CHAPTER XITHE ETHER
CLASSICAL science assumed that, those manifestations we called electricity, magnetism, and light were nothing but strains, compressions and wavelike motions in an imponderable medium, the stagnant ether, floating in space. This belief was not altogether blind guesswork. In view of the stresses and strains that clearly appeared to surround electrified bodies, electric currents and magnets, and in view of the well-established wave nature of light propagation, some medium had to be postulated in order to give these stresses, strains and waves physical significance. Of this mysterious ether itself, practically nothing was known; but from what scant information could be gathered, it appeared to possess strange and contradictory properties.
Its resistance to motion was practically nil—far less than that of a gas like the atmosphere; since the frictional effects due to the atmosphere are sufficient to cause shooting stars to become incandescent, while no such effect was observed in those regions of ether-filled space extending beyond the limits of the atmosphere. Besides, if motion through the ether generated friction, mechanical phenomena should be influenced by the velocity of our Galilean frame through space and hence through the ether; but so far as experiment was able to decide, no such influences had ever been detected. (This was indeed the essence of the Newtonian principle of relativity.) It appeared, therefore, that the ether must be assimilable to some ultra-rarefied gas. On the other hand, the transverse vibrations of light waves were compatible only with the existence of a rigid medium; but between the properties of rigidity and of extreme rarefaction there was an obvious contradiction. Yet, however baffling and artificial the ether appeared to be, it was extremely hard to banish it from science owing to the great mass of experimental evidence that appeared to lend support to its existence.
At any rate, once the existence of a semi-material ether was accepted, it was natural to suppose that the motion of our optical and electrical apparatus through its substance should exert a perceptible influence on the results of experiment. Just as the velocity of the wind adds itself to the velocity of sound waves propagated through the atmosphere, so was it logical to anticipate, in view of our understanding of light waves and of electrical phenomena, that an ether wind should carry the light waves and ether strains along with it. Optical and electrical experiments conducted with sufficient refinement should therefore be susceptible of detecting the velocity of our planet through the ether; so that in contradistinction to the relativity of Galilean motion formechanical phenomena with which the ether was not concerned, Galilean motion would be anything but relative were electromagnetic or optical experiments to be attempted.
Now this duality which was thus assumed to exist in the nature of Galilean motion or velocity, making it relative for mechanical phenomena and absolute for electrodynamic ones, was perfectly acceptable, provided it was permissible to draw a sharp distinction between mechanics and electrodynamics, between space and the ether. But the entire trend of recent research had been to show that this distinction was unjustified. In the first place, matter seemed to be constituted by electrons and protons, hence to be reducible to phenomena of an electromagnetic nature. Then again, electromagnetic phenomena were known to develop mechanical forces. Where, then, was the essential difference between mechanical and electromagnetic phenomena? Under the circumstances how could we account for this anticipated duality in the palpable effects caused by a velocity through the ether, relative or physically meaningless for mechanical experiments, and capable of producing physical effects in electromagnetic ones?
It appeared as though mechanical and electromagnetic phenomena should be susceptible of being placed on the same footing. We should then have to assume that mechanical phenomena together with electromagnetic ones would be affected by velocity through the ether, hence through space, or else to recognise that both electrodynamic and mechanical phenomena could never be influenced by this type of motion. If we should accept the first hypothesis, the Newtonian or mechanical principle of relativity would be overthrown, and with it the entire structure of Newtonian mechanics; and if we should accept the second hypothesis, our understanding of electromagnetic processes and of the ether would have to be modified profoundly. In either case, whether or not electromagnetic and optical experiments succeeded in detecting absolute Galilean motion, science seemed to be faced with a difficult situation.
