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One general remark, however, it is necessary to make and to bear in mind constantly throughout the discussion. When one is dealing with a particular problem in physics (or in anything else, for that matter), it must inevitably appear with a prominence, in relation to the whole subject, that it did not at all possess at the time of its origin. When I spoke of the state of physics at the beginning of the twentieth century, I meant the state of physics in so far as it was concerned with the problem which we are now discussing; but, in fact, only a small proportion of physicists were then interested in that problem. The great majority occupied themselves either with detailed applications of the familiar nineteenth-century physics to particular situations, or pursued the exciting new experimental discoveries associated with X-rays, electrons, radio-activity and such things, and left to a few specialists the discussion of the difficulties concerning fundamentals, confident that, puzzling and unexpected as these were, their solution would be forthcoming in due time in terms of traditional basic conceptions. The field of thought with which Einstein's theory is associated, though now it seems so outstanding, was then relatively obscure and insignificant. That being understood, I shall for simplicity take the liberty of referring to 'the state of physics', 'prevailing conceptions', and such things as though no other physical problem existed, except where it becomes necessary to emphasise the isolation of these considerations in order to explain the later difficulties that arose in grasping them when they emerged into prominence.

I begin, then, not with Einstein, but with the general state of the subject at the end of the nineteenth century. The basic difficulty that then faced physicists in their fundamental work was that the elementary principles of the two most comprehensive fields of thought - mechanics and electromagnetism - were incompatible with one another. Despite a few superficial difficulties, Newtonian principles appeared to be the inevitable foundation for all mechanical problems, while by this time Maxwell's field theory, as I have already remarked, appeared the equally inevitable foundation for all electromagnetic problems; and these two sets of fundamental principles were mutually contradictory. We need not consider all the discrepancies that appeared, but the most essential one, as we can now see, was that mechanics, but not electromagnetism, obeyed the relativity principle - what we now call the special or restricted relativity principle, relating only to uniform motions - that all states of uniform motion (including a state of rest) were equivalent to one another, so that, of any single body it was equally true to say that it was resting or moving with any uniform velocity that one chose: this indifference is expressed in Newton's first law of motion, that implies, in effect, that these states are all indistinguishable one from another. It was quite otherwise in electromagnetism. An electric charge at rest was surrounded only by an electric field, but an electric charge in motion was equivalent to an electric current and was surrounded by a magnetic field also. There was thus an observable physical difference between the two cases, so that motion in electromagnetism was not merely relative — the motion of one body with respect to another — but absolute — something that had detectable consequences quite irrespective of any visible standard of rest to which the motion could be referred. But since the very idea of motion implied such a standard, an invisible universal medium — the ether - was regarded as acting in this capacity, and, this, as we have seen, was made by Maxwell the basis of his theory and the indispensable physical medium for conveying light and electric waves.

For many years this appeared to contain no necessarily fundamental contradictions, because it was quite conceivable that motion of an electrified body through the ether might produce observable effects, while that of a non-electrified body — ordinary mechanical motion - might not. The ether was just another physical body, with properties that were certainly mysterious, but certainly something that could serve as a standard of rest to which the motion of ordinary material bodies could be referred. Indeed, the velocity of a material body through the ether could be determined by measuring its velocity with respect to light; for light, according to Maxwell's theory, was an electromagnetic phenomenon having a known constant velocity through the ether. Nevertheless, delicate experiments based on Maxwell's theory — of which the famous Michelson-Morley experiment was the chief - failed to detect any difference at all between the velocities, with respect to light, of bodies that were known to be moving with respect to one another. This led in-escapably to the conclusion that either the ether theory or the apparently self-evident requirement of Newtonian mechanics -that two bodies moving with respect to one another must have different velocities with respect to a third body - must be wrong. Notwithstanding the respect, almost amounting to veneration, which Maxwell's theory had by that time come to command, it seemed inevitable that it was the ether theory that had to be discarded. Michelson concluded his account of his experiment with the words: 'the hypothesis of a stationary ether is thus shown to be uncorrect and the necessary conclusion follows that the hypothesis is erroneous'².

