PART IITHE SPECIAL THEORY OF RELATIVITY
CHAPTER XIIIEINSTEIN’S SPECIAL THEORY OF RELATIVITY
HOWEVER unsatisfactory, for the numerous reasons already discussed, Lorentz’s theory might appear, it constituted for some years the only possible explanation of the negative results of all electromagnetic experiments performed on the earth’s surface. But in 1905 Einstein published a paper on the “Electrodynamics of Moving Bodies,” a document destined to prove one of the most epochal events in the history of human thought. In this paper, all the cobwebs of electrodynamics were swept aside.
The essence of Einstein’s position was that the difficulties which had beset the study of electrodynamics (we have mentioned only a small number of them) had arisen from our retention of the stagnant ether as a fundamental frame of reference; but that in view of the anomalies this attitude had brought about, the time had come to submit it to a critical analysis. After all, we knew little or nothing about the ether; why then start by stating it to be an absolute medium floating in space and hampering thereby all future progress? Why state that velocity through the ether must have a physical significance, then under the evidence of the negative experiments proceed to postulate complicated hypotheses in order to explain away the absoluteness we had ourselves introduced? Would it not be simpler to adopt a more cautious attitude, deriving knowledge from experiment rather than trying to reconcile experiment with a series ofa prioribeliefs which, for all we knew, might be totally erroneous?
If with Einstein we follow this line of argument, we must assume that the large number of negative experiments prove conclusively that velocity through the stagnant ether or through space is physically meaningless, not only from a purely mechanical point of view, as was the belief of classical science, but fromeverypoint of view. If we accept this relativity of the ether and space for Galilean motion as a fundamental fact of nature, holding for all manner of experiments, our past difficulties are seen to be of our own making. We had endeavoured to discover that which was meaningless, and then blamed nature for tricking us and hiding it from us. Instead of saying that velocity through the ether appeared meaningless because it was meaningless, we had complicated matters by saying that velocity appeared meaningless but of course was not meaningless.
Quite apart from the negative experiments, Einstein lays special stress on another type of phenomenon. Thus, whether we displace a magnet before a closed circuit or the closed circuit before the magnet, thecurrent induced in the wire is exactly the same in either case, so far as experiment can detect. That which appears relevant is the relative motion between magnet and circuit; the respective absolute velocities of magnet and circuit through the ether, which are of course different in both cases seem to be totally irrelevant.
In view of the importance of the question, let us mention another example. We remember that when discussing electrical phenomena in the first pages of the preceding chapter, we mentioned that an electrified body was surrounded by an electric field of force, whereas a current was surrounded by both an electric and a magnetic field. Subsequent experiments performed by Rowland confirmed the view that a charged body in motion generated the same electric and magnetic fields as a current flowing along a wire, so that we had to agree that a charged body in motion developed a magnetic field by the sole virtue of its motion.
Now here again we are in a quandary to understand what is to be meant by motion. Classical science assumed that motion in this case meant motion with respect to the stagnant ether, and that an electric current was constituted by the rushing of electrons through the ether. Numerous difficulties beset this view. Owing to the earth’s motion through the ether, every charged body on the earth’s surface would constitute an electric current; so that around every electrically charged body a magnetic field should be present. Yet experiment failed to detect this magnetic field. Was it due to the crudeness of our experiments? This solution was scarcely possible; for if we displaced our charged body before a magnetised needle (Rowland’s experiment), the needle was deflected, proving that experiments were perfectly able to detect the magnetic field when it was truly produced. It appeared as though the type of velocity that constituted a current was not velocity through the ether at all, but velocity relative to the recording instrument or, more generally, to the observer. Once again, the only type of velocity which appeared to have any significance in nature was relative velocity, and never velocity through the stagnant ether or absolute space.
Hence, Einstein postulated hisspecial principle of relativity, according to which Galilean motion through the ether or space is meaningless. This principle is, as we see, merely an extension of the Newtonian mechanical principle to the case of the ether, or in other words to electromagnetic and optical experiments.
