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A uniform change of size of all space-time intervals could not be detected, since the measuring instruments would be changed too. Therefore, a principle of similarity is proposed requiring that the equations of physics be invariant under such changes. This is shown to correspond to the principle that all units of interval are equivalent for expressing physical laws. It is pointed out that a given metrical tensor in the usual tensor calculus defines a specific unit of interval, so that the principle of similarity requires an enlargement of the tensor formalism and a corresponding change in the underlying geometry.
Banesh Hoffmann (Thu,) studied this question.