2002/02/14 by John D. Fearns, John David Fearns, Fearns, John D. · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0202079
30 pages. Submitted to IJTP for publication and available at http://theory.ic.ac.uk/Papers/
arxiv created 2002/02/14 · openalex publication_date 2002/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a mathematical universe different from that represented by set theory, we show that more thought and a better appreciation of the assumptions going into any mathematical model of the physical world are needed. We reflect on some of the mathematical consequences of this wider perspective of physics, explaining one interpretation of probabilistic values and numerical calculations in two mathematical universes governed by the less restrictive intuitionistic logic, and known to support the theory of synthetic differential geometry.