Transformations of units and world's geometry

Details Transformations of units and world's geometry Transformations of units and world's geometry

2000-04-05

arxiv.org/abs/gr-qc/0004014v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, Revtex, no figures. New material and references added

Scientific paper

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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