Authors: Felix M. Lev
We consider a system of two free bodies in de Sitter invariant quantum mechanics. De Sitter invariance is understood such that representation operators satisfy commutation relations of the de Sitter algebra. Our approach does not involve quantum field theory, de Sitter space and its geometry (metric and connection). At very large distances the standard relative distance operator describes a well known cosmological acceleration. In particular, the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for solving this problem. At the same time, for systems of macroscopic bodies this operator does not have correct properties at smaller distances and should be modified. We propose a modification which has correct properties, reproduces Newton's gravity, the gravitational redshift of light and the precession of Mercury's perihelion if the width of the de Sitter momentum distribution δ for a macroscopic body is inversely proportional to its mass m. We argue that fundamental quantum theory should be based on a Galois field with a large characteristic p which is a fundamental constant characterizing laws of physics in our Universe. Then one can give a natural explanation that δ = constR/(mG) where R is the radius of the Universe (such that λ = 3/R2 is the cosmological constant) and G is a quantity defining Newton's gravity. A very rough estimation gives G ~ R/(mNlnp) where mN is the nucleon mass. If R is of order 1026m then lnp is of order 1080 and therefore p is of order exp(1080). In the formal limit p → ∞ gravity disappears, i.e. in our approach gravity is a consequence of finiteness of nature.
Comments: 94 pages, 2 figures. Chapter 3 (considering observable gravitational effects) has been considerably revised.
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