## Geometry as an object of experience: Kant and the missed debate between Poincar\'e and Einstein

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Hacyan, S.

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Poincar\'e held the view that geometry is a convention and cannot be tested
experimentally. This position was apparently refuted by the general theory of
relativity and the successful confirmation of its predictions; unfortunately,
Poincar\'e did not live to defend his thesis. In this paper, I argue that: 1)
Contrary to what many authors have claimed, non-euclidean geometries do not
rule out Kant's thesis that space is a form of intuition given {\it a priori};
on the contrary, Euclidean geometry is the condition for the possibility of any
more general geometry. 2) The conception of space-time as a Riemannian manifold
is an extremely ingenious way to describe the gravitational field, but, as
shown by Utiyama in 1956, general relativity is actually the gauge theory
associated to the Lorentz group. Utiyama's approach does not rely on the
assumption that space-time is curved, though the equations of the gauge theory
are identical to those of general relativity. Thus, following Poincar\'e, it
can be claimed that it is only a matter of convention to describe the
gravitational field as a Riemannian manifold or as a gauge field in Euclidean
space.

Comment: 13 pages

Comment: 13 pages

##### Keywords

Physics - History and Philosophy of Physics, Physics - General Physics