Taking physical infinity seriously

TL;DR

This paper explores the potential of integrating the concept of infinity into physics, examining speculative ideas and challenges, including the use of nonstandard analysis, to advance understanding of physical theories.

Contribution

It proposes considering physical infinity seriously and discusses the speculative application of nonstandard analysis to physics, highlighting both possibilities and difficulties.

Findings

Infinity could offer new insights into physical theories

Nonstandard analysis may provide a mathematical framework for physical infinity

Significant conceptual and technical challenges remain

Abstract

The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might be warranted in physics. Several threads will be speculatively examined, including some involving nonstandard analysis. While there are intriguing possibilities, there also are noteworthy difficulties.