dorsal/arxiv
View SchemaSome Reflections on the Status of Conventional Quantum Theory when Applied to Quantum Gravity
| Authors | C. J. Isham |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206090 |
| URL | https://arxiv.org/abs/quant-ph/0206090 |
Abstract
All current approaches to quantum gravity employ essentially standard quantum theory including, in particular, continuum quantities such as the real or complex numbers. However, I wish to argue that this may be fundamentally wrong in so far as the use of these continuum quantities in standard quantum theory can be traced back to certain {\em a priori} assumptions about the nature of space and time: assumptions that may be incompatible with the view of space and time adopted by a quantum gravity theory. My conjecture is that in, some yet to be determined sense, to each type of space-time there is associated a corresponding type of quantum theory in which continuum quantities do not necessarily appear, being replaced with structures that are appropriate to the specific space-time. Topos theory then arises as a possible tool for `gluing' together these different theories associated with the different space-times. As a concrete example of the use of topos ideas, I summarise recent work applying presheaf theory to the Kochen-Specher theorem and the assignment of values to physical quantities in a quantum theory.
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"abstract": "All current approaches to quantum gravity employ essentially standard quantum\ntheory including, in particular, continuum quantities such as the real or\ncomplex numbers. However, I wish to argue that this may be fundamentally wrong\nin so far as the use of these continuum quantities in standard quantum theory\ncan be traced back to certain {\\em a priori} assumptions about the nature of\nspace and time: assumptions that may be incompatible with the view of space and\ntime adopted by a quantum gravity theory. My conjecture is that in, some yet to\nbe determined sense, to each type of space-time there is associated a\ncorresponding type of quantum theory in which continuum quantities do not\nnecessarily appear, being replaced with structures that are appropriate to the\nspecific space-time.\n Topos theory then arises as a possible tool for `gluing\u0027 together these\ndifferent theories associated with the different space-times. As a concrete\nexample of the use of topos ideas, I summarise recent work applying presheaf\ntheory to the Kochen-Specher theorem and the assignment of values to physical\nquantities in a quantum theory.",
"arxiv_id": "quant-ph/0206090",
"authors": [
"C. J. Isham"
],
"categories": [
"quant-ph",
"gr-qc"
],
"title": "Some Reflections on the Status of Conventional Quantum Theory when Applied to Quantum Gravity",
"url": "https://arxiv.org/abs/quant-ph/0206090"
},
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