The solution of the Sixth Hilbert Problem: the Ultimate Galilean Revolution

TL;DR

The paper advocates for a fully mathematical formulation of physical theories, eliminating physical primitives to ensure logical coherence and falsifiability, proposing this as the solution to Hilbert's Sixth Problem.

Contribution

It introduces a novel approach to physics based on pure mathematics and algorithms, aiming to resolve the Sixth Hilbert Problem by removing physical primitives.

Findings

Mathematical theories can achieve logical coherence and falsifiability.

Recent information-theoretical derivations support a purely mathematical physics.

This approach offers a potentially universal and eternally valid framework for natural sciences.

Abstract

I argue for a full mathematisation of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: "physics from no physics". Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either don't have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as "clock", "rigid rod ", "force", "inertial mass" (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the Sixth Hilbert's Problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.