dorsal/arxiv
View SchemaCould quantum statistical regularities derive from a measure on the boundary conditions of a classical universe?
| Authors | Bruno Galvan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806083 |
| URL | https://arxiv.org/abs/quant-ph/9806083 |
Abstract
The problem of defining the boundary conditions for the universe is considered here in the framework of a classical dynamical theory, pointing out that a measure on boundary conditions must be included in the theory in order to explain the statistical regularities of evolution. It is then suggested that quantum statistical regularities also could derive from this measure. An explicit definition of such a measure is proposed, using both a simplified model of the universe based on classical mechanics and the non-relativistic quantum mechanics formalism. The peculiarity of such a measure is that it does not apply to the initial conditions of the universe, i.e. to the initial positions and momenta of particles, but to their initial and final positions, from which the path is derived by means of the least action principle. This formulation of the problem is crucial and it is supported by the observation that it is incorrect to liken the determination of the boundary conditions of the universe to the preparation of a laboratory system, in which the initial conditions of the system are obviously determined. Some possible objections to this theory are then discussed. Specifically, the EPR paradox is discussed, and it is explained by showing that, in general, a measure on the boundary conditions of the universe generates preinteractive correlations, and that in the presence of such correlations Bell's inequality can no longer be proven true. Finally, it is shown that if one broadens the dynamical scheme of the theory to encompass phenomena such as particle decay and annihilation, the least action principle allows for an indeterministic evolution of the system.
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"abstract": "The problem of defining the boundary conditions for the universe is\nconsidered here in the framework of a classical dynamical theory, pointing out\nthat a measure on boundary conditions must be included in the theory in order\nto explain the statistical regularities of evolution. It is then suggested that\nquantum statistical regularities also could derive from this measure. An\nexplicit definition of such a measure is proposed, using both a simplified\nmodel of the universe based on classical mechanics and the non-relativistic\nquantum mechanics formalism. The peculiarity of such a measure is that it does\nnot apply to the initial conditions of the universe, i.e. to the initial\npositions and momenta of particles, but to their initial and final positions,\nfrom which the path is derived by means of the least action principle. This\nformulation of the problem is crucial and it is supported by the observation\nthat it is incorrect to liken the determination of the boundary conditions of\nthe universe to the preparation of a laboratory system, in which the initial\nconditions of the system are obviously determined. Some possible objections to\nthis theory are then discussed. Specifically, the EPR paradox is discussed, and\nit is explained by showing that, in general, a measure on the boundary\nconditions of the universe generates preinteractive correlations, and that in\nthe presence of such correlations Bell\u0027s inequality can no longer be proven\ntrue. Finally, it is shown that if one broadens the dynamical scheme of the\ntheory to encompass phenomena such as particle decay and annihilation, the\nleast action principle allows for an indeterministic evolution of the system.",
"arxiv_id": "quant-ph/9806083",
"authors": [
"Bruno Galvan"
],
"categories": [
"quant-ph"
],
"title": "Could quantum statistical regularities derive from a measure on the boundary conditions of a classical universe?",
"url": "https://arxiv.org/abs/quant-ph/9806083"
},
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