Classical physicists held to the view that optical and electromagnetic experiments would surely reveal absolute Galilean motion, and they were not perturbed by the fact that as a result Newtonian mechanics might have to be abandoned. Indeed, doubts as to the validity of Newtonian mechanics already presented themselves when Kaufmann and Bucherer showed that electrons in very rapid motion appeared to increase in mass—a phenomenon which was of course incompatible with the Newtonian belief in the invariance of mass, unless some hypothesisad hocwas to be invoked. It is true that Michelson’s very refined test attempted in 1887 failed to detect any influence of absolute Galilean motion in a certain optical experiment; but it was always assumed that an explanation for this failure would be forthcoming sooner or later, and that other experiments would be successful where Michelson’s had failed. When, therefore, Einstein suggested as a principle of nature that, regardless of whether or not the ether was a necessary hypothesis, Galilean motion through the ether or through space wouldnever be detected by any type of experiment, whether optical or electromagnetic or mechanical, the majority of physicists paid little heed to the new doctrine.
It must not be thought that this hostility of classical physicists to the Einstein theory in its initial stages was due solely to their belief in the absolute and objective nature which it appeared inevitable to credit to the ether. It was due also to other reasons which we shall now proceed to investigate.
From a mathematical point of view, a physical phenomenon reduces to the systematic variation in intensity and in orientation from place to place and from time to time of a number of magnitudes. A physical phenomenon as referred to some arbitrary frame of reference can therefore be expressed by mathematical equations in which the space and time co-ordinates with respect to the frame figure as variables. Now a fundamental problem of theoretical physics is to determine how the equation of a phenomenon referred to a frame,which is in motion with respect to a frame,can be obtained from its equation referred to the frame,by purely mathematical means without any further appeal to experiment. The solution of this problem would enable us to anticipate the change in appearance of a phenomenon when observed, first from the frame,then from the frame.Obviously some kind of mathematical operation would have to be performed on the equation as referred to.This operation is called amathematical transformation; and the equation operated upon is said to have been transformed. In the type of problem we are considering, where one frame of reference is followed by another, the transformation will bear on the space and time variables or co-ordinates present in the equation; and transformations of this character are termedspace and time transformations. The entire problem reduces, therefore, to the discovery of those space and time transformations which hold in this world of ours. These transformations cannot be guessed ata priori; and a study of the behaviour of physical phenomena is a prerequisite condition for their determination. Inasmuch as all the experiments known to classical science appeared to corroborate the impression that a distance in space and a duration in time were absolutes, remaining unaltered when we changed our frame of reference, a certain definite species of space and time transformations followed as a matter of course.
Consider, for example, a train moving with constant speed along an embankment. If an event occurs in the moving train at any instant of time, say at two o’clock, this event will obviously have occurred at precisely the same instant (two o’clock) when referred to the embankment, since time is assumed to be absolute, the same for all. In other words, time and duration for the observer in the moving train are identical in all respects with time and duration for the observer on the embankment. This fact is expressed by,whereis the time for the train, andthe time for the embankment.
Now suppose that a ball is rolling along the moving train with a speed,and suppose that owing to the train’s motion the train observer is carried past the embankment observer at the instant of time when the clocks mark noon. If the ball leaves the train observer at this precise instant of time, its distance from the train observer at a time(i.e.seconds after the noon instant) will be(sinceandare identical). But then its distance from the embankment observer will be the sum of the distance between the two observers, and of this distancewe have just expressed (distances being absolute). It will be, therefore,(whereis the velocity of the train along the embankment).[38]This last deduction is obvious provided we assume that a distance is an absolute concept which would turn out the same whether measured by one observer or another, and such was precisely the assumption that classical science always made. In short, knowing the pointwhere an event takes place at a given instant as referred to the train we can deduce immediately the point where the same event takes place when referred to the embankment. All we have to do is to replaceby,and the trick is done.
These space and time transformations permitting us to pass from one Galilean frame to another were the celebratedGalilean transformationsof classical science, and they were, as we have seen, the necessary consequences of our belief in absolute duration and distance. They were given by:or again byApplying them to particular problems, as,e.g., to the change in the shape of the trajectory of a falling body when viewed successively from a moving train and from the embankment, or to the change in the colour of a monochromatic source of light, or in the pitch of a musical note, the anticipations of the transformations were always found to be verified, to the order of precision of our experiments. Corroborations of this sort, among others, were considered to prove the correctness of the transformations, hence also of our traditional belief in the absoluteness of duration and distance.