Various attempts were made to avoid this conclusion by suitable amendments of the ether theory. I shall consider these later, but I have said enough of the general situation to indicate the circumstances in which Einstein's theory was born, and I shall now proceed to give an account of that theory. This is, in a sense, an interruption, because his approach to the problem bore little relation to that of anyone else, and it did not for many years make any impact on general thought. However, it is our chief subject now, and I have said enough of the main stream of thought to indicate the point at which it made its almost unnoticed intrusion. Einstein has left it on record that the Michelson-Morley experiment — and presumably the other experiments directed towards the same end — was not an important influence in the deliberations that led to the special relativity theory.³ We must, of course, believe him, and it is not difficult to do so, but there is no doubt that it was the chief preoccupation of other physicists working in this field and that Einstein's theory, if it was valid, did solve the problem that confronted them. I shall now attempt to describe what Einstein did in his 1905 paper, and show, I hope, that, although it was revolutionary and profoundly original, it was in no degree at all esoteric, mystical, metaphysical, or in more than a very elementary way mathematical, but was and is wholly intelligible to any normal person acquainted with the rudiments of traditional physics. Its reputation as the supreme model of the incomprehensible is wholly spurious.

Einstein's ultimate aim, of course, was to reconcile kinematics with electromagnetism, and his method of approach differed from that chosen almost automatically by others in that it proposed a modification of kinematics rather than of electromagnetism for this end. This was its most distinctive feature, and so little is it still understood that, as we have seen elsewhere (e.g. p. 143), it is still thought by most physicists that the theory can be vindicated by electromagnetic experiments. Since it was essentially and quite openly expressed as a reform of kinematics made for the very purpose of explaining such experiments, it can be tested only in kinematical terms. All that its success in electromagnetism, however extensive and various, can show is that, if the proposed kinematics is tenable, then it has achieved its object; it can do nothing at all to show whether the theory is right or wrong. Einstein divided his paper into two parts, which he called 'I. Kinematical Part'; 'II. Electrodynamical Part'. The whole essence of the theory is contained in the former, on which, for the reason stated, I should concentrate attention. If that is right, the rest follows without question; if it is not, its application to all electromagnetic phenomena, of whatever kind, is worthless, despite the profound impression it has made on the 'experimenters'.

The genius of Einstein is shown most clearly in his perception of an omission from Newton's system of kinematics that had not previously been noticed and that might, as he saw, provide an opening for a reform that would reconcile the two conflicting branches of physics. In such insight he was pre-eminent in his generation: his weakness, as we shall see, lay in his relative inability to follow up the implications of his insight and in a too great readiness to accept a promising starting-point as an achieved goal. He was rather like one of a body of men imprisoned in a dungeon, who alone perceives an opening offering a means of escape, but omits to verify that it does not lead merely to another part of the dungeon. However, it is Einstein's achievement, not his psychology, that is our concern, and what he perceived was that no one had thought of the necessity of providing some means of determining the time (instant) at which a distant event occurred. Physicists were agreed on the means of measuring the time (instant) of an event close at hand — in other words, they had adopted a standard clock - but if one said that an event at a distant, inaccessible place occurred at 4 o'clock, and another said that it occurred at 5 o'clock, no unquestionable means existed of deciding which, if either, was right. Moreover, according to all the knowledge available at the time. It was impossible to choose a means that did not depend on some assumption that it was impossible then to test. Accordingly, since it was often necessary in physics and astronomy to assign an instant of occurrence to a distant event, it was necessary to bring to light the assumptions that had unconsciously been made, for, as Einstein saw, it might be that the discrepancy between kinematics and electromagnetism lay in the falseness of those assumptions. If so, their abandonment and the adoption of others might bring about a reconciliation; and indeed, if it did so, that fact would itself be a strong argument for the correctness of the new assumptions, and one might expect them in due course to be confirmed when it became possible actually to transport clocks to places then beyond reach. Einstein not only saw this possibility but also, as he believed, achieved it. Let us now see how this was done.

