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In this chapter I am going to assume that the disproof of Einstein's special relativity theory has been established. I make this assumption not only because I see it with a clearness that would have satisfied Descartes's criterion of truth - I know how deceptive such convictions, standing alone, can be Ч but also because of the universal failure to extract an answer to the simplest of questions. Only one sentence is needed to save the theory, and all I am offered, if anything at all, from those regarded as authorities on the theory are replies so vague and irrelevant as to be quite useless. Bondi 'does not feel able' to give the sentence asked for, but refers me to two published works of his where it is to be found (he does not say in what parts, and I cannot find it there). Temple tells me that I shall find a reply in Synge's book on the theory, but does not say where, and again I cannot find it. Synge himself does not mention his own book, but implies that the answer is in 'relativistic physics', which my expectation of life does not allow me time to explore. McCrea, alone among English speaking people, finds the question 'meaningless'. Science tells me that the answer appeared in that journal in 1957Ч8, but gives no reference and does not repeat the answer. So it goes on: the answer is everywhere but where it can be found.

The question then arises: in what state is physics left when deprived of this fundamental theory? Although some aspects of this question are fairly obvious, it is in the main a matter of more or less probable conjecture - unlike the question of the tenability of Einstein's theory, which is open to settlement here and now by pure reason. The theory is based on two postulates and a definition: if these are granted the rest follows logically, so there must be an incompatibility in these foundations. The postulates arc; (1) the postulate of relativity - that nature contains no absolute standard of rest, such as the Maxwell-Lorentz ether, for example, would provide, that would enable a unique state of uniform motion to be ascribed to a single observable body; (2) the postulate of constant light velocity - that the velocity of light, with respect to any chosen standard, has a constant value c which is independent of the state of (uniform) motion of the source from which it is emitted; i.e. that if, from two sources in uniform relative motion, light pulses are emitted in the direction of motion at an instant at which the sources are adjacent to one another, those pulses will thereafter remain adjacent and reach a distant point at the same instant. The definition' is that the time (instant) of an instantaneous event, occurring at a distance r from a clock which is accepted as a standard (r being measured by a standard scale at rest with respect to the clock) is given by subtracting r/c from the clock-reading when a light-pulse, emitted at the time (instant) and place of occurrence of the event, reaches the clock.

It should be observed, however, that if, according to pre-relativity kinematics, which in this respect was never questioned by Einstein, we define the velocity of a uniformly moving body as the distance it covers in unit time (duration), the definition follows from the second postulate, so the incompatibility of the theory lies between the two postulates alone. Our problem, therefore, is to determine which of these is wrong: possibly, of course, both are wrong, but at least one must be so.

The first postulate is not susceptible to definitive proof, for it is impossible to prove the non-existence of something that might conceivably reveal itself. In this respect the postulate of relativity is like the second law of thermodynamics: we know of no violation of it in the whole field of physical investigation, but the discovery of only one such violation would be fatal to it. Whittaker has called attention to the prevalence in physics of what he calls 'postulates of impotence' Ч i.e. postulates of the impossibility of something Ч and he points out that a large part at least of modern physics is based on such postulates.

The paradox that the whole of positive physical knowledge might be inferred from the unprovable assumption of impossibility deserves, I think, more attention than it has yet been given by philosophers of science, but this is no place to discuss it. We note only that Einstein's first postulate (not the whole of his theory), is a direct example of Whittaker's postulates, which has been not very happily expressed as 'It is impossible by any experiment to detect uniform motion relative to the aether.'² Ч not very happily, because it implies the existence of an ether with respect to which uniform motion is undetectable only for practical reasons, whereas Einstein's postulate, which he expressed as 'the phenomena of electro-dynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest', implies that the very idea of such an ether is excluded from physics. I think it is still true to say that no phenomenon has revealed itself that would disprove this postulate, so we may continue to use it in our theories so long as we do not forget that it is unprovable and might be false. All we can do is to keep our minds open to the possibility, when we meet with difficulties in interpreting experimental results, that we might have come across a fact that destroys it.

