had as Poincare pointed out 'reached its final limit in Lorentz's theory of 1904'.
But Einstein would soon realise that such a mechanical model was probably no longer appropriate and without it, the Michelson result may well have been as expected - at least when considered from the perspective of an observer on Earth, (which was as Michelson conceived it). There would thus be no need to posit the contraction or local time explanations as suggested; they wouldn't be needed if they hadn't in fact occurred. Possibly there was also no ether - still or otherwise - to so affect the speed of light? They might propagate in some other unknown, non-mechanical way and, more importantly, the fast-moving light source (as the Earth's motion) may well not influence the measured speed of light either (or was it just 'time'?) - if its speed was a true constant. This could also explain why no differences were found according to the material used in different arms. By 1909, Lorentz, would be partly won over to these views, but still felt that a stationary ether medium must be a reality '..as the seat of the electromagnetic field with its energy and vibrations - having some degree of substantiality - however different from all other matter'. He certainly hung on - longer than anyone else - to the mechanical model that he (as everyone else) was no doubt imbued with. By 1915 though, little or no further defence was offered. (Michelson was another long-term doubter, apparently.) These ideas are developed later.
226. In the meantime, while working on his contraction hypothesis, Lorentz discovered that for mathematical consistency another assumption was required to account for the surprising equality of all electromagnetic phenomena (ie the seeming constancy of light's speed when the possibility of such constancy was seemingly still not properly addressed) whether occurring in systems moving through the supposed ether or at rest in it. It appeared that the classical/mechanical principle of relativity held true only partly by means of the contraction of a body's spatial dimension and partly by a variation in measured time - at least if the underlying equations were to be consistent. This is not that surprising when one considers that any outcomes involving the motion and velocities of moving bodies (or of imponderables) must concern both distance and time - by definition; that was what motion/velocity was. Thus, he concluded (as touched on above) that in any system that was moving uniformly, a new local time appeared to be needed - ie one that (conveniently) differed in all differently-moving systems. So, both space and time were said to be different in moving systems (up to the speed of light) than in those at absolute rest with the still ether. The true underlying nature of some of these things was thus dictating the direction and results of the search - ie up to the speed of light. The latter was thus a built-in upper limit and Lorentz's theory apparently recognised this which could imply that Newton's original mechanics were somehow not quite correct.
Lorentz developed precise mathematical equations (to replace those named after Galileo) by which due allowance could be made for both sources of these differences - known later as Lorentz transformations when Poincare credited Lorentz with their first derivation - and while his suggested post hoc physical basis for their necessity was later to be questioned and shown to be wrong, their apparent quantitative reality, accuracy and significance as a fact of nature within this same sphere seemed undeniable - however they came about. And thus Poincare's remark that with both Newton and Lorentz wrong only in parts, a 'new mechanics' (but still 'mechanics') was needed to reconcile matters.
227. Nevertheless and most amazingly, the transformation equations which Lorentz had derived to take account of his hypothesised contractions and time effects proved to be quantitatively identical to those that Einstein would also derive - quite independently (it is alleged) - but on a totally different basis (as to the 'cause' of the time and space effects) and which were to have a profound significance in regard to our conception of the laws of nature. They did not reflect any physical contraction of an interferometer arm, however, (or of anything else) but rather the implications of adjusted perceptions of time and distance (by measurers/observers) required by the dictates of the velocity of light being a true constant and the upper limit of the speed of any motion. The primacy of this reality necessitated a suggested revision in the components that underlie the (velocity considerations of the) principle of relativity - a suggestion that would eventually be described as the theory of relativity.
This seems such a remarkable coincidence that one is tempted to seek some communality for these two sets of phenomena which shows that they are in fact just two different perspectives on the (quantitative aspects) of the ?qualitatively same thing. Certainly they both concern the effects on time and distance measurements/perceptions according to the differences in speed at which certain systems of reference are moving in relation to each other. It is not unknown for certain 'realities of nature' to force being recognised so that 'end' will be arrived at from different routes (means) - even if only one such route represents the true cause and effect sequence. In any case, because these accurate equations had been first advanced by Lorentz (albeit on false premises), they were later referred to primarily as 'Lorentzian transformations' - eg by Poincare and later Einstein - and replaced the 'Galilean transformations' of mechanics and the original principle of relativity. They give precisely the adjustments required by Einstein's theory of relativity. We may assume that he derived these same values from his different premises however.
228a. This seems another example of how the reality of nature can dictate or force the direction of the mathematics and conclusions based thereon even if their implications are misconstrued and their ultimate basis may not be revealed quite as quickly. Thus, at about the same time, both Larmor (1900) and Poincare (1902) had apparently arrived at similar conclusions. And a comparable point of view was apparently expounded even earlier by Voigt (1887) when the elastic theory of light was still being investigated. Movement did appear to affect measures of space and time - but how, why and to what extent? Was it just perceptions of same or some real variation? It does seem odd that the hypotheses proffered by Fitzgerald and Lorentz as a reasonable explanation of the Michelson result (in terms of their premises), while actually wrong (for an experiment viewed as they saw it - from Earth) somehow turns out to actually apply validly (if differently explained) for such experiments - and many other situations - when viewed from other frames of reference - a view not relevant or appropriate for the immediate objective of the Michelson experiment. For the contraction of space and dilation of time to be advanced as an explanation for anything seems quite preposterous. For it then to be confirmed as wrong and yet - to apply nevertheless (and validly) - in a related sphere, explained differently - seems most uncanny.
228b. [Note: It seems to me that Lorentz, accepting the same assumptions as Maxwell, Fresnel and Michelson regarding the role of the ether in electromagnetic processes, sought to maintain this view (as put to the ultimate test by Michelson's experiments) by his hypotheses concerning the contraction of moving bodies and an associated dilation of time. But rather than present the relevant equations and transformations rather directly - in terms of the velocities of moving bodies per se, in relation to the speed of light - he preferred to derive them in terms of his conception of the role of the ether on atomic level processes (as begun by Maxwell) - ie within his theory of the electron - and then generalize this to whole bodies themselves (as eg the interferometer arm). So, buried within his complex derivation, one would assume that, in effect, he must have started from the point that motion through the ether causes contraction and time effects (at whatever level) - depending on the relevant velocity as a proportion of the speed of light - and that if the equations were held to this fundamental reality (serving as independent variables) for whatever frames of reference or velocities might apply, it must follow that the speed of light (as a dependent variable) would thereby show an unexpected constancy and 'masking' effect) in contrast to what it might have been otherwise - ie not constant. [Which speed did he take c to be in his derivations ? And did it represent the velocity of light or the maximum possible velocity (of anything) ? NB. In a Book 'Geometry of Electromagnetic Systems' by Baldomir & Hammond (2004), they stste that "...Lorentz had deduced the constancy of the velocity of light from the assumption of a stationary ether "...while Einstein suggested instead that this constancy should be made an accepted postulate - ie as a starting point not something deduced from prior data - and then determine what would have to change to accommodate that reality. It appears to me that these authors should have phrased their remark as: 'Lorentz had deduced the apparent constancy of the velocity of light...' in that this outcome was only the case, as I understand it, due to the masking effect of the assumed 'non-constancy' of that velocity - in which he, Maxwell and Michelson implicitly believed (it being the very means by which they sought to establish the existance and stillness of the ether. They couldn't have it both ways!] ]
228c. The actual values by which length and time are assumed to so alter (physically) in Lorentz's conception would presumably have to prove to be the same (albeit not physically so) as those derived independently by Einstein (also based on a part of Maxwell's theory) since he did so by a similar (if crucially different) means wherein it was, rather, the (independent) speed of light which in the derived equations should remain the same with respect to its measurement from differently-moving frames of reference. That is, this was his starting point) and only thereby would length and time be found necessarily to be the dependent factors - which are thus 'forced' to vary - again in accord with the relevant ratio of velocity to the speed of light, and without any intervention of an ether. [See the next section - on Einstein - for more detail in this regard. It would be most useful (to myself) if Einstein's clear derivation as shown in the Appendix of his 1920 book could be utilized as a structure/framework/model in terms of which Lorentz's derivation, thus delimited or constrained to its 'bare bones', could be compared and contrasted!] Finally, we may mention that in Lorentz's conception, the mechanistic model of nature is thereby retained, with its original principle of relativity (or are time and space now assume to vary by Lorentz - when ever applying that principle?), while in Einstein's, a new such, more general principle (with that qualification) is indicated and the mechanical model is replaced by a more encompassing, more general electrodynamic one.]
229a. We may in any case enquire what consequences this final form of Lorentz's theory may have for the concept of the absolutely still ether/field? The original principle of relativity would appear to hold under this interpretation (viewed retrospectively or ?) - not only for all mechanical phenomena but for light and other electromagnetic phenomena as well (treated as extensions of the mechanical model). Several new experiments re-affirmed the null findings of Michelson-Morley. Thus, an observer moving uniformly in a system will perceive the same phenomena - whether mechanical or electrodynamic as he would in one at rest in the still ether. Had the Michelson experiment found that light's speed was affected by that presumed ether, Lorentz would presumably have held to his earlier absolutist position. The negative result would normally have required him to adapt or even drop that view (and accept some relativity alternative) but, by accounting for that result with the hypothesised effects of motion on both space and time, he could possibly still retain his original absolutist position on the matter.
