dorsal/arxiv
View SchemaQuantum mechanics without spacetime - a possible case for noncommutative differential geometry?
| Authors | T. P. Singh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112119 |
| URL | https://arxiv.org/abs/quant-ph/0112119 |
Abstract
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter sources. Thus it could be said that the currently known formulation of quantum mechanics pre-assumes the presence of classical matter fields. A more fundamental formulation of quantum mechanics should exist, which avoids having to use a notion of time. In this paper we discuss as to how such a fundamental formulation could be constructed for single particle, non-relativistic quantum mechanics. We argue that there is an underlying non-linear theory of quantum gravity, to which both standard quantum mechanics and classical general relativity are approximations. The timeless formulation of quantum mechanics follows from the underlying theory when the mass of the particle is much smaller than Planck mass. On the other hand, when the particle's mass is much larger than Planck mass, spacetime emerges and the underlying theory should reduce to classical mechanics and general relativity. We also suggest that noncommutative differential geometry is a possible candidate for describing this underlying theory.
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"abstract": "The rules of quantum mechanics require a time coordinate for their\nformulation. However, a notion of time is in general possible only when a\nclassical spacetime geometry exists. Such a geometry is itself produced by\nclassical matter sources. Thus it could be said that the currently known\nformulation of quantum mechanics pre-assumes the presence of classical matter\nfields. A more fundamental formulation of quantum mechanics should exist, which\navoids having to use a notion of time. In this paper we discuss as to how such\na fundamental formulation could be constructed for single particle,\nnon-relativistic quantum mechanics. We argue that there is an underlying\nnon-linear theory of quantum gravity, to which both standard quantum mechanics\nand classical general relativity are approximations. The timeless formulation\nof quantum mechanics follows from the underlying theory when the mass of the\nparticle is much smaller than Planck mass. On the other hand, when the\nparticle\u0027s mass is much larger than Planck mass, spacetime emerges and the\nunderlying theory should reduce to classical mechanics and general relativity.\nWe also suggest that noncommutative differential geometry is a possible\ncandidate for describing this underlying theory.",
"arxiv_id": "quant-ph/0112119",
"authors": [
"T. P. Singh"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"title": "Quantum mechanics without spacetime - a possible case for noncommutative differential geometry?",
"url": "https://arxiv.org/abs/quant-ph/0112119"
},
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