Now if, instead of restricting ourselves to any particular phenomenon, we consider all phenomena of the same type, such as all mechanical or all electrodynamic phenomena, we know that these phenomena in their aggregate satisfy the requirements of certain general laws or equations: the laws of mechanics or the laws of electrodynamics, as the case may be. To say, therefore, that Galilean motion or velocity is relative so far as a certain type of phenomenon is concerned means that the general laws governing such types of phenomena remain unchangedin form when we pass from one Galilean frame to another. Expressed mathematically, this means that when the space and time transformations are applied to the general laws, these laws or equations are transformed into equations possessing exactly the same mathematical appearance; they are then said to have been transformed into themselves.
When the transformations were applied to the general laws of mechanics, these laws suffered no change in form; and this fact constituted the mathematical expression of the Newtonian or mechanical principle of the relativity of Galilean motion. But when the transformations were applied to the equations or laws of electrodynamics, a distinct change in form was noted; the laws or equations lost their simple appearance. This suggested that the electrodynamical laws as accepted by classical science held only in their simple form for a privileged Galilean frame, which for reasons of symmetry was naturally assumed to be one at rest in the stagnant ether. But then, the laws changing in form according to the Galilean frame to which they were referred, it followed as a necessary consequence that electromagnetic experiments should pursue a different course and yield different results according to the frame in which the observer and his instruments were placed. It should then be possible to discover the magnitude of the velocity of the frame through the ether by means of electromagnetic or optical experiments, so that once again, independently of any particular ether hypothesis, mathematical reasoning as well as commonplace reasoning confirmed the physical reality of velocity through the ether.
Of course these mathematical anticipations were dependent on a twofold hypothesis: first, that the classical transformation-formulæ based on absolute distance and duration were accurate; and, secondly, that the equations or laws of electrodynamics were correct. To question the first assumption appeared unjustified, and to question the validity of the mathematical expression of the laws led to conflict with experiment. True, we could modify the laws of electrodynamics (by suppressing those mathematical terms which were the cause of their variability), rendering them thereby invariant under the Galilean transformations, but these terms turned out to be those responsible for the phenomenon of electromagnetic induction. To suppress them would have been equivalent to denying the existence of induction, hence of wireless, radio, dynamos and light propagation. Obviously, a solution of this kind could not be accepted, since dynamos, etc., were known to exist.
In view of all these facts, not the slightest doubt was entertained by scientists that experiments sufficiently precise in nature would yield us the velocity of our instruments, hence of our planet, through the stagnant ether.
We must now pass on to a rapid survey of those so-called negative experiments which were primarily responsible for all the trouble. Let us recall once more the point at issue. We wish to ascertain to what extent the velocity of our Galilean frame through the ether is capableof modifying the results of our electromagnetic and optical experiments.
First in order among these tests we must mention the well-known phenomenon of astronomical aberration, according to which the direction of incidence of a ray of starlight varies annually as the earth circumnavigates the sun. The obvious analogy of this phenomenon is the slanting direction followed on the window pane of a moving train by raindrops which to an observer stationed on the embankment would appear to be falling vertically. This analogy might tempt us to assume that inasmuch as the slant of the raindrops on the pane permits us to deduce the speed of our train through the stagnant atmosphere, so now the slant of the ray of starlight resulting from the earth’s motion should yield us our velocity through the stagnant ether. But the conclusion would be faulty; for if we reflect we shall see that we were able to deduce our motion through the atmosphere, solely because we had reason to assume that had our train stood motionless in the atmosphere the raindrops would have appeared to fall vertically. But in the case of astronomical aberration we have no means of basing our deductions on any such preliminary information. We cannot tell from what directions the rays of starlight would appear to issue were we at rest in the ether; for we ignore the true positions of the stars. And so all that astronomical aberration can yield us is the annualvariationin our velocity through the ether, hence our velocity relative to the sun.[39]In short, astronomical aberration does not enable us to detect our absolute speed through the ether, and we must rely on other means.