The second postulate, on the other hand, is directly testable by experiment or observation, and so is open to conclusive proof or disproof. Numerous so-called tests have been made, and have all given results, which have been held to prove the truth of the postulate. The failure to perceive that they are all invalid is, I think, one of the most remarkable examples of the paralysis of the intellect by which physics has been afflicted through the abandonment by the 'experimenters' of the use of their intelligence and their submission to the dictation of 'mathematicians', for the invalidity of these 'tests' is so easy to see when one looks at them with an unprejudiced mind that it could not possibly have been overlooked by anyone of even moderate intelligence had he used that modest gift.

The best known, and for long the chief, if not the only, 'proof of this postulate (it is the only one cited, for example, by Einstein and Infeld in their book. The Evolution of Physics, in 1938) was given by de Sitter in 1913.3 There are certain double stars whose two components revolve around one another (to use colloquial language) in a plane, which passes through the Earth. As seen from the Earth, therefore, there will be instants at which one component is approaching and the other receding, while half a revolution later - it may be a matter of hours or days - these motions are reversed. We may suppose for simplicity, without affecting the essence of the argument (though strictly speaking, of course, it is usually not quite true), that the system as a whole - the centre of gravity of the double star - is at rest with respect to the Earth, and that the maximum velocities of approach and recession of the components are both equal to v. The point to be decided, then, is said to be whether the two beams of light emitted towards the Earth by the components at an instant when one is approaching and the other receding from the Earth with velocity f, travel to the Earth with the single velocity c, or with velocities c + v and cЧv, respectively. Now these stars are very distant, so that the light takes a long time (duration) to reach the Earth - let us say 100 years, to fix our ideas - and let us suppose that the period of revolution of the components is 2 days and their distance apart 1 light-minute - quite normal values. If, then, light from both components travels through space with the same velocity c (as the postulate states), the greatest discrepancy that can occur in assuming that light from the two components, received on the Earth at the same instant, actually left the components at the same instant, will be 1 minute - the time taken by the light from the farther component to cover its distance from the other. This, in an interval of 2 days, is negligible, so the orbits drawn from the times (instants) of reception of the light will be practically identical with the actual orbits of the components. On the other hand, if the beams, issuing at velocities c + v and c Ч v, maintain those velocities throughout the journey, then, since v would be about 300 kilometres a second in the case under consideration, it is easily calculated that the beam from the approaching component would reach the Earth about 70 days before that from the receding component. One day later, however, the motions of the components would be reversed, so that the component issuing the winning beam on one day would issue the losing beam on the next, and during the interval there would be a continuously varying difference of time of travel of the two beams. An Earthbound observer would therefore see a hopeless confusion of light from the two components, bearing no resemblance at all to the orderly revolution that would actually be taking place. In fact, however, he does see such an orderly revolution. The conclusion drawn from this is that light must actually travel at the same speed c from both components at all times, as Einstein's postulate requires.

This is, I think, the most remarkable example in the history of science of the wish fathering the thought - with the possible exception of the 'proofs', following the Copernican heresy, that it was the Sun, and not the Earth, that moved, to which, in fact, this argument bears some resemblance. A finite velocity, of course - and it is not disputed that light in vacuo has a finite velocity - must be measured with respect to some standard, and if we do not accept the postulate, here regarded as on test, that the standard is empty space (Einstein's postulate says that 'light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body'), the only alternative with any claim to consideration is that the velocity c is maintained with respect to the emitting body. But all that de Sitter's argument disproves is that the velocity is maintained constant with respect to the Earth, for it is with respect to the Earth that the velocities c + v and c Ч v are reckoned, and surely no one in his senses would now maintain that the Earth provided a standard of rest for all the light in the universe. If we consider the same observations on the supposition that each beam of light moves throughout with velocity c with respect to its own source it is at once evident that after any time (duration) t, however great, each beam will be at a distance ct from its own source, and therefore the beams can never be farther apart than their sources, i.e. 1 light-minute. The maximum discrepancy, therefore, between emission-intervals and arrival intervals is 1 minute - exactly the same as on Einstein's postulate, so these observations tell us precisely nothing to enable us to choose between Einstein's postulate (which is, of course, that of the Maxwell-Lorentz electromagnetic theory) and the postulate that light keeps a constant velocity with respect to its own source (which was proposed in 1908 by Ritz as an alternative to the Maxwell-Lorentz view, but he died before de Sitter's argument was conceived).

