quences to which it leads, however extraordinary they may be, provided that they are not inconsistent with one another nor with known experimental facts.
The consequences which one of us has obtained from a simple assumption as to the mass of a beam of light, and the fundamental conservation 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 conservation laws and the two postulates of the principle of relativity.
The first of these postulates is, that there can be no method of detecting 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.[1] 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 constant 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,
- ↑ 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.