In all the experiments we shall have occasion to mention, the velocity through the ether which we shall seek to determine will be that of our earth; for, attached as we are to the earth’s surface, this will be the speed we shall best be in a position to determine. Unfortunately, the earth does not constitute a truly Galilean frame on account of its acceleration or rotation round its axis. However, this acceleration of the points on the earth’s surface is very small and the centrifugal force to which it gives rise is scarcely perceptible. Calculation shows that, so far as optical and electromagnetic experiments are concerned, we may regard a frame attached to the earth as constituting a Galilean frame, possessing velocity but no acceleration, at least as a first approximation. Nevertheless this statement is not altogether correct. Experiments can be devised both in mechanics and in optics which would reveal the earth’s acceleration or rotation. Of course this is only natural, sinceacceleration, in contradistinction tovelocitythrough space, is known to be absolute.
A proper understanding of Einstein’s theory requires that this point be fully understood, so we must be excused for repeating once more that all we are concerned with at present is to reach a decision on therelativity or the absoluteness of velocity or Galilean motion through the ether. In the case of the earth there is no danger of our confusing any possible effects of acceleration with those due to velocity because, owing to the comparative slowness of the earth’s rotationary motion, any effects that might arise from acceleration would in any case be far feebler than those arising from velocity through the ether.
Summarising, we may say that a veritable ether hurricane must be blowing over the earth, varying both in intensity and in direction at the different points of the earth’s surface and also at the various times of the day and year. It is this ether hurricane or ether drift that we must proceed to detect. Now all experiments, whether optical or electrical, obstinately refused to detect the slightest trace of this ether drift; so that one of two things was obvious. Either there was no drift; or else, if drift there was, it was completely concealed by compensating phenomena of which as yet nothing was known. Stokes adopted the first alternative and suggested that the earth in its motion round the sun might possibly drag the ether along with it, in its immediate vicinity at least. It would follow that there could never be any drift on the earth’s surface; and all the negative experiments which had failed to detect the drift would be explained. The obvious objection to Stokes’ hypothesis was the existence of astronomical aberration, which seemed to imply that the earth was moving through a stagnant ether. Stokes, however, proved mathematically that aberration was no argument against his hypothesis; that this phenomenon would still be in order, provided the earth’s motion did not set up whirlpools in the convected ether.
In addition to a number of other difficulties to be explained shortly, we may mention that for the motion of the ether to be such as to satisfy Stokes’ requirements, hence the observed phenomenon of astronomical aberration, calculation proved that the ether could not be incompressible. In fact, Planck showed that on the earth’s surface the ether would have to be 60,000 times denser, and thus correspondingly more compressed than in distant regions; and it would seem strange indeed that this considerable increase in the density of the ether should fail to manifest itself when we compared the results of optical experiments performed on the summit of a high mountain and at sea level. Moreover, light vibrations being transversal, the hypothesis of a rigid ether appeared to be inevitable, so long as we wished to conceive of light as due to vibrations in the ether. Here again the Stokes-Planck theory was difficult to accept.
Lodge endeavoured to subject Stokes’ hypothesis to a direct experimental test. He argued that if the earth were capable of dragging the ether along with it in its motion, the same should be true of other moving bodies. But when he investigated this anticipated drag effect in the case of rapidly revolving disks of steel, he found it entirely absent.
Even if we ignore these contradictions and assume that the terrestrial atmosphere is able to drag the ether along bodily, a new series of difficulties awaits us. A total drag of this sort would be incompatible with a general phenomenon predicted by Fresnel andverified by Fizeau according to which dielectrics in motion (electrical non-conductors), such as water, glass and air, drag the ether along only in a partial way; the percentage of drag increasing with the refractivity of the dielectric. Inasmuch as the refractivity of the atmosphere is comparatively feeble it would be impossible to credit the total drag of the ether to the atmosphere.