How could such a simple fact have escaped notice for half a century? It was pointed out several years ago,4 and universally ignored - which is to me inexplicable on any other grounds than the universal inability of present-day physical scientists to believe that any criticism of special relativity that they cannot answer can proceed from anything but misunderstanding, which entitles them to ignore it. I do not think this would have been possible had not the unconscious purpose of the argument been to prove that the postulate was true and not to test if it was true. From die reactions of astronomers to whom I have put this criticism personally I have received the impression that their immediate reaction was one of incredulity that light could approach us with a continuously varying velocity with respect to the Earth - fast, slow, fast, slow, . . . from one component, and slow, fast, slow, fast, . . . from the other Ч though when pressed they cannot offer any reason why it should not. It is a modern form of the difficulty that intelligent sixteen-century thinkers experienced in believing that the Earth could be moving, and a most instructive one, for it helps us to appreciate how, in one climate of thought, what seems simple to anyone but a fool, may in another be almost impossibly difficult to men of high intelligence. 'I cannot find any bounds for my admiration,' wrote Galileo, 'how that reason was able in Aristarchus and Copernicus, to commit such a rape upon their Sences, as in despight thereof, to make her self mistress of their credulity.'

It is most interesting, however, to note that Ritz's hypothesis is entirely in keeping with the conception of Faraday - a man of imagination, if ever there was one, who commands our admiration in both the seventeenth- and twentieth-century meanings of the word - which Maxwell (pp. 132-3) wrongly identified with his own. If each (atomic) source of light is accompanied by a system of rays, proceeding in all directions, which move instantaneously with it, and light consists of vibrations transmitted along these rays at constant velocity with respect to them, then it naturally follows that the velocity of light is constant with respect to its source, however the source may move. More serious attention to this idea is long overdue.

Although de Sitter's argument may be regarded as, in a sense, the canonical observational 'proof of Einstein's second postulate, there have been a large number of others in more recent times, which it is unnecessary to consider individually because they all suffer from the same fatal defect - they involve a circular argument. In brief, though they take various forms, they all involve the assumption, at some stage, of the present electromagnetic theory of light. Now, as I have already pointed out, Einstein stressed many times that his special theory was devised to justify that electromagnetic I theory (or, to be strictly correct, to justify the equations of that theory, for the theory itself is meaningless without an ether of the [kind that Einstein discarded), including the requirement that Einstein's second postulate expresses. All that these 'proofs' can possibly do, I repeat, is to show that if we use the present electromagnetic theory of light, we must supplement its equations by those of the Lorentz transformation in order to get agreement with experiment. They cannot throw any light at all on me truth or falsity of either the electromagnetic theory of light or the special relativity theory.

To this class, I again repeat, belongs the argument concerning cosmic rays advanced by Sir Lawrence Bragg (p. in). It would be too complex a task to trace out in detail how the original calculations of the times taken by the particles in question to reach the Earth (which do not accord with observation) would be impossible without using the electromagnetic equations of which Einstein's second postulate is a necessary feature, but it is a matter about which there is no question or possibility of controversy. Sir Lawrence - repeating, of course, an argument that had previously been advanced and accepted by many - was contending that because the equations of special relativity succeeded in correcting the false requirements of the classical electromagnetic theory, special relativity must be true. This ignores both that the special relativity equations belong also to the very different theory of Lorentz, and that a true electromagnetic theory would need no correction. My article in the Appendix treats in a little more detail a much simpler example of arguments of this class - the experiment of Alvдger, Nilsson and Kjellman⁸ - but the mere fact that any argument for the truth of Einstein's second postulate in which the 'sources' arc hypothetical particles and not observable bodies, necessarily requires, in some form or other, the assumption of an electromagnetic theory that itself implies the truth of the postulate - that fact shows that the argument is circular and therefore invalid: further analysis of it would be redundant.

It should be remarked, however, that the double star argument of de Sitter, which I believe is the only one free from this circularity, has fairly recently been questioned by J. G. Fox⁸ on grounds quite independent of the simple consideration I have already given. Fox's criticism depends on highly theoretical considerations involving what is known as 'the extinction theorem', which, in effect, would nullify any test of the postulate in which the light whose velocity is measured passed through any transparent medium at all after emission from the source. What the extinction theorem seems to amount to is the proposition that light passing through a transparent medium is absorbed by the particles of that medium and re-emitted by them, so that the velocity of the source of the emergent light is really that of the particles of the medium, and not that of the original source (it is suspected that the components of the double star in de Sitter's argument are surrounded by a gaseous envelope which does not share their orbital motion). Fox concludes that 'the material considered as evidence [for Einstein's second postulate] in the past has been shown to be possibly either irrelevant or inconclusive. This is a surprising situation in which to find us half a century after the inception of special relativity'.

