Does the Differential Structure of Space-Time Follow from Physical Principles?

Research output: Contribution to journalArticlepeer-review

Abstract

This article examines Wigner’s view on the unreasonable effectiveness of mathematics in the natural sciences, which was based on Cantor’s claim that ‘mathematics is a free creation of the human mind’. It is contended that Cantor’s claim is not relevant to physics because it was based on his power set construction, which does not preserve neighborhoods of geometrical points. It is pointed out that the physical notion of Einstein causality can be defined on a countably infinite point set M with no predefined mathematical structure on it, and this definition endows M with a Tychonoff topology. Under Shirota’s theorem, M can therefore be embedded as a closed subspace of (Formula presented.) for some J. While this suggests that the differentiable structure of (Formula presented.) may follow from the principle of causality, the argument is constrained by the fact that the completion processes (analyzed here in some detail) required for the passage from (Formula presented.) to (Formula presented.) remain empirically untestable.

Original languageEnglish
Article number179
JournalEntropy
Volume26
Issue number3
DOIs
StatePublished - 1 Mar 2024

Keywords

  • differentiable structures
  • relativistic causality
  • uniform completion

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Electrical and Electronic Engineering

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