A quite recent experiment of Michelson (not to be confused with the celebrated experiment of Michelson and Morley) also renders Stokes’ hypothesis extremely unlikely. The essence of this particular experiment is to send two light rays round the earth in opposite directions. Its result was to prove that the ray travelling eastward required a longer time to complete its circuit than the one travelling westward. Such would not be the case were the earth to drag the ether around with it in its rotation on its axis. True, this experiment did not prove that the ether was not dragged along by the earth’s motion along its orbit, but, on the other hand, it did prove that the earth’s rotationary motion produced no such drag. This, of course, rendered extremely improbable the hypothesis that the earth’s motion along its orbit should be any more successful in producing an ether drag. The aforementioned experiment of Michelson is an apt illustration of the type of experiment which enables us to detect by optical means the earth’s rotation or acceleration through the ether, and is therefore irrelevant to the problem we are here investigating, namely, that of its velocity through the ether. The only reason we mentioned the experiment was because of its bearing on Stokes’ hypothesis.
Stokes’ hypothesis was thus discarded, and the most satisfactory explanation of all negative experiments that had been suggested was given by Fresnel. It must be realised that up to this stage all the experiments attempted were of an optical nature, and related to the transmission of light rays through dielectrics (glass, water, etc.). Such experiments had been performed by Foucault, Airy, and Arago. Fresnel succeeded in proving by mathematical analysis that if dielectrics carried the ether along in their interior in a partial manner, increasing in a definite degree with their refractive power, all the negative results attained up to his day would be explained, provided they were not pursued to too high an order of accuracy. This required percentage of drag of the ether by dielectrics was calledFresnel’s convection coefficient.
Fresnel’s hypothesis was subjected to a direct experimental test. Fizeau discovered, exactly as had been anticipated by Fresnel, that when a ray of light was propagated through running water, the total speed of the light ray with respect to the tube was equal to its speed through the water, when the water was stagnant, plusonly a fractionof the water’s velocity in the tube; and that this fraction was precisely equal to the convection coefficient predicted by Fresnel.
In view of this remarkable confirmation, Fresnel’s hypothesis was considered fairly established, so that the situation confronting science was the following: The ether was stagnant in that the earth moved through it without disturbing it in any way. Velocity throughthe ether had therefore a definite physical significance, and a real ether hurricane must be blowing over the earth’s surface in various directions according to the time of day. Experiments had failed to detect it, not because it did not exist, but on account of this compensating effect of the partial drag of the ether by dielectrics in motion. Such a failure, however, could only be regarded as temporary; for Fresnel’s hypothesis specifically showed that this compensating effect was but partial, and that experiments of a still more refined order ought certainly to detect the ether drift on the earth’s surface, revealing thereby the earth’s absolute velocity.
Obviously Fresnel’s hypothesis would fall if more refined experiments should also fail to detect the ether hurricane. Furthermore, even to the order of precision contemplated by Fresnel, if in our experiments we should appeal to phenomena in which dielectrics played no part, his showed that this compensating effect was but partial, and that experiment of Michelson and Morley was of this type. Not only was it far more precise than the ones hitherto attempted, but in addition refraction played no part in it. Yet, in spite of all, the Michelson and Morley experiment again gave a negative result.
The next great advance in our understanding of the problem was due to Lorentz. He, however, like all his predecessors, dared not take the great step, but still endeavoured to explain the negative results of experiment while holding to the view of a real stagnant ether. As might have been expected, Lorentz was compelled to appeal to new compensating influences. But before going farther it appears indispensable to devote a few pages to the general subject of electrodynamics; for as we proceed, we shall see that theoretical considerations are destined to play a part of ever-increasing importance.