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 criterion by which we shall be able to fix upon a definition as the only appropriate one. We must be guided by the demands of convenience, and by this alone.

In view of these considerations there is nothing unthinkable about the conclusion (in the theory of relativity) concerning simultaneity which we have given in section III. An observer A on one system of reference regulates clocks so that they appear to him to be simultaneous. It is apparent that to him the notion of simultaneity appears to be entirely independent of position in space. His clocks, even though they are separated by space, appear to him to be running together, that is, to be together in a sense which is entirely independent of all considerations of space.

But when B from another system of reference observes the clocks of $$A$$'s system they do not appear to him to be marking simultaneously the same hour; and their lack of agreement is proportional to their distance apart, the factor of proportionality being a function of the relative velocity of the two systems.

Thus instants of time at different places which appear to A to be simultaneous in a sense which is entirely independent of all considerations of space appear to B in a very different light; namely, as if they were different instants of time, one preceding the other by an amount directly proportional to the distance between the points in space at which events occur which mark these instants. Even the order of succession of events is in certain cases different for the two observers, as one can readily verify.

It thus appears that the notion of simultaneity is relative to the system on which it is determined. In other words, there is no such thing as the absolute simultaneity of events which happen at different places. The only meaning which simultaneity can have is that which is given to it by convention.

Remark. — The difficulties which we have investigated in this and the preceding section are not peculiar to the theory of relativity. The fact that the quantitative measurement of time is relative to the observer who measures it has been insisted upon by philosophers, notably by Poincaré in his Value of Science already referred to. The considerations on which these conclusions have been based have been largely of a speculative character.

The interest of the subject from the point of view of the theory of relativity is that here we have an experimental basis for the conclusions which were previously reached by speculative considerations. Starting out from certain laws which we have (tentatively) accepted as demonstrated by experiment we have by logical processes alone reached these