What is called thespecial theory of relativityconcerns the rational consequences that must follow from the special principle. These consequences may be anticipated as follows: If Galilean motion through the ether is meaningless, the laws of electrodynamics must remain invariant in form when we change our Galilean system of reference. But this implies that the space and time transformations which the co-ordinates of all points undergo, when we change systems, must be given by the Lorentz transformations.
In Einstein’s theory, however, the significance of the transformations is entirely different. It will be remembered that in ordinary language these transformations implied the FitzGerald contractionand the slowing down of time. In Lorentz’s theory these modifications arose as a result of a real velocity through the ether; and though it was impossible for the observer in the moving frame to detect their presence, yet in spite of all they were physically real. In Einstein’s theory, on the other hand, velocity through the ether being meaningless, the modifications arise only as a result of the relative motion of one frame with respect to the other, and are thus due to conditions of observation and not to any intrinsic change. For instance, if in any two Galilean frames originally at relative rest, two identical clocks and two identical cubes are placed, and if then the two frames are set in relative motion, either observer would discover as a result of his measurements that the other man’s clock had slowed down and that his cube had become flattened in the direction of the relative motion. Nothing would have happened to the cubes and clocks; only the conditions of observation would have been changed.
Expressed mathematically, this means that the variablewhich enters into the Lorentz transformations now stands for the relative velocity of one frame with respect to the other, and no longer for velocity through the ether. In this measure the transformations of Einstein’s theory, though identical in appearance with those of Lorentz’s, are far different in meaning. To avoid confusion, the appellationEinstein-LorentzorLorentz-Einstein transformationsis accordingly often made use of.[45]
There is still a further difference, a most important one, distinguishing the implications of the transformations in the two theories. In Lorentz’s theory there was a privileged observer situated in the frame at rest in the ether. In Einstein’s theory there is no such privileged observer; for since a privileged state of rest in the ether is meaningless, all observers in Galilean frames are on the same footing. Hence, Lorentz’s distinction between the true time of the frame at rest and the distorted, local or electromagnetic times of the frames in motion through the ether loses its significance. Henceforth, all these so-called local times given by the Lorentz transformations constitute the true times lived, sensed and experienced by the respective observers in their respective Galilean frames.
There being no longer any reason to subordinate one frame to another, the descriptions ofall phenomenain terms of space and time are on the same footing inall Galilean frames; and there is no longer any reason to follow Lorentz in limiting the validity of the transformations to the sole case of electromagnetic phenomena. Henceforth, these transformations appear of universal application, holding for mechanics, for the composition of velocities, and indeedfor the entire universe of physical phenomena. This belief is not dependent on the fact that, matter being constituted electronically, all mechanical experiments must be regarded as electrodynamic experiments viewed microscopically. Rather is it due to the fact that these changes in space and time are absolutely general. They arise from the relative motion of the observer and not from the peculiar microscopic constitution of the phenomena observed.
The method of presentation of Einstein’s theory we have followed up to this stage is not the one usually adhered to, but it has appeared preferable to proceed as we have done in order to bring into prominence certain important features which are obscured in the customary presentation (these features will be better understood later). We will now fall in with the usual procedure.
As Maxwell proved many years ago, a necessary consequence of the laws of electromagnetics was that light wavesin vacuoin the stagnant ether should travel with a velocity of 186,000 miles per second. This was the celebrated law of light propagation of classical science. Now we have seen that the laws of electromagnetics (and with them their immediate consequence, the law of light propagation) held only for privileged observers, those situated in any frame at rest in the stagnant ether. As referred to all other Galilean observers situated in frames moving through the ether, an application of the classical transformations showed that the equations of electromagnetics, and with them the velocity of light propagation, would be modified. But since the essence, of the relativity of Galilean motion is to deprive any particular Galilean observer of his privileged position, the laws of electromagnetics must now maintain the same form for all Galilean observers. Hence the law of light propagation, which is a mathematical consequence of these electromagnetic laws, must likewise hold in exactly the same way for all Galilean observers. Whence the new result: “Light waves must travel with the same invariant speed of 186,000 miles through any Galilean frame when this speed is measured by the observer located in the frame.” It is this statement which Einstein has called theprincipleor thepostulate of the invariant velocity of light.
