From the Weyl theory to a theory of locally anisotropic spacetime

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Abstract
It is shown that Weyl's ideas (1923), pertaining to local conformal invariance, find natural embodiment within the framework of a relativistic theory based on a viable Finslerian model of spacetime. This is associated with the peculiar property of the Finslerian metric which describes a locally anisotropic space of events. Such a metric, in contrast to the Riemannian one, is conformal invariant, in which case the local conformal transformations of the Riemannian metric tensor, apart from spacetime intervals, leave invariant rest masses as well as all observables and thus appear as local gauge transformations. The corresponding Finslerian theory of gravitation turns out, as a result, to be an Abelian gauge theory. It satisfies the principle of correspondence with Einstein's theory and predicts a number of non-trivial physical effects accessible for experimental test under laboratory conditions.

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