Physics Beyond The Set : Theoretic Axiom of Foundation

• Classicalmechanics implicitly use Archimedes' axiom, according to that everything maybe measured by a rigid scale. Uncertainty in quantum mechanicsshows the limits of applying Archimedes' axiom. The negation ofArchimedes' axiom is derivative from the negation of the set-theoreticaxiom of foundation. The latter postulates that the set-membership relationis well-founded: for every set there exists no infinitely descendingchain. Denying the foundation axiom in number systems implies settinga non-Archimedean ordering structure. The main claim of our paperis that physical reality may be regarded as non-well-founded inthe framework of probabilities distributed on non-Archimedean ordering structures, inparticular, distributed on p-adic numbers

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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MATHEMATICS

MATEMATIK

Matematik

Mathematics

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