If we combine this principle with the relativity of the ether for Galilean motion and endeavour to construct the transformations which will be compatible with these two principles, we are again led to the Lorentz-Einstein transformations.[46]This should not surprise us since, as we have seen, the principle of the invariant velocity of light is but a direct consequence of the invariance of the electrodynamical equations; so that the transformations ensuring invariance will be the same in either case.
In short, we see that without appealing directly to the equations of electrodynamics, we can deduce the Lorentz-Einstein transformations merely by taking one of their consequences into consideration, namely, the invariant velocity of light, and combining it with the relativity of Galilean motion. From a mathematical point of view, this procedure is the simpler. Hence, Einstein posits as his fundamental assumptions:
1. The relativity of space or of the ether for Galilean motion, or, more simply, the relativity of Galilean motion without particular reference to the ether or to space.
2. The postulate or principle of the invariant velocity of light.
This procedure followed by Einstein offers a number of advantages. In the first place, as we have said, the mathematical discovery of the Lorentz-Einstein transformations is considerably simplified. Secondly, as the classical law of light propagation, though a consequence of the laws of electromagnetics, insusceptible of being tested by direct experiment without any reference to the laws of electromagnetics, there is no necessity for dragging in these highly complex laws. In fact, even had the laws of electromagnetics been unknown, the relativity of velocity and the classical law of light propagation are all that would have been required to construct the theory. Hence, from the standpoint of mathematical elegance, the procedure is certainly one of extreme simplicity. Furthermore, inasmuch as in Einstein’s theory the Lorentz-Einstein transformations are of general application and do not concern only electromagnetic phenomena, it is preferable to avoid conferring on them an exclusively electromagnetic aspect. This aim is achieved by deducing them from a general law of propagation, such as that of light.
On the other hand, this method of presentation, by appealing to the propagation of light, is likely to confuse the beginner, who is apt to assume that Einstein postulated the invariant velocity of light as a hypothesisad hocfor the sole purpose of accounting for Michelson’s negative experiment. In this way the entire theory is supposed to hinge on Michelson’s experiment, and the critic assumes that could Michelson’s experiment be explained in some other way, Einstein’s theory would be obviated. This assumption appears all the more natural to the critic as Michelson’s experiment is, nine times out of ten, the only negative experiment he is acquainted with. The result is that he assumes Einstein’s theory to be nothing but a wild guess grafted on one of those highly delicate experiments where the chances of error are always great. As a matter of fact, by reasoning in this way, the critic loses sight of the entireraison d’êtreof the theory. It is safe to say that even had Michelson’s experiment never been performed, Einstein’s theory would have been forthcoming just the same (though, of course, had Michelson’s experiment given a positive result, enabling us to measure our velocity through the ether, the theory of relativity would have been untenable).
This explains why, in presenting the theory, we started by showing how it arose as a necessary consequence of the irrelevance of absolute velocity in all electromagnetic experiments, hence sprang from the invariance of the equations of electrodynamics, which expressesmathematically the aggregate of all the negative results. If the reader has grasped the significance of these Lorentz-Einstein transformations, we may proceed to examine certain of their particular consequences, and to show how, quite apart from the negative experiments, the theory of relativity has cleared up a number of obscure points in our understanding of electromagnetics.
For instance, we mentioned that a charged body at rest was surrounded by an electric field of force, whereas the same body in motion (or an electric current) was surrounded both by an electric and a magnetic field. Ampère had given a formula describing the distribution and intensity of the electromagnetic field surrounding an electric current of any given intensity. But this formula was purely empirical, and it was felt that we should have been able to anticipate the existence of this electromagnetic field and derive an exact expression of its disposition and magnitude by purely rational methods. These hopes were disappointed; for there appeared to be no rational connection between the field developed by an electrified body when at rest and its field when set in motion.