229b. However, that particular means of explanation was also fully consistent with the criteria used to support equally the converse position of the principle of relativity! The observer has no means of distinguishing the moving frame of reference from one that was absolutely still. Even the motion of other bodies in the world - moving independently of him - can inform him only of his relative motion with respect to them and never of any absolute motion with respect to an allegedly absolutely still ether. Equally, he could assert that he was himself absolutely at rest in the still ether and no one else could contradict him - on the same basis. If someone else in a comparable situation asserted the same, one of them could actually be moving - but there is no way to establish this - either empirically or theoretically. In fact, it could be argued that, therefore, there is probably no still ether or reference system (as this was unprovable); only relative motion was possible - as Poincare seems to have concluded by 1902 - as the more probable of the two possibilities. [This is a further basis for Poincare's doubts about Lorentz and thus a need for a 'new mechanics'.] But this seemed unsatisfactory. A more definite statement of the reality of that latter position would be preferable - one that could form a basis on which that view could be tested and hopefully supported. Like the principle of thermodynamics, statements had to be advanced as axioms and then evidence reasonably sought on that basis to support them (and deductions arising therefrom) as representing the best current truth.
230. Because of this impasse, we arrive at the same position in respect of Lorentz's ether - still in absolute space - as we were in respect of Newton's absolute space; that is, as far as the principle of relativity is concerned. In Newton's case, it was accepted that his concept of an underlying absolutivity was essentially a theoretical one. But pure space with no bodies in it possesses no realisable means whereby any fixed point in the universe could be ascertained or found a second time in order to confirm its alleged stillness or serve as an ultimate reference marker. It is not a substance with spatially distributed parts that could ever be located or positionally defined. By like reasoning, there is no way that any specified position could be physically defined in the ether and hence it too has no substantive/spatial/ positional property on which this absolutivity caould be based. It thus appeared that a principle of relativity based on equivalent inertial systems alone - with no absolute 'backup' - was the more likely and that there was no ether - whether still or otherwise - nor any verifiable stationary space. After all, Lorentz's interpretation of the electromagnetic basis of the contraction hypothesis did not actually rely on any direct physical action of the ether on the dimensions of moving bodies - but rather on its inherent electromagnetic action due to hypothesised real motion of charges in relation to that fixed 'space' alone (I think).
231. There was of course still the original reason why the ether was posited (as thought necessary, I believe, by Maxwell) - ie as a mechanical carrier or medium of light's waves across the vacuum of space. Partly for this reason but seemingly also because of his views on an ultimate still reference system, Lorentz and other's hesitated for some time before considering abandoning all that had been devoted to this concept. In the end most did, although as mentioned, Lorentz himself equivocated to the end - feeling that of the infinite number of equivalent (moving) inertial systems which his own theorising had concluded to be the case, one of them must be that ultimate absolute reference system at rest in space (ie the above 'backup'), even if it wasn't needed by light as a carrier. Interestingly, Michelson too held to some belief in an ether well into the next century and on the idea that the contraction effects were real. [What about time?] While Lorentz's contraction hypothesis was certainly consistent with Michelson's results, the ultimate test was whether or not there was any objective evidence of such contraction when any body travelled at speed through the assumed ether. I don't believe there has been.
232a. It was very likely that the physicists working in the last decade of the 19th century weren't so much trying desperately to maintain a mechanical interpretation of all physical phenomena - in opposition to some suspected alternative (of which, indeed, they probably had no suspicions) - as they were simply trying to find, as they had always done, explanations for each new phenomenon as it came along - within the only context they were aware of or interested in - the mechanical one - which alone had served science so well for 250 or more years. Its logic and relevance was simply taken as an unquestioned given. There simply wasn't a 'suspected alternative' as no alternative was thought necessary. While there was one, in a sense, waiting unseen in the wings (as Poincare implied), it was quite understandable that ever more ingenious manipulations of the existing concepts and principles - within the mechanical model - would continue to be advanced. Such had always worked in the past. Hence the gradual evolution of the concept of the elastic luminiferous ether to that of the non-elastic electromagnetic ether/field and the arrival of Lorentz's contraction and local time hypotheses.
232b. Eventually, though, Poincare in effect suggested pulling back the curtains on those wings to see what else might be there (in view of continuing anomalies; Lorentz's picture, especially in regard to the measurement of time, wasn't really adequate) and Einstein soon obliged. And in like manner, we may suggest that during the latter half of the 19th century, there wasn't some loosely-knit group of like-minded philosophers of science promoting a concept of 'absolutism' - of space, time and motion - which continually guided contemporary researchers in physics and then, a little later, another such group who promoted 'relativism' as a preferable alternative. There were no such groups. What there was was an established model of science based in part on Newton's ideas which were long-since taken for granted (passively) but had virtually no active role in guiding research (ie as one option of several) over some centuries until, around 1900, one or two lone voices suggesting certain traditional unquestioned assumptions should be re-examined. Much later, many of those writing about this relatively sudden transition appeared to find it convenient to set up a false picture of two competing 'camps' of ideas that had battled it out over some extended period of history. It appears however that there wasn't such an on-going battle - just a single 'bomb' very latterly out of the blue - that cleared the air.
233a. Lorentz and Poincare, if not individually then jointly, appeared to possess all the necessary ingredients and understanding on which the theory of relativity depended but, unlike Einstein, they hadn't by mid-1905 found the correct way to combine these into a logical cause and effect sequence - ie such that all laws of nature, including the constancy of the velocity of light, accorded with a generalised principle of relativity - without invoking a concept of an unproven still ether and physically (rather than perceptually) varying measures of time and space characterising the velocity of all moving bodies. Over the past century, there have thus been countless attempts by a kind of 'anti-Einstein industry' to point out the possession by Lorentz and Poincare prior to mid-1905 of all these necessary components with which to formulate a potential theory (some of which Einstein may well have utilised) but without being able to quite grasp their perinent inter-relations and so synthesizs these into the final correct causative arrangement. Einstein did have this ability.
233b. By about 1910, five years after Einstein's 'bombshell', the transition from the purely mechanical through a confused interim of duality to a final non-mechanical, electrodynamic model (hiding in those wings) - with the concepts of space and time being re-evaluated - was complete and generally accepted. It did appear to be a kind of 'new mechanics' (now called 'electrodynamics') - one that encompassed the old mechanics, within which had apparently always existed the minute and hidden effects or realities revealed by Einstein - albeit not of any immediate practical relevance at the typical slow speeds involved in 'everyday' activities (or within just one frame of reference?). But its implications for understanding reality were profound. Thus, time and space would have no absolute values (?beyond a given frame of reference or...? Note that when v = 0, space and time cease to vary; this may be viewed as a 'special case' at the extreme end (start) of velocity differences between different frames of reference) but otherwise would depend on one's speed relative to some other comparative frame of reference - as a proportion of the speed of light. Their values could be anything when thus determined. Only light's speed was certain, constant and absolute seemingly - whatever the speeds of any moving source which would always be relative only to some other (moving) reference. All else must adjust to prove consistent with the reality of this solitary constancy of motion from wherever observed or measured (as this is the only way information about our reality can be transmitted and perceived; see later). The substantive aspect of mechanics - requiring an ether medium for light (and a still one at that - for absolute space and time and positional concepts) - would be cast out. The 'new mechanics' would in fact now be seen as 'electrodynamics' - within which the mechanics of old, as only part of that (but now slightly 'adjusted'), would be subsumed and better understood. And, for bodies that moved at a larger proportion of that of light, several other important deductions would be hiding in those electrodynamic wings.
To Einstein's Answer (To 'The Problem')
FROM PLATO TO NEWTON
[The following serves here as an introduction to the Background section of the Problems Addressed by Einstein - commencing at paragraph 3 of that account - with which there may be some overlap. It can also be called up as a separate webpage of its own - from the Relativity Homepage.]
In the summer of 1684, Isaac Newton, then Professor of Mathematics at Cambridge, was visited by the future Astronomer Royal, Edmund Halley, to discuss current ideas on 'celestial mechanics'. Some 70 years earlier, Johannes Kepler in Germany had carefully analysed the mass of observations then recently made by the Dane Tycho Brahe on the movements of the planets and found them to have slightly elliptical orbits around the Sun, and not the circular ones previously assumed. The consistency of his findings led him to generalise three empirical 'laws' on this subject, although he was the first to admit he had no theoretical explanation to account for these findings - which overturned long-accepted views by Aristotle and Ptolemy. Some powerful celestial 'force' seemed to be responsible for such orbits but in the early 17th century, no one had a very clear conception of its nature or source. The underlying physical principles at work were largely unknown.
By the 1680s, however, it was being suggested by various contemporary thinkers that this previously unrealised motion of the planets might be due in part to a major force emanating from the Sun - one which appeared to weaken rapidly as the distance from the Sun to any planet increased. But no one had been able to affirm this idea with a rational explanation. Thus, during his visit, Halley asked Newton what he thought about the problem and was surprised to hear Newton say he had already sorted it out, having accounted precisely for Kepler's findings in terms of just such a force, centred on the Sun, which did indeed diminish rapidly with distance. He had given similar thought to the mutual forces that appeared to attract the Earth and Moon to each other (or at least kept the latter in its orbit). He claimed he had mislaid the crucial proof, but told Halley he could work it out again and send it to him. He may have wanted to clarify some aspects.
