Mathematical Physics

   

A Minimalist Derivation of the Theory of Everything

Authors: Alexandre Harvey-Tremblay

In this work, I present a minimalist approach to first-order logic and show how it implies a restriction on any possible Theory of Everything in physics (ToE) of sufficient strength to recover actual laws of physics. The minimalist approach is, in many ways, similar to the constructivist project in mathematics but taken to the extreme. The approach starts from first-order logic with no axioms and further removes all rules of inference with the exception of the proof by construction. Although this severely cripples first-order logic it nonetheless impairs it with the following advantage. From an argument originally made by Plato, I argue that each axioms or rules of inference that are removed increases the "epistemological irrefutability" of the theory. Taken to the extreme, once all axioms and all rules of inference are removed, the theory becomes entirely irrefutable and specifically in the case of this approach, as the first-order logic system is minimal, the epistemological irrefutability of its theorems is maximal. Using this approach, I construct a universal language defined by a small list of first-order sentences. Each of these sentences claims the existence of an object of language which is provable by construction, the only rule of inference allowed by the minimalist system. As a result of being a theorem of a minimal system, the existence of the constructed universal language is therefore maximally irrefutable. On the grounds that any ToE must at the very least recover all maximally irrefutable knowledge, I recover a strong restriction applicable to any possible ToE candidate. Part I is the minimalist derivation of the ToE restriction. From this derivation I obtain a master equation formulated as a Gibbs ensemble and relating the algorithmic notions of provable-sentences to that of entropy. Part II is the derivation of the physical laws. I recover, from the master equation, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR) and the holographic principle. These equations are derived entirely from pure reason with no appeal to physical observations. All physical laws obtained are shown to be emergent from informational entropy. Naturally, deriving both the Dirac equation and general relativity from the same theory is highly suggestive that the ToE-restriction should be promoted to a ToE-candidate. This result motivates the ToE claim made in this paper.

Comments: 64 Pages.

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Submission history

[v1] 2017-05-18 09:56:01
[v2] 2017-05-18 12:57:31
[v3] 2017-05-23 14:09:54
[v4] 2017-05-26 07:05:40
[v5] 2017-07-11 20:36:09
[v6] 2017-07-12 07:20:57
[v7] 2017-07-21 13:53:03
[v8] 2017-07-22 05:29:56
[v9] 2017-07-23 13:00:22
[vA] 2017-07-24 06:58:20
[vB] 2017-07-25 12:50:01
[vC] 2017-07-25 19:07:22
[vD] 2017-07-26 07:05:11
[vE] 2017-07-26 08:04:32
[vF] 2017-08-14 10:34:44
[vG] 2017-08-16 20:21:03
[vH] 2017-09-11 12:00:42
[vI] 2017-09-12 09:43:06
[vJ] 2017-09-17 15:07:54

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