LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 713 



quences to which it leads, however extraordinary they may be, pro- 

 vided that they are not inconsistent with one another nor with known 

 experimental facts. 



The consequences which one of us has obtained from a simple assump- 

 tion as to the mass of a beam of light, and the fundamental conserva- 

 tion laws of mass, energy, and momentum, Einstein has derived from the 

 principle of relativity and the electromagnetic theory. We propose in 

 this paper to show that these consequences may also be obtained merely 

 from the conservation laws and the principle of relativity, without any 

 reference to electromagnetics. 



In dealing with such fundamental questions as we meet here it seems 

 especially desirable to avoid as far as possible all technicalities. We 

 have endeavored to find for each of the following theorems the simplest 

 and most obvious proof, and have used no mathematics beyond the 

 elements of algebra and geometry. 



The Units of Space and Time. 



The following development will be based solely upon the conserva- 

 tion laws and the two postulates of the principle of relativity. 



The first of these postulates is, that there can be no method of de- 

 tecting absolute translatory motion through space, or through any kind 

 of ether which may be assumed to pervade space. The only motion 

 which has physical significance is the motion of one system relative to 

 another. Hence two similar bodies having relative motion in parallel 

 paths form a perfectly symmetrical arrangement. If we are justified in 

 considering the first at rest and the second in motion, we are equally 

 justified in considering the second at rest and the first in motion. 



The second postulate is that the velocity of light as measured by 

 any observer is independent of relative motion between the observer 

 and the source of light. 7 This idea, that the velocity of light will seem 

 the same to two different observers, even though one may be moving 

 towards and the other away from the source of light, constitutes the 

 really remarkable feature of the principle of relativity, and forces us to 

 the strange conclusions which we are about to deduce. 



Let us consider two systems moving past one another with a con- 

 stant relative velocity, provided with plane mirrors aa and bb parallel 

 to one another and to the line of motion (Figure 1). An observer, A, 

 on the first system sends a beam of light across to the opposite mirror, 



7 We will imagine that the observer measures the velocity of light by- 

 means of two clocks placed at the ends of a meter stick which is situated 

 lengthwise in the path of the light. 



