782 



NATURE 



[February 17, 192 1 



A Brief Outline of the Development of the Theory of Relativity. 



By Prof. A. Einstein. 

 [Translated by Dr. Kolx;rt W. Lawson. ] 



its aid H. A. Lorentz was also pre-eminently 



'T~'HERE is something attractive in presenting 

 -»- the evolution of a sequence of ideas in as 

 brief a form as possible, and yet with a complete- 

 ness sufficient to preserve throughout the con- 

 tinuity of development. We shall endeavour to 

 do this for the Theory of Relativity, and to show 

 that the whole ascent is composed of small, almost 

 self-evident steps of thought. 



The entire development starts off from, and is 

 dominated by, the idea of Faraday and Maxwell, 

 according to which all physical processes involve 

 a continuity of action (as opposed to action at a 

 distance), or, in the language of mathematics, 

 they are expressed by partial differential equa- 

 tions. Maxwell succeeded in doing this for 

 electro-magnetic processes in bodies at rest by 

 means of the conception of the magnetic effect 

 of the vacuum-displacement-current, together with 

 the postulate of the identity of the nature of 

 electro-dynamic fields produced by induction, and 

 the electro-static field. 



The extension of electro-dynamics to the case 

 of moving bodies fell to the lot of Maxwell's suc- 

 cessors. H. Hertz attempted to solve the problem 

 by ascribing to empty space (the aether) quite 

 similar physical properties to those possessed by 

 ponderable matter; in particular, like ponderable 

 matter, the a;ther ought to have at every point a 

 definite velocity. As in bodies at rest, electro- 

 magnetic or magneto-electric induction ought to 

 be determined by the rate of change of the elec- 

 tric or magnetic flow respectively, provided that 

 these velocities of alteration are referred to sur- 

 face elements moving with the body. But the 

 theory of Hertz was opposed to the fundamental 

 experiment of Fizeau on the propagation of light 

 in flowing liquids. The most obvious extension 

 of Maxwell's theory to the case of moving 

 bodies was incompatible with the results of 

 experiment. 



At this point, H. A. Lorentz came to the rescue. 

 In view of his unqualified adherence to the atomic 

 theory of matter, Lorentz felt unable to regard 

 the latter as the seat of continuous electro- 

 magnetic fields. He thus conceived of these fields 

 as being conditions of the aether, which was 

 regarded as continuous. Lorentz considered the 

 aether to be intrinsically independent of matter, 

 both from a mechanical and a physical point of 

 view. The aether did not take part in the motions 

 of matter, and a reciprocity between aether and 

 matter could be assumed only in so far as the 

 latter was considered to be the carrier of attached 

 electrical charges. The great value of the theory 

 of Lorentz lay in the fact that the entire electro- 

 dynamics of bodies at rest and of bodies in motion 

 Was led back to Maxwell's equations of empty 

 space. Not only did this theory surpass that of 

 Hertz from the point of view of method, but with 

 NO. 2677, VOL. 106] 



successful in explaining the experimental facts. 



The theory appeared to be unsatisfactory only 

 in one point of fundamental importance. It 

 appeared to give preference to one system of co- 

 ordinates of a particular state of motion (at rest 

 relative to the aether) as against all other systems 

 of co-ordinates in motion with respect to this one. 

 In this point the theory seemed to stand in direct 

 opposition to classical mechanics, in which all 

 inertial systems which are in uniform motion with 

 respect to each other are equally justifiable as 

 systems of co-ordinates (Special Principle of Rela- 

 tivity). In this connection, all experience also in 

 the realm of electro-dynamics (in particular 

 Michelson's experiment) supported the idea of the 

 equivalence of all inertial systems, i.e. was in 

 favour of the special principle of relativity. 



The Special Theory of Relativity owes its origin 

 to this diflSculty, which, because of its fundamental 

 nature, was felt to be intolerable. This theory 

 originated as the answer to the question : Is the 

 special principle of relativity really contradic- 

 tory to the field equations of Maxwell for empty- 

 space? The answer to this question appeared to 

 be in the affirmative. For if those equations are 

 valid with reference to a system of co-ordinates- 

 K, and we introduce a new system of co-ordinates 

 K' in conformity with the — to all appearances 

 readily establishable — equations of transformation 



x'=x—vt'\ 



^' Zp' i(Galileo transformation), 



f =t ] 

 then Maxwell's field equations are no longer valid 



(.v', y' 



t'). But 



in the new co-ordinates 



appearances are deceptive. A more searching 

 analysis of the physical significance of space and 

 time rendered it evident that the Galileo trans- 

 formation is founded on arbitrary assumptions^ 

 and in particular on the assumption that the state- 

 ment of simultaneity has a meaning which is 

 independent of the state of motion of the system 

 of co-ordinates used. It was shown that the field 

 equations for vacuo satisfy the special principle 

 of relativity, provided we make use of the equa- 

 tions of transformation stated below : 



(Lorentz transfomiation). 



V I - v*lc*' 



In these equations x, y, z represent the co-ordi- 

 nates measured with measuring-rods which are 

 at rest with reference to the system of co-ordi- 

 nates, and f represents the time measured with 

 suitably adjusted clocks of identical construction, 

 which are in a state of rest. 