Contrast our ignorance on this score with our ability to understand the nature of other problems attendant on relative motion. For example, a monochromatic source of light at rest appears yellow, whereas, when moving towards us with a sufficiently high speed, it appears greenish. But there is nothing mysterious about this change in colour; we could have foreseen it, knowing what we do of the wave nature of light. The situation was much more obscure in the case of electromagnetics.
Einstein’s theory solves the entire problem. Consider the simple case of a charge in uniform motion. We have said that owing to its motion it develops a magnetic field (just like a current), in addition to its electric field. But in Einstein’s theory velocity through the ether is meaningless; hence there is no such thing as a charge in uniform motion in any absolute sense. If we were to rush after the electrified body and accompany it in its motion, it would cease, according to Einstein, to be a moving charge and would become a charge at rest in our frame; but then its erstwhile magnetic field would necessarily have vanished, the electric field alone remaining. We must assume, therefore, that the appearance of the magnetic field arises only because we have changed our Galilean frame of reference by passing from one fixed with respect to the charge to onein relative motion.
Now, the Lorentz-Einstein transformations tell us how our space and time measurements change under these circumstances; and by applying the transformations to the equations of electrodynamics we are able to ascertain how an electric field which is purely electric when viewed from one frame should appear to us when viewed from another Galilean frame. Proceeding in this way, we do in fact find that the electric field of the electrified body at rest will appear as an electromagnetic field when the body is set in relative motion. Likewise, the precise mathematical formula for the new field is obtained, provingincidentally that our classical empirical formula was only approximate. Thus a rational justification for the appearance of a magnetic field round an electrified charge in motion is finally obtained, and this field is seen to be a direct consequence of the variations in those fundamental space and time forms of perception—variations which are expressed by the Lorentz-Einstein transformations.
In exactly the same way a magnetic pole in motion develops an electric field around it in addition to its magnetic field when at rest, and it is this phenomenon that gives rise to the electromagnetic induction on which we base our generators and dynamos. Here again the Lorentz-Einstein transformations throw complete light on the subject.[47]
In a general way the transformations show us that a field which appears to be exclusively electric or exclusively magnetic in one Galilean frame will appear to be electromagnetic in another frame, thereby compelling us to recognise the relativity of electric and magnetic forces. We shall see in due course that this relativity of force is general.
Let us consider another type of phenomenon which is also explained by the transformations. We refer to the Fresnel convection coefficient illustrated by Fizeau’s experiment. Experiment proves that the ray of light progressing through the running water is not carried along bodily by the water; it lags behind a little. Lorentz who, though he had discovered the transformations, did not recognise their general validity, sought to explain this phenomenon by postulating a suitable electronic constitution for the water. But Einstein by merely applying the transformations, without having to appeal to our highly problematic knowledge of the precise electronic constitution of matter, found that they anticipated Fizeau’s result with marvellous precision; for according to the transformations, velocitiesdo notadd up like numbers, as they did in classical science. It follows that the velocity of the light with respect to the tube must necessarily be less than the velocity of the light through the water plus the velocity of the water in the tube.[48]
Consider again the FitzGerald contraction. Here Lorentz thought it permissible to apply the transformations; but owing to the slight difference in their significance in his theory, he concluded that a body in motion was really contracted owing to its real motion through the ether. Although the observer carried along with the body could not detect the contraction, yet it was physically real and would be observed by the observer at rest in the ether. A similarinterpretation would have to be placed on the slowing down of phenomena. In Lorentz’s theory the difficulty consisted in accounting for an identical contraction manifesting itself in exactly the same way for all bodies, soft or hard. Lorentz again appeals to the electronic and atomic constitution of matter and has to take into consideration elastic forces.
