Page:The Meaning of Relativity - Albert Einstein (1922).djvu/30

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THE MEANING OF RELATIVITY

the more important equations of physics from this point of view.

The equations of motion of a material particle are

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is a vector; , and therefore also , an invariant; thus is a vector; in the same way it may be shown that is a vector. In general, the operation of differentiation with respect to time does not alter the tensor character. Since is an invariant (tensor of rank 0), is a vector, or tensor of rank 1 (by the theorem of the multiplication of tensors). If the force has a vector character, the same holds for the difference . These equations of motion are therefore valid in every other system of Cartesian co-ordinates in the space of reference. In the case where the forces are conservative we can easily recognize the vector character of . For a potential energy, , exists, which depends only upon the mutual distances of the particles, and is therefore an invariant. The vector character of the force, , is then a consequence of our general theorem about the derivative of a tensor of rank 0.

    oriented differently. We shall meet with this point of view again in the theories of special and general relativity.