On the logical structure of physics
Abstract
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The paper introduces such a model for the fragment which covers ``free theories'', that is physical theories with Gaussian (quadratic) potential. The model is pseudo-finite (equivalently, a limit of finite models), based on a pseudo-finite field in place of the field of complex numbers. The advantage of this unusual setting is that it treats the quantum and the statistical mechanics as just domains in the same model and explains Wick rotation as a natural transformation of the model corresponding to a shift in scales of physical units.
Cite
@article{arxiv.2410.01846,
title = {On the logical structure of physics},
author = {Boris Zilber},
journal= {arXiv preprint arXiv:2410.01846},
year = {2024}
}