A few months later, true to his word, Newton sent Halley a short treatise in which he showed that the Sun's suspected force would largely account not only for Kepler's elliptical orbits but for his other empirical laws of planetary motion as well. Halley soon realised that this was a key to understanding the workings of the universe as it was then known. He urged Newton to publish at once but Newton felt it needed further development and so worked on certain implications over the next 3 years. In 1687, at Halley's expense, Newton's masterpiece - 'Philosophie Naturalis Principia Mathematica' - was finally published - the work on which modern science was to be based for over two hundred and fifty years. Einstein was later to say that Newton's Principia was "perhaps the greatest intellectual stride it has been granted to any man to make". It put into a unified, coherent form many disparate facts and principles that had accumulated from earlier times, but never truly understood. [One wonders if Halley appreciated that the 'workings of the Universe' implicit in Newton's explanations of Kepler's findings would in fact prove as comprehensive in application as it did? It would generalise to much more than 'celestial mechanics' alone.]
Newton said that if he saw further than most, it was because he was able to stand upon the shoulders of giants who went before him. The first of these was probably Copernicus whose ideas replaced those which had been accepted for over a thousand years - since the time of three earlier giants of ancient Greece. There follows a brief resume of the contributions of these several great thinkers on these fundamental questions.
1. Plato
The early Greek philosophers had views on most things and certainly a giant amongst these was Plato. In the 4th century B.C., he devised a scheme of physical reality in which the world was at the centre of a series of perfect circular spheres in which all heavenly bodies moved in circular orbits. This was an idealised world view based on the most perfect of forms - the circle and the sphere. It relied upon observation and conjecture - as does all science. It was a necessary beginning. And because Plato was so respected, this view held sway for many centuries. However, no basis was proffered for any forces that might underlie or account for such movement.
2. Aristotle
Aristotle developed Plato's scheme further - conceiving the universe as consisting of four basic elements or 'essences'; the earth at the centre, surrounded by water, then air and finally fire in ascending spheres. Natural motion occurred, he claimed, when these elements 'tended to find their natural place' in this arrangement. Thus earth, rock, minerals, etc sank (fell) through air or water while bubbles of air or other gases rose up through it and smoke and fire, in turn, rose through the air. All other motions were seen as violating these natural movements (with an implication of gravity) and occurred when some immediate, proximate cause impressed itself upon any object, as when a horse pulled a cart. Beyond these four elemental spheres were the celestial ones composed of a fifth or 'quint-essence' in which the heavenly bodies revolved around the world at constant speed in perfect circles. Thus, these early attempts to understand the nature of the universe, of its 'workings', focused essentially upon 'movement'. This is of course as should be expected; without movement, nothing happens and there would be nothing to enquire into or explain. But what causes such movement and what laws control it? This was the beginnings of 'classical mechanics' - the fundamental core of that most basic of sciences - physics.
Aristotle's conception was upset somewhat by the fact that careful observation showed that the planets didn't quite follow perfect circles but because Plato's view was still accepted, their orbits were said to be centred within yet other truly circular paths which seemed to correct for this anomaly.
3. Ptolemy (c100-170)
The Platonic-Aristotlean system of astronomy, with its corrective circles within circles (today called a 'Fourier series'), was further refined and codified by Ptolemy of Alexandria in the 2nd century A.D. in his classic book - the Almagest. This remained the accepted textbook of astronomy for fourteen hundred years - that is, until the time of Copernicus. With it, continued also the unquestioned acceptance that the basic motion here on Earth - falling - was due simply to things tending to find their natural place - towards the earthly centre of the universe. This geo-centric view of astronomy and mechanics accorded well with the teachings of the Christian church, centred in Rome, which had become the accepted authority in all such matters throughout Europe. God had somehow favoured the Earth as a true centre of all things. [Thanks to various Arabic scholars, much of the science of the ancient Greek and Eastern world was preserved and translated around 1000 AD at the library in Cordoba in Moorish Spain. Much of this, otherwise lost during the 'dark ages', was thus available for later thinkers in Europe.]
4. Copernicus (1472-1543)
The need for the awkward system of corrective circles could however be largely removed, said Copernicus, a brilliant Polish priest, if one placed the Sun as a fixed reference 'point' at the centre of the universe - rather than the Earth, or the so-called 'fixed stars' - thus relegating the Earth to being 'just another (moving) planet'. He maintained publicly that this adjustment was merely for mathematical convenience when working out positions and orbits of the planets (of concern to agriculture and navigation) - still of the ideal circular form - but this appears to have been a cover for his true convictions. Fearing the church might not accept his new conception of astronomy in which the Earth lost its primacy (written in 1530), Copernicus delayed publication of his famous book 'De Revolutionibus Orbium Coelestium' - until shortly before his death in 1543. It would eventually overturn our long held convictions about our assumed primacy in the universe as promulgated especially by the church.
5. Tycho Brahe (1546-1601)
Twenty years after Copernicus died, during which time little attention was paid to his revolutionary ideas or his book, young Tycho Brahe, a Danish nobleman with time to spare, became interested in observing events in the heavens - including solar eclipses and the conjunction of planets. He noticed that most tables concerned with these events were quite inaccurate, including even those of Copernicus. He continued to observe carefully and soon discovered a new star - something not expected in terms of the ancient schemes of Aristotle and Ptolemy. He was then given Royal support - first by his own King and later by Rudolph, the Holy Roman Emperor in Prague. His readings of Copernicus did persuade him that some revision of Ptolemy might well be required and so devised a new cosmology which, in contrast to Copernicus, returned the Earth to the centre. He conceded that the planets did revolve around the Sun, as Copernicus maintained, but that the Sun, with these revolving planets, then revolved 'en mass' around the Earth. It was a compromise between the cosmologies of Ptolemy and Copernicus. He made, without the aid of telescopes, hundreds of vital observations in an attempt to justify this new conception but did not possess the mathematical skill to analyse properly all his data. In all Europe, there was probably only one person with this ability:
6. Johannes Kepler (1571-1630)
Kepler was from a poor German family but displayed exceptional intelligence and won a scholarship to Tubingen university where he learned of Copernicus's alternative world view. He was convinced of its essential validity and by 1595 devised a model of the planetary orbits which best fitted most known facts about them. He noted certain regularities in the ratios of the diameters of different orbits, involving considerable calculation, and published his views in a book 'Mysterium Cosmographicum'. This was brought to the attention of Tycho Brahe who realised that Kepler had the mathematical skills to more thoroughly analyse his own data. He asked him to join him at Prague, which he did - in 1600. Kepler began organising Brahe's extensive data but was not quite persuaded that it supported the latter's conception of the universe. Brahe was soon to die - in 1601; But Kepler remained in Prague as the new Imperial Mathematician for Emperor Rudolph and began re-analysing Brahe's data - but more in terms of his own Copernican model. Over the next 25 years, he worked out his three empirical laws of planetary motion which proved reliable and consistent. Usefully, the telescope was invented during this time.
But early in this period, Kepler found great difficulty in fitting the path of Mars into its expected circular orbit. Prior to Brahe, the uncertainty in the measurements of planetary observations was of the order of 10 minutes of arc. Within this degree of error, Kepler found he could calculate the path of Mars as an approximately circular orbit, even after adjusting for the fact that Brahe's data had now, in Kepler's new scheme, to take account of its measurement from another planet (ie the Earth) that was of course itself in orbit. But now, with Brahe's more accurate observations, this degree of error was no longer tolerable and no amount of Kelpler's prodigious calculations could fit Mars into the exact circular orbit that he (following Copernicus) believed it had. He did find, however, that he could describe the path of the Earth itself as a virtual circle, if he placed the Sun slightly off the centre point of such an orbit. He tried to make a similar adjustment for Mars, but it's orbit would still not be persuaded into such a circle or even near circle.
At this point, Kepler apparently recalled the views of the ancient Greeks that the Earth, unlike the distant, 'true' planets, was not in their state of untrammelled perfection - since it supported organic life and showed change and decay over time. But if he was right and it too was truly 'just' a planet, maybe all of them displayed imperfections such that none of them need be constrained into the idealised Platonic or even Copernican circles after all. He then shifted the position of the Sun in relation to the orbit of Mars even further from the idealised centre - calling this new position its 'focus' (from the Greek for 'a place of fire') - and quickly concluded that the correct orbits for all planets around the Sun weren't in fact circles after all - but ellipses.
He published his new findings in 'Astronomia Nova' in 1609, when he showed that the orbits of all the planets, including the Earth, were indeed ellipses, with the Sun in each case occupying the position of an off-centre focal point. This assertion, based on detailed empirical analysis, became known as Kepler's first law of planetary motion - or the law of ellipses. His observations and calculations also discovered another consistency in the nature of the cosmos - namely that when the planet is further from the Sun in its elliptical orbit it moves more slowly than when it is nearer that focal point. And while it moves at this slower speed at its more distant path, it covers (sweeps across) a greater area between itself and the Sun, and conversely so when nearer the Sun. If the time for such coverage of these areas of arc is made equal, the areas covered would thus also be equal, despite the different speeds of the planet in these different parts of its orbit. This became known as his second law. Finally, ten years later, he expounded a third law - in his book 'Harmonices Mundi'. In this, he considered not planets generally but compared the size of particular individual orbits. He discovered that the greater the orbit, the slower a given planet travelled and that its speed was proportional to that orbit - specifically to a particular measure of the orbit (comparable to its radius) - raised to the power of 3/2. [This can also be expressed in other ways.]