With Einstein the explanation is simple. The contraction is due solely to a modification in our space and time measurements due to relative motion, and is completely irrelevant to the hardness or softness of the body, whose atomic or electronic structure need not be taken into consideration at all. In much the same way an object appears magnified under the microscope, and this magnification is independent of the body’s nature.
In short, the modifications are due to variations (as a result of relative motion) in our space and time measurements and perceptions, and in every case they are irrelevant to the microscopic constitution of matter. We see, then, that so far as all these curious modifications are concerned, Einstein s theory does not require any particular knowledge of the microscopic constitution and hidden mechanisms that are assumed to underlie matter. Herein resides one of the principal advantages of Einstein’s theory over that of Lorentz; for we know very little about the mysterious nature of electricity and matter, and were all progress to be arrested until such knowledge was forthcoming, we might have to wait many a day without result.
One of the chief difficulties attendant on an atomistic theory such as Lorentz’s was due precisely to this interpretation of observable effects in terms of invisible ones about which practically nothing could be known and where hypothesesad hochad to be invoked at each stage. As for the mathematical difficulties, they, of course, grew in proportion to the complexity of the hidden mechanisms which we had to postulate. Einstein’s theory is thus a return to universal principles induced from experiment, and in this respect is analogous to the physics of the general principles which appeared in the course of the nineteenth century. There again such comprehensive universal principles as those of entropy, of least action, of the conservation of energy, mass and momentum, took the place of the hidden mechanisms whereby the atomists had endeavoured to account for observed phenomena.
These periodic swings in the scientific viewpoint have always been necessitated by the continuous advance of knowledge. Both attitudes are fruitful and have yielded important results. In the present case Lorentz had progressed about as far as it was possible to go in his speculations on hidden mechanisms, and a theory such as Einstein’s was the necessary antidote to the increasing difficulties which were hampering further developments.
We have now to consider certain important consequences of Einstein’s theory which affect our traditional concepts of space and time. The FitzGerald contraction is no longer a real physical contraction, as itwas assumed to be in Lorentz’s theory. It no longer arises as a result of a perfectly concrete motion of a body through a stagnant ether; the stagnant ether with respect to which velocity acquired its significance having been banished by Einstein. The FitzGerald contraction is now solely due to the relative motion existing between the observer and the body observed.
If the observer remains attached to the body, there is no contraction; if the observer is moving with respect to the body, or the body moving with respect to him, the FitzGerald contraction appears. If the observer once more changes his velocity relative to the body, the FitzGerald contraction of the body will likewise change in magnitude. Nothing has happened to the body and yet its length has altered. Obviously, physical length is not what we once thought it to be; it can in no wise be immanent in the body, since a body has no determinate length until the relative motion of the observer has been specified. A length is therefore but the expression of a relationship between the observer and the observed, and the two partners of the relationship must be specified before the length can have any meaning.
In the same way the colour of an opal has no meaning. It is red from here, green from there, blue from elsewhere, and yet the opal has not changed. It is our position with respect to the opal which has changed, and the colour of the opal is indeterminate until such time as we have specified our relative position. In other words, length and the colour of the opal both express relations and not immanent characteristics.
Similar considerations apply to the slowing down of time. Duration, and time are mere relatives, mere expressions of relationships, and have no absolute significanceper se. This does not mean that the duration we sense is a myth; for as our consciousness always accompanies our human body wherever we go, we always experience the same flow of time. All that is implied is that this rate of time-flow cannot be credited with any unique significance in nature, and a comparison of time-flows characteristic of various Galilean frames will reveal differences in the rate of flow.
We have mentioned elsewhere a further illustration of relativity, when discussing electric and magnetic forces. We showed how it was that an electric field, as such, was indeterminate; how according to the observer it would present itself as a purely electric or as an electromagnetic field. As all these conditions of observation are on the same footing, there is no sense in distinguishing between apparent fields and real fields, or apparent lengths and real lengths, or apparent durations and real durations. All these concepts, of themselves, are mere phantoms, to which substance can be given only when the conditions of observation are specified.