The problem is to define a process for determining the instant of occurrence of a distant event - or, what amounts to the same thing, for setting a hypothetical clock, situated at the scene of the event, so that it is synchronised with our standard terrestrial clock. To understand the problem clearly, let us begin with a simple, purely terrestrial case. Suppose that our standard clock P, whose readings are accepted as giving the instants of occurrence of events happening at the place where it is, is fixed to the ground at a point A, and we wish to set a similar clock Q, at another fixed point B on the ground, in synchronisation with P. We might, of course, bring P and Q together at A, set them in agreement, and then carefully transfer Q to B, but it would be impossible to apply this process to inaccessible places, so we must devise an alternative method. Such a method would be to take Q to B, send something that we know travels at a constant speed from A to B, and immediately back to A again, and set Q so that its reading when the travelling agent (which for brevity we will call the signal) reaches it is half-way between the readings of P at emission and return of the signal. It does not matter what the signal is, or at what speed it travels so long as that speed is constant with respect to the relatively stationary clocks throughout the double journey; the result will hold good irrespective of these things.

This is most important, because it means that if any independent, uniformly-working clock, (which may or may not be similar to the clocks of our set X) travels from any one to any other clock of the set X, and the difference of its readings at the beginning and end of the journey is less than the difference between the readings of the clocks of the set X with which it coincides at the beginning and end of the journey, then the travelling clock is working at a slower rate than the clocks of set X. For example, if the travelling clock leaves a clock of set X when both read 1 o'clock, and reads 2 o'clock when it reaches another clock of set X which then reads 3 o'clock, the travelling clock is running at half the rate of the X-clocks, for it gives a duration of 1 hour for the journey while the X-clocks (which all run at the same rate) give a duration of 2 hours. It does not matter in the least that different X-clocks are used to give the instants of beginning and end of the journey, for all the clocks of the set give the same instant for every event. This at once disposes of McCrea's objection (p. 85) that, according to the theory, one cannot compare the rates of two single clocks with one another. The process of synchronisation was devised for the very purpose of timing events by clocks, which were at a distance from them, and indeed, merely to say that two single clocks are synchronised is to compare them with one another.

A second very important point is that the process of synchronisation prescribed by the theory is an experimental one, and therefore wholly objective. It does not matter who makes the experiment: if f he does it correctly he will get one unique result. The clocks are synchronised if the reading of the distant clock when it receives the signal is halfway between the readings of the standard clock at emission and return of the signal. It is, however, extremely common to read that, according to special relativity, clocks which are synchronised for one observer are not synchronised for a relatively moving observer. It is sufficient to cite as an example a letter from W. Barrett⁴ in the Nature correspondence following my discussion with McCrea (see Appendix), in which he claimed to refute my argument by the consideration that clocks which are synchronised for A are not synchronised for a relatively moving observer B. But it should surely be obvious that the readings of the clocks when they encounter the signal cannot depend in the least on who happens to observe them; their photographs could be examined afterwards by anyone at all and it is the relation between those readings alone that determines whether the clocks are synchronised or not. This is just one of the many evil effects of introducing 'the observer' into the theory, where he has no place at all, and in this case not even co-ordinate systems are relevant: if clocks are synchronised they are synchronised absolutely, for all observers and all co-ordinate systems.