Kepler summed up his own findings, and Brahe's meticulous observations, in a book of tables entitled after the Emperor the 'Rudolphine Tables' in 1627. This provided the scientific world with the first really accurate basis of astronomy and navigation and, significantly, an inspiration to later thinkers, especially Newton. Kepler realised that he could not account for his empirical findings on planetary orbits by any known general principles and that further work was required. He did suggest that some 'influence' emanating from the Sun may somehow be involved but did not attempt any quantitative analysis of this idea - to which Newton would one day apply himself. But first, there was a contemporary of Kepler whose contributions were to be just as vital; another shoulder-possessing 'giant':
7. Galileo Galilei (1564-1642)
Another early advocate of Copernicus was Galileo who, like Kepler, was of a mathematical bent and earned his early living by lecturing in this subject - at Pisa University. He became well known after his early discoveries in the sphere of 'forces' - in his laws of 'fall' and of 'pendular motion'. He believed in the essential validity of Copernicus (as did Kepler) but kept his views to himself, or expressed them ambiguously for fear of persecution by the church. Kepler sent him a copy of his book 'Mysterium Cosmographicum' in 1597 and in his thank you note, Galileo said he was pleased to find a friend in science who was also 'a friend of Truth' - apparently a disguised reference to Copernicus - if not to a more objective, independent approach to science generally. By the early 1600s, the church had put Copernicus's book on its banned list, claiming its main thesis to be erroneous. And common sense seemed to support the church; for Copernicus said the Earth spun on its axis - once every 24 hours - so that it was the Earth that moved (from west to east) and not the Sun - in the opposite direction, as it clearly appeared to do. Moreover, he said that the Earth also revolved, like the other planets, around the Sun - thus providing it with yet more alleged movement - of which again no one on the Earth was in the slightest aware. And, in any case, surely God put the earth at the centre of things.
If Copernicus was right, therefore, how could this be shown? This was the challenge Galileo was faced with. He had somehow to overcome a very compelling reality: If the earth really moved as Copernicus said, its speed could be easily calculated - to be some thousands of miles per hour (ie in relation to the Sun). Not only was no one aware of such alleged motion, but it should be testable by dropping some object from a high tower - such as the famous one at Pisa - and observing whether, as it fell under the influence of gravity (then still just a name given to Aristotle's natural motion where objects tend to 'find there own place'), the Earth with the tower attached to it, moved at speed its predicted distance for that period so that instead of the object landing near the foot of the tower, it should land some miles behind the 'new' position of the Earth and Tower. Of course, it didn't behave that way, but landed at the foot of the tower. Why was this? The church said it was because the Earth did not in fact move as the object fell - but was the solid, stationary centre of the universe around which everything else moved and on which things naturally fell towards its centre. How to disprove this? (And show that the object was already moving horizontally - with the earth - before it was released.)
Galileo decided the best thing he could do was to learn much more about falling objects generally - by measuring the details of such actions more precisely than anyone had previously thought necessary - as objects allegedly found their 'natural place'. By this means, he discovered that objects fell at the same accelerating speed whatever their size or weight - when one accounted for the effects of air pressure. The distance travelled increased per unit time as the square of the time and did so uniformly. This was his 'law of falling bodies' and resulted from one of mankind's first planned experiments as a way of gaining knowledge. [There was however an important early Arabic experimenter at Alexandria. I believe - ca 1000 AD.] Because bodies fell vertically so quickly and timing methods were then quite inaccurate, Galileo made use of a range of very smooth inclined planes down which polished metal balls were rolled. The times taken for their descent was thereby sufficiently slowed to allow accurate 'falling' measurements. He found that such balls would, after rolling down such a plane and displaying the acceleration that he discovered, then roll up another slope, with which it was in direct continuity, until it reached the same height as that at which it started. If the slope of the rising plane was gradually reduced, the balls kept rolling longer until eventually achieving their original height, even if this was very gradually over quite a distance.
One of the most fundamental and profound laws of nature was then discovered by Galileo. For he reasoned that after a ball had been given its initial impetus by rolling down such a sloping plane (through the energy available from the force of gravity), if the continuing tracks on which it was rolling did not then begin to slope upwards, even gradually, but remained absolutely level, the ball would (if friction and air pressure are ignored) roll on, and at a constant speed, forever! This was at variance with the ideas of Aristotle who felt that except for objects seeking out their natural place (as falling down), any such horizontal motion was only possible where there was an immediate (proximate) and oft-repeated force applied; otherwise it would stop. But it appeared that the initial force applied to a movable object remained with it (as a transfer of energy) permanently - unless opposed by an equal and opposite force. This finding or conclusion by Galileo was eventually to be formalised by Newton as his first law of motion - the law of inertia: 'Any object either remains at rest or continues in a state of constant motion (ie forever) - unless acted upon by some other force'. A force is thus that which opposes inertia and 'changes motion' - ie causes 'acceleration' or 'deceleration'. Much of physics follows from this basic law.
Amazingly, this fundamental principle, arrived at by Galileo through his methodical probing of such a basic phenomenon as falling objects, provided the clue to resolving both of the problems he started with - that is, why no one senses any movement of the earth despite its claimed speed of both rotation and revolution, and why a tower and the earth to which it is attached doesn't move several miles away from an object dropped from it while in free fall, before reaching that (fast-moving) ground. For the earth and everything attached to it, including not only the tower but the object itself (about to be dropped), are already all moving together - under the influence of their shared inertia due to whatever prior force initiated same. And after the object is dropped, this impetus, by the law of inertia, continues to act upon it also - throughout its period of falling - such that it remains next to the tower as both the object and the tower continue to sail horizontally through space together (despite being unjoined) each with their respective, pre-existing inertias. While the additional force of gravity admittedly does now act also - to pull the object to the ground - it does so quite independently, pulling it vertically down parallel to the (comparably-moving) tower without interfering with the on-going horizontal movement of the object as it, and the tower, continue to move in that shared plane in unison - ie with the Earth. Similarly, all sentient beings on earth, born as we are into our already fast-moving world, continue moving with it with no sense of varying acceleration or deceleration - under the influence of an unperceived inertia - quite unaware of our immense on-going speed of revolution (relative to the Sun) nor our rotation (relative to our own axis).
Galileo's two laws thus provided an exact explanation of what occurs when, for example, a cannon ball is fired. Once given its initial impetus by the exploding gunpowder, it should (if one ignores air pressure and friction) continue horizontally at a constant speed (law of inertia) - after its initial acceleration - for as long as it remains air borne; that is, until the law of fall (due to gravity) - acting as it does in the vertical plane - brings it to earth. He showed that the trajectory of such a projectile, long known to be of a curved nature, was in fact a compound of these two forces - in the form of a parabola (again ignoring air pressure). He seemed to sense that this form, like the ellipse noted by Kepler, being two of the four classical 'conic sections', could hold some fundamental significance in unravelling the secrets of nature. Galileo wrote up these thoughts in his book called 'Two New Sciences' in 1638. This was very prescient; Newton was to open up the power of science by applying exactly these two principles of Galileo - one of those indeed on whose high and broad shoulders he in particular was later to see further and more clearly than anyone of his day (or many a day).
8. Rene Descartes (1596-1650)
One more crucial advance was needed however before Newton could formulate his masterly synthesis. Galileo was not quite ready to abandon the almost unconcious influence of Plato; when he conceived his law of (horizontal) inertia, it was within the constraints of a global environment. An object would continue indefinitely in a given direction parallel to the earth's surface - ie globally and thus becomes not motion 'in a (truly) straight line' but in effect 'circular motion'. In France, Rene Descartes appreciated that the effect of inertia should be in a truly straight line only. It was in this form that Newton was able to formalise this principle as part of his famous set of laws of physics in 1687. Descartes, like Brahe, also attempted to re-cast the Copernican world view into something more acceptable to the Catholic church but it proved to be unsustainable in logic. The discoveries of Copernicus, Brahe, Kepler and Galileo were thus to be combined finally by Newton, but Descartes did put into place that important late piece of the puzzle - the necessary true straightness of inertia. [But in relation to what?]
Isaac Newton (1643-1727)
Much of Newton's work was done during the 1660s and '70s - both in Cambridge and at his home estate in Lincolnshire during several 'plague years' - when the curriculum in such a conservative institution was still dominated by Aristotle's conceptions of the nature of the universe. The work and writings of the five giants described above were not shared and disseminated with anything like the manner of science today or even during the coming 18th century. Such works, usually written in Latin (via those Cordoban translations?), had to be sought out and analysed within prevailing conceptions and limitations. We view all these matters from hindsight - having taken 'on-board' conclusions that in those days were often suspect hypotheses, with many gaps and uncertainties. By about 1685 or so, Newton was, with the help of Galileo's findings, ready to challenge and replace the Aristotlian world view with his own elegant solution to the unrealised potentialities provided by such forerunners. This came about when he sought to answer the question: Is there a set of general rules or principles of nature, concerning an interaction of forces, bodies and movement, which will adequately explain or account for Kepler's empirical observations of the motion of planets? And if so, will they not account equally for all other activity (motion) within the universe, both microscopic and macroscopic, including Galileo's laws of Fall and of the Pendulum? How to account for a parabolic trajectory of a canon ball as influenced by two forces acting at right angles and an elliptical trajectory of a planet - acting under unknown forces? Newton would apply a more precise quantitative analysis to Galileo's partly qualitative findings, based on a few simple motions, and then generalise his conclusions to all motion. This quantitative analysis took him many years of concentrated mental manipulations - the work of a true genius of immense mental powers and determination.
Newton was able eventually to reduce the ideas and empirical findings of the previous century, coupled with new postulates of his own, into a set of just three rules or laws by which such questions could be answered. The first concerned inertia: 'Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it'. The second law describes what happens if such a force does so act: 'The change in motion (thus arising) is proportional to the motive force impressed and is made in the direction of the straight line in which that force is impressed'. By 'change in motion', Newton apparently implied a change in the 'amount of motion' rather than just its change in direction, since this latter aspect is addressed separately in the second part of this law.
