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Constructibility in Physics

BenDaniel, David J. (2013) Constructibility in Physics. [Preprint]

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Abstract

We pursue an approach in which space-time proves to be relational and its differential properties fulfill the strict requirements of Einstein-Weyl causality. Space-time is developed from a set theoretical foundation for a constructible mathematics. The foundation proposed is the axioms of Zermelo-Frankel (ZF) but without the power set axiom, with the axiom schema of subsets removed from the axioms of regularity and replacement and with an axiom of countable constructibility added. Four arithmetic axioms, excluding induction, are also adjoined; these formulae are contained in ZF and can be added here as axioms. All sets of finite natural numbers in this theory are finite and hence definable. The real numbers are countable, as in other constructible theories. We first show that this approach gives polynomial functions of a real variable. Eigenfunctions governing physical fields can then be effectively obtained. Furthermore, using a null integral of the Lagrange density of a field over a compactified space, we produce a nonlinear sigma model. The Schroedinger equation follows from a proof in the theory of the discreteness of the space-like and time-like terms of the model. This result suggests that quantum mechanics in this relational space-time framework can be considered conceptually cumulative with prior physics.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
BenDaniel, David J.djb16@cornell.edu
Keywords: set theoretical foundations of physics, relational space-time, Einstein-Weyl causality
Subjects: Specific Sciences > Physics
Depositing User: David Jacob BenDaniel
Date Deposited: 11 Mar 2013 16:01
Last Modified: 30 Jul 2013 07:18
Item ID: 9610
Subjects: Specific Sciences > Physics
Date: 10 March 2013
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/9610

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