It is worth while slightly to anticipate what is to follow by pointing out here that this, in fact, is another of the anomalies of the theory that might have been chosen to show its untenability. For, as we shall see, the theory requires that although clock-readings, which are events that can be observed, are absolute, the times (instants) at which the clocks have those readings vary with the co-ordinate system chosen. Thus, if two separated clocks are synchronised, the times (instants) at which they read 2 o'clock, say, will both be 2 o'clock in a co-ordinate system in which they are regarded as being at rest, while in a co-ordinate system in which they are regarded as moving (with the same velocity, of course), the times (instants) will not only be different from 2 o'clock but different from one another. Hence the theory requires that clocks which are synchronised by the process which it prescribes ('They are "good" clocks and are synchronised, which means that they show the same time simultaneously' - Einstein and Infeld, The Evolution of Physics, p. 190), nevertheless give different times (instants) for the same event. It is clear enough, I think, that these requirements are contradictory, and might have been used, as I say, to show the untenability of the theory, but I have thought it best to choose as the paradigm contradiction the one given on p. 45, since that puts the matter in the form of a question, and the absence of a reply to a question speaks more eloquently than the absence of comment on a statement.

Let us, however, return to our description of the theory. We have shown how two relatively stationary terrestrial clocks, fixed at points A and B on the ground, can be synchronised. But now suppose that the points A and B, instead of being fixed to the ground, are carried on two aeroplanes, the same distance apart, and travelling at the same speed in the same direction, which is that of the line joining them, so that they are relatively at rest but both moving uniformly with respect to the ground and to the air, in which we suppose no wind blows. Suppose, to complete the picture, that A is in the rear. In this case, unlike the former one, it does matter what kind of signal we use, and at what speeds it and the aeroplanes travel, for we shall get different results for different choices of these things. If the signal is a bullet fired from a gun at A, it will travel at the same speed both ways (we neglect any resistance offered by the air) with respect to A and B, but not with respect to the air or the ground. If, on the other hand, the signal is a sound wave emitted from a whistle on A, it will travel at the same speed both ways with respect to the air and ground, but not -with respect to A and B, for the speed of sound depends only on the properties of the air through which it travels, and not at all, like the bullet, on the velocity of the source from which it is emitted. The result will be that the reading which is halfway between the readings of A at emission and return of the signal will be different in the two cases — and, moreover, the difference will vary with the speeds of the signal and aeroplanes. Consequently, before we can set Q so that it synchronises with P, we must decide what signal we shall use and what its speed shall be.

In this case, of course, in which we have other means of synchronising P and Q so as to get the result most suitable for conducting terrestrial affairs, we have no difficulty in deciding that it is the bullet that gives the 'right' result, and its speed is immaterial however fast the aeroplanes are moving. But it is quite otherwise when we are dealing with great distances, for here there is nothing to guide us in making our choice other than the need to make our observations fit together in a rational way. This was what Einstein saw, and accordingly he proposed the choice that he realised would reconcile mechanics with electromagnetism. He chose light (or, in general, electromagnetic waves) as the signal, and assumed, on the basis of electromagnetic theory, that it travelled between any two points with a constant velocity c which, like the velocity of sound through air, was independent of the velocity of the source from which the light was emitted. But that meant, just as with the clocks on the aeroplanes synchronised by sound waves, that the synchronisation of the clocks (and therefore the instant, according to the standard clock, at which a distant event occurred) depended on the speed of the standard clock - i.e. on the speed of the Earth, for the standard clock of physics must be stationary on the Earth. Hence we must know the speed of the Earth through the medium in which light waves travel (which is the ether, according to the Maxwell-Lorentz theory) before we can assign a time (instant) to the occurrence of a distant event. But this we do not know; the Michelson-Morley experiment, like all others, had failed to determine it. Here Einstein made his second assumption, (it is usually called the first, and the assumption that the velocity of light is independent of the motion of its source is called the second, but that is immaterial), which was that there was no ether with respect to which velocity had any meaning, so that all states of uniform motion of bodies were equivalent.

