516 On the Common Sense of Relativity. 



statements about particles moving according to the Newtonian 

 dynamical formulae. In this sense a physical theory is im- 

 possible if the Principle of Relativity be accepted, for the 

 same reason that a corpuscular theory of light is impossible, 

 if the undulatory theory of light be accepted. Newtonian 

 dynamics and the Principle of Relativity are two theories 

 which deal in part with the same range of facts ; they both 

 pretend to be able to predict how the properties of observed 

 systems will be altered by movement. If they are not 

 logically equivalent they must be contradictory: in either 

 case an li explanation " of one in terms of the other is 

 impossible. 



It can be easily shown that they are contradictory : if the 

 Principle of Relativity is true, Newtonian dynamics must be 

 abandoned *. I shall deal with this point rather fully in a 

 later paper ; here it will suffice to point out that Einstein has 

 been forced in his development of the subject to deny 

 Newtonian dynamics at an early stage. He states that the 

 fundamental equations of his electron theory are 



7?z.i' = eX_, etc., 



and then puts x = v, where v is the velocity of the electron 

 relative to the instrument exerting the force eX. But, if 

 Newtonian dynamics are true, i' is not this relative velocity, 

 but the velocity of the electron relative to the centre of mass 

 of the electron and the instrument. Since the mass of the 

 electron can conceivably become infinite, the distinction, 

 negligible in practice, is of great importance theoretically. 



On the other hand, if a " physical theory " of light means, 

 as I think it means, a theory which draws an analogy between 

 light propagation and the propagation of a disturbance 

 through some mechanism, composed of rods and strings and 

 fluids and such things, then there is no reason apparent why 

 a physical theory of light should not be constructed which is 

 consistent with the Principle of Relativity. But, of course, 

 the laws according to which rods and strings and so on are 

 supposed to act, must be changed from those predicted by 

 Newtonian dynamics to some laws predicted by a mechanical 

 theory consistent with the Principle. This development also 

 is left for future discussion. 



* This conclusion is reached by Sommerfeld in a recent paper, Ann. d. 

 Thys. xxxiii. p. 684 ; &c. (1910). " 