For the present, however, since we do not know, all we can do is to consider the alternative possibilities. If the first postulate Ч the postulate of relativity - is wrong, men Lorentz's theory would seem me only way of reconciling mechanics and electromagnetism. This would have many advantages, for it would save the electromagnetic theory which has so many successes to its credit, but would present the problem of working Lorentz's ad hoc hypotheses into the theory - and, of course, that of reconciling it with quantum phenomena which appear so difficult to make compatible with a wave theory of light. It would restore the ether, with all the unsolved problems, which it presented to the nineteenth-century physicists. This would be decidedly unwelcome to physicists, but mat is merely a matter of fashion; those physicists - and they are many - who now regard belief in the possibility of an ether as a superstition have simply not learnt the lessons of history, which teach us that discarded ideas have a way of returning to favour. The title of the editorial article in Nature reproduced in the Appendix, 'Don't bring back the ether' (can one imagine Lockyer or Gregory heading an editorial on Rutherford's early hypotheses, 'Don't bring back alchemy'?) shows, however, how sadly we have unlearnt the lessons of history through the influence of our uncritical acceptance of the uncomprehended relativity theory. Nevertheless, the great difficulties, which a return of the Maxwell-Lorentz ether would bring, in view of quantum phenomena, must be set against the advantages, and these are most formidable.

A failure of Einstein's second postulate would, of course, have the opposite effect of converting the successes of the present electromagnetic theory of light into serious problems. Their seriousness, however, might be less than appears at first sight. It is often overlooked that the Maxwell-Lorentz theory rests on a very limited experimental basis, which we tend to imagine much larger than it is because we misinterpret theoretical requirements as facts of observation. This is particularly so with regard to velocities: we think we have reached velocities approaching that of light when we have, in fact, only inferred them theoretically as possessed by theoretically inferred particles. Our actual experience of directly measured velocities Ч the experiments, for instance, of which a celebrated one by Rowland is the chief, on the basis of which we connect a current of electricity with the movement of an electrostatically charged body by a particular formula Ч is confined to a range of velocities very small indeed compared with the velocity of light. It is conceivable that a modification of the formula by the introduction of a factor v(1 Ч v²/c²) Ч a modification far too small to be invalidated by any existing experimental evidence - might convert the equations of Maxwell's theory into a form invariant to the Galilean instead of the Lorentz transformation, and permit the velocity of light to depend on that of its source in the way imagined by Ritz. This, of course, is a mere speculation, but it is certainly worth exploring by those experts in the theory of electromagnetism.

From the point of view of astronomy and cosmology, however, an acceptance of Einstein's first postulate, the postulate of relativity, has the most profound effect on current ideas, the failure to recognise which can again be attributed only to the complete state of confusion which exists between the requirements of Einstein's and Lorentz's theories. This is so, no matter whether the second postulate fails or not, and it is most evident in the phenomenon of the Doppler effect. This, considered purely as a fact of observation, quite apart from its interpretation, is simply a relation between (1) the relative motion, along the line joining them, of a source of light and an observer, and (2) the spectrum of that light as seen by that observer (for 'observer' here we may, of course, substitute 'spectrometer', for the effect can be recorded wholly by instrumental means, and the record may or may not be observed; if it is, all who observe it, however moving, will see the same thing; the effect is wholly objective). If source and observer are approaching one another, the spectrum is shifted in one direction (which, without prejudice, we may describe as towards the shorter wave-lengths) and if they are receding from one another, it is shifted in the opposite direction - with respect, in each case, to its position when source and observer are relatively at rest.

