Abstract
COPIES have reached us of five of Prof. Levi Civita's recent mathematical papers,1 three of which deal directly with Einstein's theory of gravitation, and suggest some remarks on the aspect of theoretical dynamics, as it appears at present to a comparative layman unable to criticise rival theories in detail. Speaking broadly, we may say that the theory of mathematical physics is based upon a comparatively small number of fundamental differential equations. Until recently time was explicitly or implicitly treated as the independent variable, in terms of which the other variables had to be found; and all phenomena were supposed to take place in a three-dimensional Euclidian space, where we can use the formula ds2 = dx + dy2 + dz for the distance between two very near points. In the theory expounded by Minkowski and others we have a different formula, ds2 = cdt2 - (dx2 + dy + dz2), where we may regard dt as an element of time, and speak of a “world-point” (x, y, z, t) determined not only by its position, but also by its age. Einstein has developed his gravita-tion-theory from the general expression, gdxidXj (i, j=0, 1, 2, 3), assumed for ds2, where ds is an element of distance in a four-dimensional space. (It may be remarked that in the previous theory, as Minkowski pointed out, we might take dt as a variation of a co-ordinate distance; then phenomenal processes in our space might be regarded as “sections,” so to speak, of a four-dimensional system.)
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M., G. The New Physics. Nature 100, 155 (1917). https://doi.org/10.1038/100155a0
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DOI: https://doi.org/10.1038/100155a0