A certain number of lay philosophers have been confused by this continual reference to the observer in Einstein’s theory, and have assumed that all things occurred in the observer’s mind, the outside common objective world of science playing no part.[49]But thisextreme idealistic interpretation cannot be defended.
The word “observer” is a very loose term and does not necessarily mean a living human being. We might replace the observer’s eyes by a photographic camera, his computation of time-flow by a clock—in fact, all his senses and measurements by recording instruments of a suitable nature, whose readings any man situated in any frame could check later. The results would still be the same.
Now it might be feared that, with this vanishing of the absoluteness of such fundamental forms of perception as duration and distance, the entire objective world of science would sink to a shadow; and without a common objective world, science would be impossible. However, we need have no fear of any such catastrophe; for, as will be explained in later pages, a new common objective world of space-time will take the place of the classical one of space and time. But even at the present stage, without appealing to space-time, we can see that objectivity is not denied us for the following reasons:
When two different Galilean observers measure the same object, or time the duration of the same phenomenon, their computations will differ according to the rules specified in the Lorentz-Einstein transformations. It follows that the observers may infer that they are discussing the same objects,notwhen their respective measurements agree according to the classical standards of absolute distance and duration, but when they agree with the new standards set by the Lorentz-Einstein transformations. Thus a definite criterion of objectivity is still possible, though its form differs from that of classical science. So in spite of the indefiniteness of the concepts on which classical science was founded (space, time, force, mass), Einstein’s theory does not deprive us of the possibility of conceiving of the existence of a common outside world.
Enough has been said even at this stage to show that Einstein’s theory cannot be considered a mere mathematical dream. The extraordinary difficulties with which classical science was confronted owing to the negative results of the experiments we have mentioned (and to numerous other problems) have disappeared. With them have vanished the miraculous compensations which Lorentz was compelled to invoke in order to explain these negative results. The complete relativity of Galilean motion explains all our troubles. Nature is no longer mischievous, but the ether or space is relative for Galilean motion. We had failed to recognise this relativity which was staring us in the face; in so doing we ourselves were the creators of our difficulties. Yet rather than abandon the classical concepts of space and time, physicists in general refused to follow Einstein. To-day criticisms have subsided (on the part of the great majority of scientists) as experiment after experiment has confirmed Einstein’s previsions. The majority of experiments, however, concerned the consequences of the theory and notits foundations. The experiments of de Sitter and Majorana have filled this gap by proving that a ray of light always passes the observer with the same invariant speed regardless of the relative velocity of observer and source.
Now one of the most important criticisms that has been directed against Einstein’s theory is that it deprives us of the possibility of conceiving of an objective ether. There is not the slightest doubt that Einstein’s theory compels us to abandon our conception of the stagnant ether of classical science, with reference to which motion could be measured. But this is not quite the same thing as holding that the theory banishes the ether entirely. Nevertheless, upon first inspection, the fact that whatever our Galilean motion may be, experiments conducted in our frame will always yield exactly the same results, would seem to relegate the ether to the realm of ghosts, making it a useless hypothesis. If this were the case we could no longer conceive of electromagnetic fields and light rays as expressing states of the ether, but should have to regard these fields as constituting independent realities of some new category, differing from matter but susceptible of existence in space without the support of a carrier, or without being the mere manifestations of its states. However, in the general theory which we shall discuss in the second part of this book we shall find that the ether is reinstated in the guise of the metrical field of space-time. But as this new ether has only its name in common with the stagnant Lorentzian ether, there does not appear to be much advantage in retaining the older appellation.
If, then, we wish to emphasise the great distinction between the classical view and the relativistic view, we must say: “According to classical science, the speed of light waves, and of electromagnetic waves generally, is constant in all directions with respect to the stagnant ether, hence also with respect to that particular observer who happens to be at rest in the stagnant ether. According to the relativistic point of view, the speed of light waves is constant throughout empty space when measured by any Galilean observer; that is, by any observer in any non-accelerated frame” (such frames being recognised by the absence of all centrifugal or inertial pushes and pulls).