The prior motion of a body - before a new force acts upon it - is, in terms of the 'amount' of such motion, a function of its then speed (or 'velocity' if its direction is specified) and the amount (mass) of that body moving with that speed. Where this amount of a body's previous, on-going 'motion' is altered by a newly acting force, the change (say an increase) of that amount of motion is in this sense proportional to the (increased) magnitude of the new force so acting. This 'change in (amount of) motion' would today be referred to as an increase in 'momentum'. Implicit in Newton's second law is the very fundamental definition of that most mysterious of phenomena - 'force' - which is today measured in terms of 'mass x acceleration', where acceleration implies an on-going change (increase) in the velocity of a body - ie an increase in amount of motion or momentum. We still do not know what 'force' is; we only know what it does and thus can only define it in those terms; it is that 'influence' which does this: it causes a mass to accelerate or decelerate - ie to change its velocity - including, possibly, its direction. Certain changes of speed and direction (in the form of say an ellipse or a parabola) may arise through the joint application of two or more such influencing forces.
Newton's third law states: 'For every action there is always an equal reaction; or the mutual actions of two bodies upon each other are always equal, and are directed to contrary parts'. By 'actions' and 'reactions', Newton seems to signify the effects of the forces implied in 'bodies in motion'. This law too has its important implications. In particular, it recognises that all bodies and more obviously very large bodies such as planets in motion possess inherent sub-forces within and between themselves which conveniently cancel out such that each can be treated as though their masses were concentrated at a point at their respective centres. [This law needs further analysis on my part; it seems to have been formulated and its fundamental reality accepted in order that anomalies arising otherwise could be eliminated. The first two laws seem relatively self-evident in terms of their prior evolution but this third one is less obvious to me. How did he arrive at it? One will just accept it for now.]
These three laws are thus concerned with 'forces acting upon bodies' - and their resultant 'movements' - ie with the 'dynamics' or 'mechanics' of nature - and as such replaced the ideas of Aristotle on 'natural' and 'unnatural' motions in this fundamental sphere of science and nature. He complemented these three laws by specifying one major force - that acting between all bodies: the force of gravity - with its virtually immovable centre concentrated (in theory) at the centre of the Sun (although all bodies 'engender' gravity). He would use the second and third laws of Kepler to deduce two important properties of this fundamental force and then, in what must comprise the most profound and important of all his discoveries, Newton established the validity of his three laws and his conception of the force of gravity centred in particular on the Sun by showing that together they (and seemingly they alone) could precisely account for Kepler's empirically established first law - describing the elliptical orbits of the planets around the Sun - that empirical reality of nature that required explanation in terms of some more general principles of the universe of nature.
Newton didn't just 'think up' his 3 laws in isolation, therefore, and then recall that, conveniently, someone had already observed an aspect of nature on which such 'theoretical' general laws could be properly tested and hopefully verified. Rather, he was only able to postulate and/or deduce his laws in the first place on the basis of an intimate analysis of Kepler's prior empirical findings. In this sense, he didn't prove the validity of such elliptical orbits; their validity was already established empirically. But he was able to show that Kepler's first law was really a consequence of the latter's second and third laws since it was they on which the implication of gravity as a Sun-determined force was based and which would eventually be shown to account for the elliptical orbits. Only the general concept of Gravity and properties deduced for it, can do this. It is thereby accepted as a fundamental reality or principle of nature. It alone works - in accounting for known empirical data. [Much later, Einstein, in turn, would provide an even more general/fundamental way of accounting for gravity.]
As each of Newton's predecessors chipped away at the former Aristotlean world view, there was still left a buzzing confusion - without the remotest hint of how it might be replaced. Descartes tried but failed. Finally Newton worked it out and gave it a coherent, valid form; that 'greatest intellectual stride' referred to by Einstein. And the proof that he was right occurred when he was able to show that his carefully formulated general laws of nature, and only these (with gravity), would account exactly for Kepler's empirical law of planetary ellipses - which described how nature actually behaved. Their validity was thereby fully supported. Other fundamental trajectories - such as those of the parabola and hyperbola - could be accounted for in similar terms.
Newton's Famous Proof.
Newton demonstrated (ie accounted for) Kepler's ellipses by a geometrical proof which relied upon the dynamic features of his new laws and ideas on gravity as expressed in the Principia. In so doing, he utilised certain accepted and proven geometrical principles pertaining to conic sections much understood by himself and his 17th century colleagues. These are rather obscure today and thus, in a demonstration to a class of Physics undergraduates at the University of California in 1964, the famous American Nobel prize winner Richard Feynman reproduced Newton's 'proof' in which these more obscure aspects were replaced with a more contemporary geometric reasoning. This lecture was subsequently 'lost' for many years but was eventually re-discovered and, in 1996, published in a book entitled 'Feynman's Lost Lecture' - by David & Judith Goodstein, fellow physicists. Most of this present account comes from this excellent little book as does the following resume of the famous proof ; it combines elements from both the Goodsteins' own re-drafting of Feynman's lecture (as he apparently tended when talking to rush the explanation of some of his reasoning) and from Feynman's lecture itself. Most of it is quite simple and straightforward but the latter portion, based on Feynman's alternative reasoning, is more complicated and lengthy (and may be condensed here). He described it himself as 'elementary' in the sense that its logic was introduced (to the student) within its own development.
Feynman (and the Goodsteins) begin by pointing out that before proceeding to establish/demonstrate that a particular interaction of moving bodies and forces, as those asserted in Newton's laws, should result in (ie account for) a certain form of planetary motion - namely an elliptical orbit - it is necessary first to agree on just what an ellipse is; what its geometric properties are. If, then, the demonstration succeeds in establishing that the application of those laws results in the relevant bodies (planets) following paths of this agreed and understood form (as established by Kepler), the correctness or validity of those laws can be accepted with confidence. However, as one can not apply them to the actual planets, this must be done by means of geometrical proofs based on two-dimensional drawings and associated reasoning which rely on meeting such criteria concerning these accepted properties of ellipses.
Kepler certainly knew what an ellipse was, just as he knew what circles, parabolas and other sections taken across a cone were. These were much in vogue in his day. Feynman points out that there are several ways to create an ellipse and demonstrates three of these as a means of exemplifying the essential properties of an ellipse, properties which in effect define it - which is his first objective. The first and traditional way is by drawing an ellipse on paper using a pencil, string and two tacks. Before doing this here, it might be useful to first describe how to draw a circle by similar means. Using a loop of string with a pencil pulling the loop taut at one end and the other looped around a tack placed in the middle of a piece of stiff paper, a circle can be drawn with a radius equal to the length of the doubled string (or diameter equal to the full length of the loop) - say about 6 inches. As the pencil draws the line - eg in an anti-clockwise direction - at the top of its curve the line is, momentarily, moving from right to left. The force impelling it in that direction, at that moment, is the drawer's hand and associated musculature. That it doesn't continue to move in a straight line further and further to the left is due to another force acting equally continuously on it. This is the taut string constantly held at the centre of the developing circle by the tack. In a sense, this force is directed via the string back to that centre point, or at least it's in a certain balance with the muscular force. The combination of these two sets of forces acting on the pencil results in the drawn circle. Planetary bodies in nature could be seen as moving in a circular or near circular path due to the influence of two similarly directed forces.
If now we push in a second tack a little to the right of the first one (say half an inch), cut the string and tie one end to the original tack and the other to the new tack such that the total length of the string is the same as before and re-draw the 'circle', it will be seen that at the top of the curve, and at the bottom, the path of the curve is virtually identical to the first one drawn, being possibly very slightly inside the original lines at these points. But at the leftmost and rightmost points, the lines will be more clearly outside the original path. This is because the length of the doubled string going from the first tack to the rightmost point on the original circle and back to the second tack (to the right of the first and thus closer to the circle) is now longer than required (to copy the first circle exactly) and when the pencil pulls it out to its full taut length, it is half that extra half an inch longer - on each (right and left) extreme point and proportionately less as the line re-joins the top and bottom parts of this now not quite circular 'orbit'. This new shape is an ellipse. True, it is one that appears to be almost a circle but this is because its two 'focal points' have been chosen to be fairly close together. In fact, if they were to coincide exactly, the resultant 'ellipse' would be a true circle which, by this definition, would be but a special case of an ellipse - one in which the two foci exactly coincide.
If a cone is cut across parallel with its base, the resulting cross section would be a circle. If that cut were made at a slight angle to the base, the result would be an ellipse and no doubt there is some mathematical relationship between the distance chosen between the two tacks in the drawn example and the degree of slope of the sectioned cone for a given ellipse. [By some alchemy which this writer does not yet understand, there is a mysterious correspondence between the static geometric forms obtained when a particular shape in nature - a cone - is sectioned, ie a circle, an ellipse, a parabola and a hyperbola (from a 'double cone'), and these same forms when they arise as orbital paths by the interaction of certain forces (often two in number) with some body/object/particle moving in nature. There must be some correspondence between the dimensions or shapes of a cone and the angles at which forces act. This aspect is touched on further at the end of the proof.]
When the two lengths of string join the two, separated tack points, each can be viewed as providing the same kind of pulling force on the pencil back towards their respective 'centres' (focal points) as the doubled string did back to the single centre in the earlier example. That is, they constrain the path of the pencil in such a way that it describes a form known as an ellipse. The farther apart the two tacks, the more elongated the ellipse. Ellipses can thus be of many different shapes but with a basic, symmetric form dictated by the two-focal-point characteristic described. That is the fundamental characteristic of their nature and production.