A reference to Maxwell's fundamental paper - or even to the extract from it given on p. 132, will show that this was a direct contradiction of Maxwell's basic axiom, that there existed an ether with respect to which the velocity of a body had a definite, in principle measurable, value. Light consisted of vibrations in that ether, that had physical properties, which also were, in principle, determinable. What Einstein was proposing, therefore, was to retain the finite velocity of light without the existence of any standard with respect to which that velocity had a meaning. Light consisted of waves, with a definite length, frequency and velocity, in nothing; it was the grin without the Cheshire cat. As I have said, this theory made no general impression at all at first, so the apparent absurdity of this called forth no appreciable protest (though I remember hearing Sir Oliver Lodge satirising it before Einstein's general theory brought his special theory into prominence), but the fact that it could have been proposed at all is inexplicable until we remember the nature of the acceptance which Maxwell's theory was accorded at that time, which was so well expressed by Hertz — 'Maxwell's theory is Maxwell's system of equations'. The physical part of the theory was expendable; only the equations needed to be saved. Einstein saw a way of saving the equations, and did not consider it worth while to 'explain' light. Kelvin was not willing to explain it in terms of 'things that we understand less of: times had so changed that Einstein was satisfied to 'explain' it in terms of things that we understood nothing of — in other words, not to explain it at all. If his assumptions were granted he did save the equations, and when his theory ultimately made its general impact on the world, mathematics had so dominated physics that the non-existence of the Cheshire cat was regarded as a triviality; the grin remained, and all was well.

However, there was an apparent absurdity that did not escape such notice as was taken of the theory, and that was that its two postulates - that the velocity of the signal was independent of the motion of its source, and that there was no ether (i.e. nothing 'corresponding to the idea of absolute rest', as Einstein put it, thus ruling out all possible kinematical connotations of the word 'ether') - seemed to contradict, not some independent fact or idea, but each other. If the velocity of light was finite, and there was no ether with respect to which it had that finite velocity, the only apparent alternative was that each beam of light had that velocity only with respect to its own source, and this the theory denied. However, apparent contradictions were at a discount, but what the two postulates, taken together, did imply was that the time (instant) of a distant event had now to be granted an infinite number of different values, all equally 'right'. For suppose we wish to date an event on a distant star. We send a beam of light from the Earth to reach the star at the moment of occurrence of the event and note the readings of our clock at the instants of sending it out and receiving it back. The time (instant) of the event is then halfway between these readings. But now suppose that, at the instant of sending out the light, there is another clock, momentarily coincident with the Earth clock, which is moving rapidly away from the Earth towards the star, and that its reading at the moment of coincidence agrees with that of the Earth clock. It also sends out a beam of light at that instant, and by Einstein's postulate that beam will travel together with the beam from the Earth as though they were a single beam. But clearly the second clock will receive the returning beam before it reaches the Earth, and therefore show an earlier reading for return. Its halfway value will therefore be earlier, and its time (instant) for the distant event will also be earlier, than the Earth clock's.

Which is right? We cannot say, because there is no ether to enable us to ascribe the relative motion of the two clocks to one rather than to the other. The motion of the star on which the event occurs has nothing to do with the matter, for all the events considered in the theory are supposed to be instantaneous, so there is no meaning in speaking of their motion. If a number of bodies, coming from all directions, happen to collide at a point at a single instant, that is one event, and it cannot be credited with the motion of any one of the bodies. There is no alternative but to allow that the time (instant) of a distant event has an infinite number of values, all equally 'right'.

However, this implication of the theory, which at first seemed so unacceptable, contains no contradiction. When it is once realised that the time (instant) of a distant event stands in need of a definition, no reason can be given why that definition should not be such as to give it many values rather than one. Neither of Einstein's assumptions, or 'postulates' as he called them, is in itself illegitimate. The postulate that the velocity of light is independent of that of its source accorded with the requirements of the already existing electromagnetic theory, and the postulate that any state of uniform motion may be ascribed to a single body accorded with the requirements of the already existing Newtonian mechanics. Although, as I maintain, there are contradictions in adopting both postulates and still regarding clocks as instruments for measuring time (instants and durations), the multiplicity of values is not one of them. The ancient Hebrews took it for granted that each star had a unique name, which only Jahweh was entitled to give it. We regard the naming of stars as a matter of free choice and free definition, and having decided to name them we do not hesitate to call one bright particular star ? Canis Majoris, Sirius or the Dog Star without feeling that we are open to criticism.