For the present we are in no position to predict what would happen if the observer, instead of being posted in a Galilean frame, were situated in a non-Galilean,i.e., accelerated or rotating, frame. All the statements we have made up to this point concern only Galilean observers. Such are the restrictions which the special principle and the special theory of relativity impose upon us. It is most important to understand this fact, as many of the criticisms levelled at Einstein’s theory are due to a failure to grasp the point. As the theory now stands, acceleration and rotation remain absolute and are therefore excluded from the special principle of relativity, which refers solely to motions in space that are relative. These are Galilean motions.
Perhaps a definite illustration will make these points clearer. Consider, for example, Michelson’s latest experiment (not the celebrated one), or, again, consider Sagnac’s experiment. The essenceof both these experiments is to show that a ray of light travelling round the earth in the direction of the earth’s rotation requires a longer time to return to its starting point than would be the case for a ray travelling in the opposite direction. Obviously the velocity of the light waves with reference to the earth is not the same in all directions, so that we are able to detect the rotation of the earth on which we stand. The critic then infers that Einstein’s principle of relativity is upset by experiment. But the critic fails to realise that the motion that has been detected is a rotation, hence an acceleration, and that Einstein’s special principle confines itself to denying any significance to absolute velocities, that is, to motions which are not accelerated. Had this not been the case, Einstein’s principle would have been untenable since it is a fact of common knowledge that a large number of experiments (Foucault’s pendulum, the gyroscope, etc.) are capable of revealing the earth’s rotation.It is absolute velocity and not acceleration that experimenthas ever obstinately refused to reveal.
A very similar criticism consists in stating that inasmuch as the speed of light with reference to the earth’s surface is greater from east to west than from west to east, the postulate of the invariant velocity of light is refuted. But once again the same error is involved. The postulate states that the velocity of light is invariant through anyGalilean framewhen measured by the observer in the frame. The postulate ceases to be true in an accelerated frame, and the rotating earth does constitute an accelerated frame. True, in the negative experiments, the earth was treated as a Galilean frame; but it was always stated that this attitude was only approximately correct, and that experiments could be devised to detect the earth’s acceleration. However, the effects due to the earth’s absolute velocity (which was then assumed to exist) would have been so much more pronounced than those due to acceleration that as a first approximation we could afford to neglect these weaker effects of acceleration.
There is still another point on which we must insist, as it has given rise to a number of criticisms. The Newtonian principle of relativity stated that the velocity of matter through empty space was meaningless or relative. Einstein’s special theory of relativity, on the other hand, compels us to consider the velocity of light as an absolute. How, then, can Einstein’s special principle be a mere extension to electrodynamics or to the ether of the Newtonian principle?
To answer this question we must realise that although velocity was a relative in Newtonian science, yet there did exist one definite velocity which was assumed to be absolute. This was the infinite velocity. It was assumed that a velocity that was infinite or instantaneous for one observer would remain infinite or instantaneous for all other observers. So far, therefore, as velocity is concerned, the sole difference between Einstein and Newton is that with Einstein the absolute or invariant velocity is no longer infinite. Though very great (186,000 miles a second), it is now finite. It is thisdifference between the invariant velocities of Newton and Einstein which is responsible for all the major differences between classical and Einsteinian science, as will be explained more fully in a following chapter. In particular, it is this finiteness of the invariant velocity which precludes us from attaching any absolute value to shape and distance.
Viewing the question in another way, we should notice that as a matter of fact the Newtonian principle of relativity merely states that velocityof matter with respect to matteralone has physical significance. Velocity of matter through empty space is physically meaningless. It is the same in Einstein’s special principle. Einstein’s theory proves (see next chapter) that molar matter can never move with the absolute speed of light. We are therefore perfectly justified in saying that the velocity of matter remains essentially relative, since it can never attain that critical velocity (i.e.that of light) which is absolute.