Feynman then defines an ellipse secondly in a more abstract geometric way as the set of all points that can exist at points P which occur at the junction of two lines which originate at these two separated focal points such that their total, combined length remains a constant at all possible orientations of such lines when meeting at those points. A third and apparently equivalent definition is that light emanating from either of these focal points and directed to any one of such points P as together comprise the ellipse will be reflected back precisely to the other focal point - ie at the same angle. This implies that at every such point a mirror-like tangent can be assumed which allows just such a reflection. Feynman provides a proof of this equivalence which we may accept here without elaboration.
An additional, fourth property of the ellipse is then described which Feynman says is important in the proof and which he will need to use later in his demonstration. It is necessary because of the difficulty he had in following Newton's use of certain aspects of the conic sections referred to earlier. In place of this, he has devised an equivalent proof which relies upon this additional property of an ellipse - one which follows from the ellipse's foregoing property of tangential reflection of light. For this purpose, an ellipse is defined as the shape that results when a specified point on a series of tangents to a curve are joined - where such tangents arise as perpendicular lines crossing a line running between a point on an enveloping circle and a focal point within that circle, the centre of which serves as a second focal point. A line drawn from either focal point to such tangents if reflected at the same angle will meet the other focal point (as in the 3rd property described above). Feynman would later show that such an outer circle can be so constructed to represent a continuity of planetary velocity changes which, in terms of Newton's laws and gravity, can only have arisen from a planetary orbit which proves to be an ellipse according to the above definition or property. That is, if the changing speed of a planet as it traverses an elliptical path is represented geometrically it 'adjusts' the elliptical shape into that of a circle. The variation in its speed must reflect (correlate with) the distance between the two focal points of the ellipse.
Proving Kepler's Laws.
The foregoing provides us with sufficient definition and description of the ellipse and its properties to constitute the objective to be realised when one applies Newton's laws of dynamics to (geometric representations of) planets orbiting the Sun in ways described by Kepler. One may draw a circle or ellipse as static geometric forms whose relationships can be analysed logically but ultimately these must represent the paths of orbiting planets actually moving in three dimensional space under the influence of known astronomical forces.
Feynman begins, as did Copernicus, Galileo, Kepler and Newton, by accepting that planets, including the Earth, are indeed moving (in particular around the Sun) and that part at least of that movement can be accounted for by Newton's 1st law - concerning inertia. If planets, given some initial impetus, were influenced by no other forces, they should, according to the law of inertia, continue such movement in a straight rather than curved orbital line and continue so indefinitely. To be moving at all, as all planets certainly appear to be doing, implies that there must have been some initial force or impetus acting on them in the past, even briefly. For such motion to continue, however, no subsequent on-going or intermittent forces are needed; inertia itself (as a transfer and continuation of the initial impetus) is sufficient to maintain indefinitely their obvious movements across the sky - at least in that theoretical straight line - unless and until subjected to any additional force(s).
If the law of inertia provides a rationale for the continued movement per se of planets and specifically for that (masked) straight part of their motion, what can account for any other part - which results in the curved paths actually observed? Newton reasoned that whether its actual motion was circular or elliptical, the tendency for a planet to continue moving otherwise - in a straight line - would be appropriately offset from same and 'forced' into one or other curved path or orbit, if they were under the additional influence of a force pulling them directly towards the centre of its orbit (typically the Sun) - just as the taut string does in the drawing. One of Newton's crucial conclusions based upon the works of Kepler and Galileo was that the strength of such a force, directed towards the Sun, diminishes rapidly across space. However, this conclusion by Newton was apparently not vital for the initial part of his proof, which actually dealt with Kepler's second and third laws, although would become relevant and necessary in respect of the crucial proof of the first law - concerning the elliptical form of such orbits (discussed later). For now, all that was required was that there was a force - of whatever strength or variability - that was directed towards the Sun and which could account for a non-straight (ie curved) orbit. To account for Kepler's 2nd law, Newton reasoned that his own first two laws would provide an adequate explanation, if he also posited the existence of such a force, simply with the direction of action required, regardless of any changing strength over distance it may or may not be shown later to have.
Feynman follows Newton exactly in the first part of this geometric demonstration (proof). He depicts a planet travelling anti-clockwise around the Sun beginning at an arbitrary point A some distance to the right of the Sun (or rather its geometric representation). He argues that with no other force acting upon it except its own inertia, it would indeed continue along a straight line from this point A, a line that would be the tangent at that point if it were a circular or near circular path were some other force applying to account for such. After a given time, the planet would then be at a new position B and after another, equal period of time, with only inertia acting on it, it would arrive at a third position 'c', where the line A through B to 'c' would be a continuation of the straight line A-B. ie:
However, the actual trajectory of the planet is the outcome, says Newton, of a competition between the two forces acting upon it - its inertia and the pull of the Sun's gravity. Hence, as it attempts to travel from A through B towards 'c', due to its inertia, it is also being acted on continuously by the Sun's gravity, throughout that time. If the effect of the latter force is however only shown at the end of each period (ie the period depicted by A-B in the first instance), as though its action was 'saved up' ready to affect the trajectory over its subsequent interval (rather than as it actual does smoothly throughout), then the true position of the planet after the interval B-'c' must take account also of this added, on-going component of its motion, a component directed back towards the Sun. This part of the force is depicted by the line B-V. The effect of the combined action of inertia acting over the component B-c and the Sun's force in the direction B-V is compounded into a parallelogram B-c-C-V - with its diagonal B-C representing the resultant 'actual' path of the planet. [This is the first corollary to Newton's laws.] The correction in the 'inertia only' path is thus the distance c-C - which equals that of B-V to which it is parallel. Note that being parallel, its extension centrally would not meet the focal point at the Sun's centre, as that of B-V would, as it occurs further along the orbit.
This same analysis can be made for all subsequent equal intervals of time such that the path of the planet assumes that of a polygon A-B-C-D-E etc. Each time interval (A-B, B-C, C-D, etc) is the same although the distance covered in these may well differ (where the speed varies). While the position of the planet on any drawn orbit represents its position in space, the orbit can be divided up in terms of distance, time or velocity changes. If it's in terms of any one of these, the others would have to be imagined. In any case, if the equal time intervals are made increasingly shorter then, in the limit, the polygon becomes a circle (or possibly an ellipse; see later) due to the actions of both inertia and the Sun's force actually being continuous.
Newton (and Feynman) then proceed, from a platform of the above reasoning that a planet does indeed move and does so in a curved path (seemingly an orbit), showing Copernicus and Galileo to have been right - to prove Kepler's second law - that such moving planets 'sweep out' equal areas in equal times. Because their speed may vary according to their distance from the Sun, one might have assumed planets would sweep out a larger area in a given time when moving through their faster segments than when moving slower, but the correlation between that changing speed and the distance the planet is from the Sun (being faster the nearer it is it) means that the wider, faster sweep at the perimeter when near the Sun is associated with a shorter segment than where there is a narrow, slow sweep at the perimeter - but a longer segment - when far from the Sun. Thus, the two segments would be of equal area - as found by Kepler. However, in terms of just this 2nd law of Kepler, any variation in the speed of planets - either within a given orbit or in different orbits - as related to distance from the Sun, does not yet arise (as it will in respect of his 3rd law) and hence the validity of Kepler's findings about equal areas swept in equal times is apparently established sufficiently in terms of the following reasoning alone:
If one considers the triangle SAB (before the interval A-B is shortened at the limit into oblivion), then its area - that 'swept out' by a planet during the first time interval considered (A-B) - should equal that of the triangle SBC, swept out in the second, equal time interval B-C, and so on. This equality is proven by way of first establishing that SAB equals the triangle SBc - that swept out by a planet in the second time interval when one assumed no force was acting from the Sun - and then showing that this latter triangle also equals that of SBC, and thus that SAB equals SBC and all successive and comparable triangles swept out by a planet in equal times. Such equality of areas is shown on the basis of them having equal altitudes and a common base.
The relevance of the triangle SBc in this reasoning is fundamental and is shown as follows: A planet will sweep out equal areas of an orbit in equal times if: 1. It moves - at a constant speed - which Newton's 1st law accounts for, and: 2. It so moves in an orbit (rather than straight) - which Newton's 2nd law and his postulate about the existence and direction of a force from the Sun accounts for; ie it changes from a straight path only if another force applies and, if that new path is curved or an orbit around the Sun, such a force must be one that is directed towards the Sun; and 3. Its constant speed is not affected by that Sun-directed force (only its trajectory). If it can be shown that such a force is compatible with Kepler's 2nd law - ie that it doesn't reduce the otherwise constant speed of the planets (and their equal areas swept per equal time therefore), then both that law and the postulate concerning this directional aspect of the Sun's force are thereby verified. This is shown by the fact that the triangle SAB, which is under the influence of both inertia and gravity, is equal to (and thus not smaller than) SBc - which is affected by the former only. The strength of the Sun's force according to distance, and the consequent variation in the speed of the planet, are thus not necessary factors to consider in respect of Kepler's 2nd law which is thus proven by the foregoing geometric reasoning alone.
The fact that any of these equal triangles also equals the areas of those triangles associated with them (eg that of SBc) where no force from the Sun was assumed, has its own significance in physics in that it implies that the addition of the Sun's force, while affecting the trajectory from eg Bc to BC, does not affect the area swept out during the given time interval - an area that was later found to be proportional to a physical property called 'angular momentum'. This is affected only by forces acting across it, not by one acting perpendicular to it - as that of the Sun - which remains neutral in this regard despite its crucial effect on the planet's trajectory per se.
