Physics in a finite geometry

TL;DR

This paper argues that rejecting the axiom of infinity in mathematics leads to a finite geometric framework in physics, ensuring all classical field theories become quantizable and resolving issues with infinities in calculations.

Contribution

It introduces a finite geometric approach to physics by negating the axiom of infinity, addressing infinities in physical theories and their quantizability.

Findings

All classical field theories are quantizable in finite geometry.

Negating the axiom of infinity prevents the emergence of infinities in physical calculations.

Provides a new foundational perspective linking finite geometry to quantum physics.

Abstract

The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However, not only does such possibility run counter to computational feasibleness, but it also leads to the most serious problem in modern physics, to wit, the emergence of infinities in calculated physical quantities. Particularly, having agreed on the axiom of infinity for set theory -- the backbone of the theoretical foundations of calculus integrated in every branch of physics -- one could no longer rule out the existence of a classical field theory which is not quantizable, let alone renormalizable. By contrast, the present paper shows that negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable.