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Transformations of units and world's geometry

Israel Quiros
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Abstract

The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this geometry rests is invariant under point-dependent transformations of units. Riemann geometry does not fulfill this requirement. Spacetime singularities are then shown to be a consequence of a wrong choice of the geometrical formulation of the laws of gravitation. This result is discussed, in particular, for the Schwrazschild black hole and for Friedmann-Robertson-Walker cosmology. Arguments are given that point at Weyl-integrable geometry as a geometry implicitly containing the quantum effects of matter. The notion of geometrical relativity is presented. This notion may represent a natural extension of general relativity to include invariance under the group of units transformations.

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Israel Quiros. 2000-10-19. Transformations of units and world's geometry. https://arxiv.org/abs/gr-qc/0004014

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