But what we are not entitled to do is to suppose, at the same time, that any of our freely chosen names is valid and also that only Jahweh's unknown unique name is valid. Einstein was justified in freely choosing a definition of distant times (instants), provided that he then meant by 'time' only what the definition required. He was not justified in supposing also that time (instant) was what the previously accepted instruments called clocks would record in prescribed circumstances, unless experiment showed that that was so, and the necessary experiment was, and still is, impossible for practical reasons. His theory, in fact, consisted in the postulate that clocks would, in fact, give readings that accorded with his definition.

But that is just what they cannot do, as may be seen without the need of experiment. To take his own example, if there are two clocks, relatively stationary and synchronised, at points A and B, and then 'the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronise, but the clock moved from A to B lags behind the other which has remained at B'.¹ But it is one of the postulates of the theory that either clock can be 'the clock moved from A to B', for you can assign the letters so that B is the point at which they finally come together. The means by which the movement is brought about plays no part in the matter, for the theory can tell you nothing about what effect, if any, it produces; it tells you only about effects of motion, however produced. If A and B are points on the station platform, then 'the clock moved from A to B' at 60 miles an hour may be the one to which a force is applied moving it from east to west. If they are points on a train moving eastwards through the station at 60 miles an hour, the same force applied to the foremost clock reduces it to rest with respect to the platform, while the other moves from west to east at 60 miles an hour. Hence, according to Einstein's statement, the clock whose rate is slowed down is in the first case that to which the force is applied, and in the second case that to which the force is not applied. It is therefore clear that, however sound Einstein's reasoning may be, he cannot maintain his definition of time (instant) and still use clocks to measure it. He did not, of course, propose to discard clocks in favour of an arbitrary definition, so he proposed, as a theory, that clocks would conform to the requirements of the definition. We may sum up the whole theory in the following way:

As I have just shown, the experimental test is unnecessary because the theory itself makes the 'stationary' and 'moving' clocks interchangeable by pure thought, and so requires the impossibility that each clock works more slowly than the other. It appears astonishing that Einstein could have overlooked so simple a fact, until one realizes the mastery which mathematics had acquired over the intelligence of even its most illustrious practitioners, and the rich reward which the theory offered if it could be right. But apart from this, there are two things, already noted but bearing repetition, that may be specially stressed.

The first is the extreme simplicity and ordinariness of the theory, and its freedom from any reference at all to time (eternity) and from all cabbalism (except, of course, the difficulty of conceiving of light waves without an ether, but that is rather the absence of what one feels ought to be said than a difficulty in understanding what is). The second is that the theory is wholly kinematical, electromagnetism having nothing to do with it. It does introduce light, but only as something having a velocity; the nature of light does not enter the theory at all. The connection with electromagnetism is simply that it was the desire to justify the Maxwell-Lorentz theory (i.e. its equations), that led Einstein to choose the particular definition of distant times (instants) that he did choose. That is why his theory was able (supposing it to be tenable) to reconcile kinematics with electromagnetism and make the Maxwell-Lorentz theory, in Einstein's words, a 'plausible' theory.⁶ But the theory itself is wholly kinematical, and stands or falls by kinematical considerations alone. As I have repeatedly said, none of the supposed electromagnetic experiments and observations (including those connected with cosmic rays/can possibly do more than show that if the theory could be right, it would achieve its purpose, it would provide an effective correcting factor to the electromagnetic equations. But such experiments and observations, individually or collectively, are, as evidence for the truth of the theory, completely valueless.