Vasily Leonidovich Yanchilin
Keywords: Riemannian geometry, general relativity, gravity, atomic size, atomic clock, universal law of compression of Solids.
Abstract: Poincaré asserted that any non-Euclidean geometry can and should be reduced to Euclidean one by correcting physics. However, Einstein proposed to describe gravity using Riemannian geometry. From the viewpoint of Poincaré, this was an unreasonable step that can lead physicists into mathematical jungles. In this paper we used Euclidean geometry instead of Riemannian geometry. To do this, we introduced a new universal law of compression and expansion of all bodies, including atoms, in a gravitational field. In the case of a weak field, a new approach leads to the same equation of motion as in general relativity. In the case of a strong field, a new approach allows us to solve the problem of black holes and the problem connected to Mach\'s principle. An experiment with atomic clocks is proposed, which will allow us to determine whether geometry in a gravitational field really becomes Riemannian or it remains Euclidean.
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