Robert Daniel Carmichael

“ Now any one who accepts postulates M and will perforce accept also all the logical consequences which necessarily flow from them. Of these logical consequences we shall now prove one which is of great importance in the theory of relativity:
Theorem I. The velocity of light in free space, measured on an unaccelerated system of reference S by means of units belonging to S, is independent of the direction of motion of S (MR') . ”

“ And if the observer cannot determine an existing effect it is clear that he cannot prove the absence of any effect whatever.
But, although the absence of this effect cannot be proved, it is probably impossible to conceive any satisfactory may in which it could be present. Physical intuition is emphatic (and it may be that this is what Tolman intended to say in the passage cited) in asserting that if the direction of the velocity of S has no effect on the observed velocity of light then the absolute value of the velocity of S has no effect on such observed velocity. ”

“ I. The Postulates of Relativity. § I. Postulates of Homogeneity. — There are two fundamental postulates concerning the nature of space and time which underlie all physical theory. They assert in part that every point of space is like every other point and that every instant of time is like every other instant. For our present purpose these postulates can best be given the following more exact and complete statement. ”

“ From the postulates stated above it is possible to draw only those conclusions of the theory of relativity which are of a general nature. If, for instance, it is desired to study the nature of mass or the relation of mass and energy in this theory, it is necessary to have some assumption concerning mass in the first case and concerning both mass and energy in the second case. ”

“ If it is one, then any length in one system, however short, would be measured in the other as infinite; and a like result holds for time. Hence β is less than 1. But , the ratio of the relative velocity of the two systems to that of light. Hence, the velocity of light is a maximum which the relative velocity of two systems may approach but can never reach. ”

“ We suppose that observers at A and B again measure the velocity of light as it emanates from S, this time in the direction of the line of motion. Each will carry out his observations on the supposition that his system is at rest, for from M it follows that he cannot detect the motion of his system. The observer at A measures the time of passage of a ray of light from A to C and return to A, the length of AC being d when the measurement is made with a unit belonging to . ”

“ That is, in our system of postulates R may be replaced by theorem IX. and postulate B, and the resulting total body of postulates and theorems will be unaltered.
Now theorem IX. was proved by means of formulae (B) alone; and formulae (B) are a direct consequence of formulae (A) above. Hence postulate R may be proved solely from postulate B and formulae (A) if these are assumed to be true. Further, the third and fourth equations in (A) are equivalent to postulate L. We shall show that a special case of the first two formulae (A) is postulate V. Putting x' = 0 we have x/t = v. ”

“ Space is homogeneous and three-dimensional.
Postulate . Time is homogeneous and one-dimensional.
One important meaning of these postulates, mathematically, is that the transformations of the space and time coordinates are to be linear. ”

“ It is obvious then that he cannot determine the effect of one of the phenomena on the other; for he can never observe the one without the other being present also and the connection which exists between them is always the same however he may vary his experiment. ”

“ So far as the writer is aware, there is no experimental evidence which is undoubtedly opposed to postulate M, while on the other hand there is direct experimental evidence which by some is believed to be definitely in its favor. ”

“ Thus the system might consist of a single light-source alone. ↑ Reference here is to the Michelson and Morley experiment. ↑ See the postulate below and the remarks which lead up to it. ↑ Physical Review. 31 (1910) : 26-40. ↑ Physical Review, 33 (1911) : 418-438. ↑ Letters attached to a theorem in this way indicate those of the postulates (exclusive of and ) on which the theorem depends. See Introduction and §1. ↑ Physical Review. 31 (1910) , p. 27. ↑ This has already been pointed out by Tolman, l. ”