Vacuum Fluctuations, Cosmogenesis and Prime Number Gaps

Mathematics – Number Theory

Scientific paper

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Scientific paper

Starting from E.Tryon (1973), idea of cosmogenesis through quantum tunnelling "from nothing" became popular. Both complimentary streams of it, inflationary models (Guth, Linde) and quantum parallelism (Everett, Deutsch), require some starting point as, e.g., concretisation of Leibnitz Principle (Omnibus ex nihil decendis sufficit unum). This leads to propositional conjecture (axiom?) that (meta)physical "Platonic Pressure" of infinitude of numbers and Cantor "alephs" becomes an engine for self-generation of physical universe directly out of mathematics: inexhaustibility of Number Theory (NT) drives cosmogenesis. While physics in other quantum branches of inflating universe (Megaverse) can be (arbitrary) different from ours, NT is not (it is unique, absolute, immutable and infinitely resourceful). Energy-time uncertainty principle (UP) allows indefinite lifetime provided we start from total zero energy. Analogue of UP in NT is theorem by H.Maier (1981) stating the existence of arbitrary long trails of isolated primes such that each next gap is arbitrary greater than average gap (logN). On physical level these arbitrary large deviations from Prime Number Theorem translate into permissiveness of (arbitrary) large quantum fluctuations.

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