March 15, 1906] 



NA TURE 



46: 



solar system, and someone were to begin to ask : Is it 

 the star that moves or ourselves? we should at once reject 

 the question as absurd, and say that the two alternatives 

 mean the same thing. But I doubt whether there will 

 be many who would be satisfied to contemplate a stellar 

 universe, each member of which has the same relative 

 velocity with respect to the sun, without feeling that here 

 is a problem which requires investigation. 



The ideal case considered might be realised if we could 

 imagine observations to be taken from a molecule in a 

 mass of gas enclosed in a box, the observations being 

 taken in the interval between two collisions. If other 

 molecules could be brought within the range of observ- 

 ation, we should, indeed, find that for the mean point in 

 each group containing a large number of molecules the 

 observed relative motion has the same value, that value 

 being the reversed velocity of the molecule itself. If there 

 were any ordinary common-sense philosopher placed on 

 the molecule, he would argue that his observations have 

 really determined the absolute velocity of his place of 

 abode in space, but his wiser colleagues will tell him 

 that he is wrong, and that he has only determined his 

 velocity relative to the rest of the system. The common- 

 sense philosopher would then justly claim that he has done 

 more than that, and point out that the whole system of 

 molecules can be divided into a great many groups, and 

 that the relative velocity in all the groups is identical 

 in magnitude and direction. With our greater knowledge 

 from outside, we know that the velocity which has been 

 determined really belongs to the molecule, and we should 

 probably add (though this is not a matter which the 

 supposed observations could have proved) that it is the 

 velocity relative to the vessel which contains the gas. 

 But even then not all the facts which the observer on the 

 molecule has discovered are accounted for. If the gas 

 could be set into violent motion, without altering the 

 velocity of the particular molecule from which the observ- 

 ations are made, the observer would still obtain the same 

 value for his relative motion, but the different groups into 

 which he has divided his space would no longer give 

 identical values. The complete conclusion to be drawn from 

 the original observations is, that a velocity has been deter- 

 mined relative to an outside body which is mechanically 

 connected with the system, and that each group of mole- 

 cules is separately at rest relatively to this outside body. 



Consider now the application of this example to our 

 problem. If we could argue by analogy we should con- 

 clude Siat the observed velocity of the solar system really 

 belongs to it, and not to the stars, but that it must be 

 taken as relative to something which is outside the stellar 

 universe, though connected with it. If that something is 

 material, we should be forced to the conclusion that we 

 have determined a velocity relative to a material body 

 which has not come into our range of observations at all. 

 The conclusion seems too absurd to be entertained. The 

 only alternative is to replace what in the case of the 

 gas was the containing vessel by something immaterial, 

 which therefore we cannot imagine to be in motion. Not 

 being capable of motion it must be at absolute rest, and 

 we may identify it with that abstraction to which we give 

 the name of space. All motion relative to space is absolute 

 motion. 



It may be said that if this argument is to be applied 

 to the actual universe, I have left out of account a large 

 number of bodies of which we have no cognisance because 

 they are not luminous. It is possible that these obscure 

 bodies would, if we could observe them, show a systematic 

 motion which would quite upset the previous conclusions. 

 To this I reply that I have treated an ideal case which 

 may or may not coincide with the actual one. I have 

 expressed no opinion as to whether, on the strength of 

 present observations, we are justified in assigning absolute 

 velocity to the solar system ; but it may be pointed out 

 that almost every theory which we now believe to be true 

 may some day be upset by facts at present undiscovered, 

 which cannot be reconciled with it. Should we come to the 

 conclusion that our solar system is in motion we may 

 have to modify that belief in the future, but this possibility 

 does not prevent our being justified in adopting views which 

 are in accordance with the facts at present known. 



There is an easy way out of the difficulty. When we 



no. i8q8, vol. yT,~\ 



are driven to our wits' end we have recourse to the aether- 

 Why, then, assume absolute motion when it is so simple- 

 to say that you have determined the motion relative to- 

 the aether? We should by this device be able to calm our.- 

 consciences as regards relative motion, no doubt, but at 

 the expense of logical consistency. A moment's reflection 

 will show. that the aether has nothing to do with the ques- 

 tion. If the aether were non-existent and the corpuscular 

 theory of light were true, the displacement at right angles- 

 to the line of sight would still be observed, and as regards 

 the radial velocities the contemplation of the correspond- 

 ing acoustical problem is decisive. The note of the whistle- 

 of an approaching engine is quite independent of the direc- 

 tion of the wind. Similarly, the observed Doppler effect 

 when the spectra of stars are examined is independent of 

 »ny uniform drift there might be in the aether. No doubt 

 we may, and probably must, consider the aether as- 

 immovable in space, and in that case absolute motion in. 

 space becomes identical with motion relative to the aether ; 

 but the direct conclusion derived from the observation of 

 stars applies to space, and not to the aether. 



All our observations of position can only be relative to 

 some standard point. Motion involves change of position, 

 hence motion can be relative only. This is the main argu- 

 ment on which the impossibility of absolute motion is 

 founded. But it proves only that observed velocity must 

 be relative, and not that there is nothing real correspond- 

 ing to absolute velocity. The argument also assumes, 

 the very doubtful proposition that velocity must be derived 

 from change of position. It may be the other way round, 

 velocity may be the more fundamental thing, and change- 

 of position may have to be derived from it. It seems to 



be equally logical to take s= vdt or v = ds/dt as the- 



equation representing the relationship between the position 

 and velocity. Indeed, if we read Poincar£'s description of 

 how we form our ideas of space, we must be struck by the- 

 importance attached to the muscular sensation which, 

 accompanies a change of position of our bodies. To quote 

 only one of his sentences : — " None of our sensations could 

 have led us by themselves to the conception of space. We- 

 ars led to this conception only by studying the laws accord- 

 ing to which our sensations succeed each other." Bearing, 

 this in mind, it seems rational to start from the idea of 

 velocity as rate of change of position, and deduce the idea 

 of position from it. Rest would become an abstraction,, 

 and would have to be defined as an infinitely small motion. 



There is, however, another way of looking at it. It is- 

 known that it is much more difficult to convince ourselves- 

 of the objective nature of time than of space or velocity. 

 In fact, I believe most metaphysicians now would deny 

 the objective nature of time altogether. It might there- 

 fore be useful to accept both position and velocity as. 

 fundamental conceptions, and deduce time intervals fromi 

 them. In any case, sufficient has been said to show that 

 the practical definition of relative motion cannot in itself" 

 be taken to prove that absolute motion is an impossible- 

 conception. 



If I suggested at the outset of this discussion that 

 most of us have all along been secret believers in absolute 

 motion, I was led to that belief partly by the manner- 

 in which the problem of solar motion in space has always 

 been treated. Those who have drawn the logical con- 

 clusion from the observations have not infrequently guarded' 

 themselves by some statement that after all it is only 

 relative motion they are trying to prove. But their dis- 

 cussion nearly always tacitly assumes, not relative, but 

 absolute motion, and I think most astronomers and 

 physicists, if taken unawares, would admit the absolute 

 motion of the solar system in space as a proved fact, 

 though on second thoughts they might try to explain it 

 away by motion relative to the aether or by some other ex- 

 pedient invented ad hoc to safeguard their true faith in 

 relative motion. 



But a tacit assumption of absolute motion is also in- 

 cluded in the definition of force which at present is much 

 in favour. " Force is rate of change of momentum." If 

 velocitv is relative, momentum is relative also. The above 

 definition is therefore incomplete, and may be misleading 

 unless it is definitely stated what the standard system is 

 relative to which momentum has to be measured. Evenj 



