dorsal/arxiv
View SchemaA Physical Quantum Model in a Smooth Topos
| Authors | John D. Fearns |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202079 |
| URL | https://arxiv.org/abs/quant-ph/0202079 |
Abstract
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.
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"abstract": "We strengthen the case that the new logical perspective afforded by topos\ntheory is suitable to the task of describing the physical world around us. In\nexploring some of the aspects of construction of a simple quantum-mechanical\nsystem in a mathematical universe different from that represented by set\ntheory, we show that more thought and a better appreciation of the assumptions\ngoing into any mathematical model of the physical world are needed. We reflect\non some of the mathematical consequences of this wider perspective of physics,\nexplaining one interpretation of probabilistic values and numerical\ncalculations in two mathematical universes governed by the less restrictive\nintuitionistic logic, and known to support the theory of synthetic differential\ngeometry.",
"arxiv_id": "quant-ph/0202079",
"authors": [
"John D. Fearns"
],
"categories": [
"quant-ph"
],
"title": "A Physical Quantum Model in a Smooth Topos",
"url": "https://arxiv.org/abs/quant-ph/0202079"
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