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SUPPLEMENT I |
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that if either
S\ or S2 is suitable the other is equally suitable, the relative motion of the two being unaccelerated.In order to bring into suitable relations the measurements made on one system of reference and those made on another it is necessary to have some agreement as to the correspondence of units on the two systems. Accordingly we shall make the following assumption concerning the correspondence of units:
Principle of Correspondence of Units.
The units of any two systems Si and S2 are such that the same numerical result will be obtained in measuring with the units of Si a quantity Li and with the units of S2 a quantity L2 when the relation of L\ to S\ is precisely the same as that ofWe shall agree that the restricted principle of relativity is to be understood in a sense which implies this assumption concerning the correspondence of units; that is, the latter will be taken as a more precise formulation of a part of the content of the former. If is clear that the possibility of realizing this latter is taken for granted in the Galileo-Newtonian mechanics; it is often passed over without remark although it is a profound fact and is a part of the essential basis of any theory of motion.
It is a grave question whether the restricted principle of relativity can be maintained in the interpretation of natural phenomena. Indeed in the more general theory of relativity, to be taken up later, it is treated merely as a sort of approximation to a more comprehensive principlean approximation strictly valid only in the absence of a gravitational field but very close to the truth for a wide variety of phenomena including most of those which are purely terrestrial.
There are two particular characteristic postulates, or 'laws of nature', lying at the base of the restricted theory of relativity. These may be stated as follows:
Postulate M.
The unaccelerated motion of a system of reference S can not be detected by observations made on S alone, the units of measurement being those belonging to S,Postulate R.
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 velocity of S and of the unaccelerated velocity of the light-source.For these two particular postulates there is the strongest possible experimental evidence. Everything known points toward their truth, and there is nothing known which in any way seems to be in disagreement with them. It is to be observed that they apply only to the ideal case, that is, the case in which there is supposed to be no gravitational field.
For the development of the restricted theory of relativity there are three additional necessary postulates, or 'laws of nature;' those that theory shares in common with the Galileo-Newtonian mechanics. Such assumptions in some form are essential to the initial arguments and to the conclusions which are drawn by means of them. To the present writer it seems to be preferable to have these assumptions explicitly stated. They may be put into the following form: |
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