Having succeeded in proving Kepler's second law (that planets sweep out equal areas in equal times), the Goodsteins pause at this point to review just how this was done. As already noted above - use was made of: 1. Newton's first law (of inertia); ie once initiated, planets do move and would continue to do so - in a straight direction - given no other forces acting on them; 2. Newton's second law (any change in motion is in the direction of an additional impressed force) - ie planets actually move in a curved path - seemingly around the Sun; and 3. Newton's postulate that the source (and direction) of this additional force is thus (towards) the Sun. Nothing else. That is, to this point, there has been no need to invoke the idea or hypothesis that the strength of the force of the Sun's gravity changes (weakens) rapidly with distance (specifically as the inverse square of the distance). Kepler's second law is not dependent upon this suspected characteristic of gravity, nor on the speed of a planet. All that is needed as part of the proof is that there is a force of some kind pulling an otherwise straight-moving planet toward the Sun - whatever any variation in its strength across distance may or may not be - and that this force has no effect upon the areas swept perpendicular to this per given time - this being due solely to the constancy of the other factor effecting the otherwise straightness of its motion - inertia. Newton's first two laws, if correct, thus account for Kepler's observations of equal areas swept by a planet in equal times when applied in conjunction with a force acting on the planet that is directed (pulling) toward the Sun. The need and existence of such a force was deduced from the application of Newton's laws to the empirical findings underlying Kepler's 2nd law.
They then discuss just where the inverse square law and variations in distance and speed do prove relevant and how that law was derived. It was, in fact, deduced from Kepler's third law - which does concern the time different planets take to complete their orbits - being a function of a measure of their respective distances from the Sun - namely of the radius (or its equivalent) of their orbit - raised to the power 3/2. This measure, rather than the exact planet-to-Sun distance per se, is used as the latter is a variable value for an elliptical orbit, with the Sun at one of the focal points. The time for each orbit is thus proportional to half the distance of an orbit's semimajor axis (like its radius but along the longer axis) raised to this power of 3/2. Where one planet's orbit has a semimajor axis twice the length of another planet, its orbit will thus take 2 times as long, raised to the power of 3/2, to be completed; that is, the square root of 2 cubed (ie of 8) which = 2.83 approx - or almost 3 times as long. This law holds true whether the orbits are obvious ellipses or even if they were the special case of the 'circular ellipse' - ie where the two focal points coincide and both the semiminor and semimajor axes equals a circle's radius exactly. Thus, a distant planet, even if in a (large) circular orbit, would move more slowly than one with a (smaller) orbit nearer the Sun (whatever its shape). And if the larger orbit is, say, double the size of a smaller one, its speed is not just twice but almost three times as slow.
The proof that Kepler's third law (concerned with orbital time) allowed Newton to deduce that his related concern - the strength of the Sun's force - weakens as the square of the distance between it and a planet, occupies 12 closely argued pages of geometry by the Goodsteins . A key element in the argument, is the use not only of positional (spatial) diagrams, but velocity. diagrams derived from them. I shall not attempt to reproduce this proof here (any reader is recommended to read the the Goodsteins' book) but will simply repeat their closing statement that 'if the orbital time T for a planet is, as Kepler's third law asserts, proportional to its distance R from the Sun , raised to the power of 3/2, then that for a planet with an orbit twice that of another would (as mentioned above) be not twice but 2.83 times as long. The magnitude of the force of gravity of the Sun is proportional to R - divided by T squared - and since T = R to the power 3/2, then T squared = the square of the latter which = R cubed. Thus, the magnitude of gravity is proportional to R/R cubed, which equals 1/R squared; that is, gravity is inversely proportional to the square of the distance concerned. [Velocity diagrams are again used in the final part of the proof - ie concerning Kepler's 1st law; see below.] Thus, as with Kepler's 2nd law, this 3rd law appears to have been accounted for by the application of Newton's laws providing he could again apply a further deduced feature of gravity - on this occasion that it was a force which weakened - as the inverse square of the distance between the Sun and planet concerned. This was a deduction which Kepler's findings (regarding the relationship of a planet's speed with its distance from the Sun) pointed to, at least in Newton's mind, when he attempted to account for those findings in terms of his own 3 laws. It could now be argued that Kepler's findings regarding the orbital times being a function of the planet's distance from the Sun (raised to the power of 3/2) was necessarily the case because of the more fundamental reality of the inverse square law deduced by Newton (albeit later). [Was it at this stage that Newton required a method to calculate velocities at each point in an orbit - in order to determine the varying strength of forces acting throughout the orbit? And did this method not rely on his invention of the calculus??]
The Goodsteins usefully pause here again to review what's been achieved and where they hope to go. First, they re-state the difference between Kepler's three empirical 'laws' and those general principles/rules/laws of nature of Newton: Kepler's are generalisations based on samples of empirical data that he carefully observed and analysed. This is how nature actually behaves. Newton's are assumptions or hypotheses about the 'innermost nature of physical reality' - ie abstract principles - suggested to him by Kepler's specific empirical findings. That is, he concluded what were the most likely general causes of that carefully observed particular behaviour of nature. If the behaviour deducible from those assumptions continue to be observed in nature more generally, then the hypothesised principles of nature (true laws) may well be correct. While it may be theoretically possible for Newton or someone like him to have formulated his laws from more meagre clues from nature and to then predict planetary data and generalisations such as produced by Kepler, one feels that such hypotheses or laws would, in practice, never have been so formulated without the very empirical data they alone could subsequently account for. Thus, when demonstrating that his laws would predict elliptical orbits, Newton appears to have accepted the validity of such observed orbits as part of the rationale of formulating his universal laws.
In more detail, it is then pointed out that in order to determine the motions that planets would assume in accordance with his new laws (ultimately that they should indeed be elliptical orbits as described by Kepler's first law), Newton had first to discover more precisely the nature or properties of the force emanating from the Sun - ie gravity. Conveniently, he was able to do this (as shown above) thanks to Kepler's second and third laws combined with his own. With the nature of gravity thus revealed, he was then in a position to show that such a force of (the Sun's) gravity (viz: one directed towards the Sun and weakening as the inverse of the square of the distance between it and any planet), acting in accord with his 3 laws, would (must) result in the elliptical orbits observed by Kepler, as described in the latter's 1st law. This would provide the crucial final piece of the puzzle on which confirmation of the validity of all three of Newton's laws depended. The development of these steps is further elaborated by the Goodsteins at this point. [This seems to entail some repetition of preceding arguments.]
Thus, they re-state that Newton's first law of inertia accounts for the on-going constant speed of any moving body - its mysterious 'inner force', said Newton - and his second law, coupled with the directional postulate of gravity, then accounts for the noted diversion in direction at that constant speed as some added force - from the Sun - is applied over a given time - the change in direction being towards the Sun. But the change in velocity becomes more than just a change in direction when the variability of the strength of that force is also considered. Kepler's 3rd law indicates that velocity changes throughout the orbit reflect changes in a planet's speed in different parts of the orbit and are proportional to the varying strength of the force at those points. While gravity's effects may thus reduce (be weaker) with increasing distance, Feynman (and the Goodstein's) point out (oddly without any discussion or development) that it also depends upon the time over which it acts. The effect of a strength of two units of such force over one unit of time is the same as that of one unit of force over two units of time. Finally, because of Newton's third law (about which there is again little discussion), such a force (conveniently) acts overall as though its origin and its application were concentrated at the centre points of the bodies concerned. [Convenient, because this allows the geometric analysis and proof to proceed more efficiently; its validity and this efficiency may, of course, be a reflection of some reality or truth of nature.]
By the above means, Kepler's latter two laws provided Newton insight into the nature of the Sun's force of gravity - eg the constancy of its direction of action towards the Sun and the variability of its strength according to the distance to a given planet. How might a force of just this dual nature, when acting in accordance with Newton's laws, predict that planetary orbits should indeed be elliptical - as actually found by Kepler and described in his important first 'law' (and thereby verify Newton's laws, as well as explain why Kepler found what he did)? As stated above, the answer to this final crucial question was given by Newton in 1687 by a geometrical method that is too obscure in its methodology to be readily understood today. However, Feynman, having some insight into what Newton was about, produced an alternative line of reasoning which proves more acceptable and comprehensible today (although still rather complicated!).
In this alternative, Feynman replaces Newton's idea of dividing orbits into imaginary segments that take equal times with that of segments that make equal angles 'at' the Sun (described below). Newton's segments each have the diagonal of the parallelograms at their base that represents the combined effects of the two forces acting on the planet as it orbits the Sun (as described earlier). As these equal time intervals are made shorter and shorter, so the orbits assumes less and less the shape of a polygon (of those short base lines) and more and more that of the smooth curve of the actual orbit - one which sweeps out equal areas in equal times (with a line from the planet back to the Sun). Planets nearer the Sun thus move faster than those in orbits farther from the Sun AND (say the Goodsteins, following Feynman), any given planet whose orbit is an ellipse (or at least eccentric) will move faster in that part of its orbit nearer the Sun than when it is farther from it (an ellipse being one such orbit which implies such an off-centred position for the Sun). Newton (and Feynman) appear to proceed from this point as though stating "if we assume that the orbit IS an ellipse, then we would expect the following to apply and if we find it does, we may then accept (until, if ever, proven otherwise) that it is indeed an ellipse...".
