The Design of a Formal System of Science: A Compelling Basis for Fundamental Physics

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Abstract
A formal system of science is presented as a more powerful replacement for the axioms of fundamental physics. Fundamental theories of physics are typically constructed axiomatically (e.g. Dirac Von-Neumann axioms of quantum mechanics, Special theory of relativity, etc); and are justified on scientific grounds. Although well respected and crucial to the exercise, scientific grounds do not at present benefit from a formal construction. Our idea here is to design a formal system of science able to support the scientific method comprehensively. Once done, our goal will then be to derive the fundamental physics, this time not axiomatically, but as an actual theorem of the system; thereby formalizing their origin and subsequently proving physics. The formalization requirements will be quite demanding, but are responsible for making this exercise surprisingly productive and precise; correcting definitions and resolving numerous open problems spawning philosophy to physics. The first part of the paper consists of constructing an experimental basis that is purely mathematical. For this we employ the set of all halting programs and we leverage modern notions of undecidability to produce a system that never runs out of new knowledge to discover, thus supporting a perpetual application of the scientific method. The exercise culminates in a definition of the observer as a measure space over the halting programs identified by the scientific method, from which the fundamental physics is entailed as a quantum theory of computation also supporting gravity; thus for the first time integrating the observer into the formalism of physics. Finally, the compatibility of our definition with that of the observer in physics is assessed, and testable predictions are proposed for the entailed fundamental physics.
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First archival date: 2019-06-26
Latest version: 133 (2021-11-23)
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