Mathematics of Relativity Lecture Notes e-bog

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. In an application of Mathematics to Physics a correspondence is established between some mathematical quantities and some physical quantities in such a way that the same relationship exists (as a result of the mathematical theory) between mathematical quantities as the experimentally established relation between the corresponding physical quantities. This view is not new, it was emphatically formulated by H. Hertz in the introduction to his Mechanics, and then emphasized again by A. S. Eddington in application to Relativity. The process of establishing the correspondence between the physical and the mathematical quantities we shall, following Eddington, call identification. An identification is successful, if the condition mentioned above is fulfilled, viz., if the relations deduced for the mathematical quantities are experimentally proved to exist between the Physical quantities with which they have been identified. From this point of view we do not speak of true or false theories, still less of absolute truth, etc.; truth for us is nothing but a successful identification, and it is necessary to say expressly that there may exist at the same time two successful identifications, two theories, each of which may be applied within experimental errors to the known experimental results; and that there may be times when no such theory has been found; and also that an identification which is successful at one time may cease to be so later, when the experimental precision will be increased.