Relativity without Spacetime by Joseph K. Cosgrove

Author:Joseph K. Cosgrove
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Space as a continuum does not figure in the conceptual system [of Greek geometry] at all. This concept was first introduced by Descartes, when he described the point in space by its coordinates. Here for the first time geometrical figures appear, in a way, as parts of infinite space, which is conceived as a three-dimensional continuum.60

Einstein then concludes his analysis on a note strongly suggestive of Klein:In so far as geometry is conceived as the science of laws governing the mutual spatial relations of practically rigid bodies, it is to be regarded as the oldest branch of physics. This science was able, as I have already observed, to get along without the concept of space as such, the ideal corporeal forms—point, straight line, plane, segment—being sufficient for its needs. On the other hand, space as a whole, as conceived by Descartes, was absolutely necessary to Newtonian physics. For dynamics cannot manage with the concepts of the mass point and the (temporally variable) distance between mass points alone. In Newton’s equations of motion, the concept of acceleration plays a fundamental part, which cannot be defined by the temporally variable intervals between points alone. Newton’s acceleration is only conceivable or definable in relation to space as a whole. Thus to the geometrical reality of space a new inertia-determining function was added.61

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