In such an (accepted) elliptical orbit, the slow moving planet at its furthest point, while covering only a short portion (arc) of its orbit because of its slow speed, would sweep an area back to the distant Sun that is equal to that swept at a faster speed (over a greater portion of arc) where the distance of the two lines of that 'sweep' - to the near Sun - are necessarily much shorter - ie long and narrow = short but broad areas - ie as described above in conjunction with Kepler's 3rd law. In his alternative proof, Feynman replaces the concept of equal areas which have such contrasting lengths of distance with that of equal angles (at the Sun) which face or oppose conversely contrasting lengths of time. The common factor between these two variables is of course the velocity or speed of the orbiting planet. The equal angles concerned are those created with lines crossing the mid-point of the Sun which run between the orbit's perimeter and define segments of time taken by an orbiting planet at its two extremes - a short time segment nearest the Sun, when the planet moves fastest, and a longer one when furthest from it, when its speed is slowest.
The two opposing segments have equal central angles but sweep out very different areas. They thus take different amounts of time, as the times taken are proportional to the areas. For example, where the time taken is half that of a slower segment, the latter's area becomes 2 x 2 = 4 times as large as the former. (In the above diagram, the segments shown on the perimeter again represent distance and the different amounts of time taken to cover such must be imagined.) In general, the area of any segment and the time taken for a planet to cover that portion of the orbit is proportional to the square of the distance from the planet to the Sun. The areas covered and times taken thus increase rapidly with distance as, say, 2, 4, 16, 256, etc. It may be recalled that the strength of the force of gravity centred on the Sun decreases similarly rapidly with the inverse square of the distance - as 256, 16, 4, 2, etc. It may be appreciated that when analysing geometric data which have several mutually affecting variables such as time, distance, velocity, angles, velocity changes and areas, one can proceed by holding particular variables constant while examining the effects on others allowed to vary. Newton analysed Kepler's data by holding time intervals constant (among other things) while Feynman sought to hold velocity changes constant (among other things). Their ultimate equivalence is apparently assumed.
The planet's orbit is changed from that due to its inertia alone (straight with constant velocity) to some kind of curved orbit depending on the strength of the force from the Sun and the length of time that force is acting on it. This implies that the change in velocity is not dependent upon the distance the planet is from the Sun per se but rather on force and time alone - the weakening effect of the former at a long distance being exactly compensated for by the longer duration of action due to the latter and vice versa. Because these are a function of the areas swept out, the changing velocities for successive identical angles with the Sun are all the same - all the way around the orbit. If the angles through which the orbit moves are not equal, the changes in velocity will also vary accordingly and with them, the shape of the orbit - compared with that of a constant change in velocity. That is, from that of a circle apparently - to that of, say, an ellipse.
As Newton described a planet's orbit (in the earlier part of his proof), the time intervals of each segment were identical and the added force towards the Sun caused successive changes in velocity to all be in that direction, but with greater changes occurring where the orbit was nearer the Sun - causing a 'sharper' curve there (as with Mercury or any planet when nearer the Sun); that is, the velocity changes are all different in each successive equal time interval. This leads to an irregular polygon which, if the equal time intervals are made progressively shorter, becomes a smooth non-circular orbit - as an ellipse - in the limit. But in Feynman's scheme, the time intervals of successive segments are all different because they are based on equal central angles instead (the equality in one implying an inequality in the other and vice versa), so now the velocity changes are all the same all the way around the orbit, each occurring over equal angles of movement (but at different speeds) - though still pulling towards the Sun as required by Newton's 2nd law. In this case, when the equal angles are the variable which become progressively smaller, the regular polygon produced must now becomes a circle at the limit.
The proof continues with a very detailed analysis of the geometric arguments based upon relevant variables such as time, distance, velocity changes, etc. The Goodstein's point out that Newton reasoned his way towards his final conclusions by means of various lines of thought which only gradually formulated themselves into his final 3 laws. We have the advantage now of idealising this process into a more concise form. Thus, one can assume that his thinking went along certain lines which approximate the following: 'Because planets sweep out equal areas in equal times, I can apply the laws of inertia, force and action/reaction to deduce that the force of the Sun's gravity on a planet is directed towards the (centre of the) Sun. Then, because the time for a planet to complete its orbit is proportional to the 3/2 power of its distance from the Sun, these same laws allow me to conclude that such gravity diminishes in strength as the inverse square of that distance. Finally, knowing and applying this dual nature of gravity, the laws support the finding of Kepler that such orbits are ellipses. And hence, the validity of these three laws is fully supported and should continue to be accepted until and unless any other data should ever materialise to the contrary. For all practical purposes, they still hold today - three hundred years later. Only at the sub-atomic level and at or near the speed of light have the later discoveries of Einstein's relativity and Bohr's quantum mechanics required some adjustments to Newton's conception of the universe. In fact, it still holds true as a limiting case and as a most significant part of these more general models of nature.
Thus, the Goodstein's point out also that, importantly, Newton's laws "..explained not only the motions of the planets but almost every other phenomenon in the physical world as well". For they are concerned with how all matter behaves (moves) when acted upon by forces. Whatever happens in this universe entails the movement of matter by forces. While science is still seeking to understand fully just what both matter and forces actually are, knowing what they do, and how they interact, is a necessary and fundamental first step. The reorganisation of our understanding of the universe, both in space and here on Earth, as discovered by Newton, began with the proof of Kepler's elliptical orbits. As brilliant as his discovery of them was, the latter could not account for or explain them. Newton did - in terms of his three fundamental laws of nature.
P.S. We may ask 'How and where would Newton's ideas on absolute vs relative motion fit into the foregoing'? Were these ideas relevant to the developments in Physics from this foundation of mechanics over the next century? Also, we might usefully enquire more into the need for Newton to develop his conception of the differential and integral calculus - seemingly needed to ascertain the values of changing velocities/accelerations at precise points in any orbit in order to establish the quantitative strength and direction of the forces applying (by determining the functions that so apply) - and hence identify/confirm their apparent origins. This was apparently not possible by simply analysing the overall, orbit shapes/trajectories; it was the size and source of the forces acting point by point as the orbit changed that held the key to knowing that Force was a function of an accelerating mass (F = ma)and what was behind that. The integral calculus would allowed him to sum up the infinitesimal bits of the orbit of a planet and conclude that with the Sun's gravity acting on these, the orbits must be ellipses. Parabolas and hyperbolas are other possible trajectories (ie as per conic sections) and depend on the strengths of the component forces so acting. With the initial velocity given to all planets, they become ellipses. Objects given lesser initial velocities but still being acted on as well by gravity, as a canon ball, will show a parabolic trajectory. Is an exact circular orbit possible? Knowing the initial conditions (velocities/forces and positions/directions) of any and every object/particle it should in theory be possible to predict the future - but quantum mechanics claims this is not so; see later. In the meantime, the electromagnetic world as per Faraday and Maxwell, meant that pure classical mechanics alone was insufficient to account for all phenomena - a new synthesis of these was needed. These aspects too are touched on later - in the main account on Relativity.
Addendum
The following is added in the event it might provide (me with) some insight into the relevance of conic sections to the dynamics of moving bodies (as per the 'alchemy' referred to earlier):
The velocity diagram as used by Feynman in his proof (but used earlier by the great Clerk Maxwell in 1877, who attributed its development to another Scots genius - Sir William Hamilton) apparently always assumes a circular shape when the inverse square law of gravity and Newton's 3 laws of mechanics are applied to any object orbiting a much larger one. The shape of the orbit depends on where the origin of the velocity diagram is. There are 4 possible categories for this position and, intriguingly, these lead to 'orbits' which represent the 4 conic sections - ie the circle, ellipse, parabola and hyperbola. As Newton used a sequence of reasoning in the latter part of his original proof which entailed obscure use of these sections, it would seem to follow that Feynman's method may well have relied implicitly on the same essential logic - albeit approached from a different perspective.
Thus, if the origin coincides with the centre of the velocity circle then the two foci of the orbit coincide also and produce a circle - where the orbiting body's speed would remain the same throughout. Secondly, the origin can occur anywhere between the centre point and the perimeter of the diagram in which case the orbit becomes an ellipse. This will be almost circular, with the two foci relatively close, where the origin of the velocity circle is close to its centre point. When the origin is nearer to the perimeter however, a very elongated ellipse will arise - as in the case of many comets. In our solar system, most planetary orbits are near circular ellipses with the distance between the foci accounting for only a small percent of the longer diameter (between 1 and 20 % compared to the 97% for Halley's comet). Nevertheless, the speed varies in such orbits as per Kepler's laws. Presumably, Feynman (and likewise Newton) chose an origin in accordance with Kepler's actual findings (of varying speed and direction) which resulted in the elliptical orbits found and proved.
Thirdly, the origin could be outside the circle. This eventually produces a change in velocity which is in the same direction as the velocity itself - that is, the 'orbiting' body ceases to change direction but tends towards a straight line as it moves away from its focus. Its trajectory is thus that of a hyperbola beginning and ending in infinity (as it were) but apparently never having a zero velocity. Finally, the origin could be on the circle itself (thus exceeding even the eccentricity of an extreme comet), in which case, its trajectory becomes a parabola in which its velocity 'at the limit' does become zero. How such a body could in practice begin its journey (from such a zero velocity), I'm presently unaware!
[We may return here to Paragraph 3 of 'The Background to the Problems...' by Clicking]:
Return to Paragraph 3: Background
[Note: Any other Appendices can be placed here.]
2. 'Was the velocity of light essentially constant or did it vary (according to the type of its media and/or the motion of its source, medium or target)'? 