Now on Lorentz's theory, in which the light consists of waves travelling through the ether, this effect has different causes according to whether it is the source or the observer, that is moving. Suppose for simplicity that at first both are at rest in the ether, at a distance r apart, and then one starts to move towards the other. If the source moves its light-waves are compressed, but the compressed waves do not reach the observer until a time r/c after the movement begins, so he does not see the spectrum shift until after the lapse of that time (duration). If, on the other hand, the observer moves, he at once receives the unaltered waves, but with a greater frequency, so he sees the spectrum shift immediately. The shift is the same in amount in both cases because, since the velocity of the waves through the ether is unchanged by the movement, being a property of the ether alone, and is equal to the product of the wave-length and frequency, a decrease of wave-length and an equivalent increase of frequency produce the same effect on the spectrum. The only observable difference, then, between a movement of the source towards the observer and an equal movement of the observer towards the source, is that in the first case observation of the effect is delayed and in the second case it is immediate. Synchronised clocks at the positions of source and observer would therefore reveal unquestionably which of the two has moved.

But now, suppose that, as on Einstein's theory, the relativity postulate is true. Then there can be no observable distinction between the movement of the source towards the observer and that of the observer towards the source. Hence, either observation of the movement is immediate in both cases, or it is delayed in both cases. Now we know from experience which of these alternatives to choose. We know that, with respect to a distant star, the orbital motion of the Earth round the Sun causes an alternation of approach and recession (on which, of course, a continuous movement between the star and the whole solar system may be superposed, but that would not affect the oscillation of the observed stellar spectrum caused by the Earth's orbital motion). The Doppler effect corresponding to this is observed to synchronise with the orbital motion in every case, so we know that, when the observer moves, the effect is seen immediately, just as on Lorentz's theory. But that means, according to the relativity postulate, that the effect must also be seen immediately when the star moves, otherwise there would be an observable distinction between the two cases. (Indeed, the very phrases, 'when the observer moves' and 'when the star moves' are a concession to ordinary modes of thought; on the relativity principle, the only proper description in each case would be 'when the relative motion occurs'). And this is true, no matter whether Einstein's second postulate is true or false, for it follows wholly and inevitably from the first. Therefore those who accept the first postulate, no matter whether they accept the whole of the special relativity theory or not, must accept that every Doppler effect observed is a result of a motion occurring at the time (instant) of observation, no matter how far away the source of light may be, and if they measure a velocity from it, that velocity must be that which exists when the observation is made.⁸

It is obvious that questions of the highest importance to cosmology arise from this consideration. It implies, for instance, that the red-shifts now observed in the spectra of the distant nebulae (if they are indeed Doppler effects, which, though it is the universal conviction, is a most hazardous speculation) denote velocities existing now, and not millions of years ago. But that is only one of the numerous examples of the general failure to appreciate the impossibility of accepting both the relativity postulate and assumptions concerning motion and gravitation that arc meaningless without a Lorentzian ether; it is the old story of identifying the quite incompatible Einstein and Lorentz theories and using whichever happens to be convenient at the moment.

There is much talk at present, for example, of 'gravitational waves', which associates the mutual gravitation of two bodies with waves travelling with velocity c between the bodies. But if gravitation is relative Ч if, for example, the gravitation between the Sun and the Earth is not something uniquely exerted by one (say the Sun) to which the other responds, but a relation between the two which cannot exist without both - then which way do the waves travel? If they travel both ways, forming standing waves, what does the velocity c mean? Nevertheless, not only have such waves been held to be possible, but also experimental observations have been interpreted as evidence of their existence by physicists who, at the same time, claim the validity of a relativity theory of gravitation.

The fact is that we know far less about these things than we imagine. The more one reflects intelligently on the nature of light, matter and gravitation, the more he realises that there arc problems connected with them that are quite insoluble in terms of our current notions. But we no longer reflect intelligently on these things. We have not only left behind Dale's conception of a science that accepts nature's answers humbly; we have cast off even the degree of humility needed to question her, and manfully overcome the fear of prejudice and preconception that so restricted science in the days of its bondage to truth. Professor Hoyle has plainly stated his advocacy of the process of telling nature what to do instead of looking to sec what she does.⁹ After uncharitable observations had compelled an abandonment of one of his confident speculations, he thus described how the speculations arose: 'The struggle has been to invent a form of mathematics operating in the manner customary in physics, namely, starting from an action principle.' But his failure in the struggle left him undaunted, and was quite powerless to drive him back to what used to be the manner customary in physics: on the contrary, he announced his continued devotion to 'the motive underlying the investigation, the avoidance of a universal singularity, rather than an experiment in the laboratory'.