dorsal/arxiv
View SchemaA Local Deterministic Model of Quantum Spin Measurement
| Authors | T. N. Palmer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9505025 |
| URL | https://arxiv.org/abs/quant-ph/9505025 |
Abstract
The conventional view, that Einstein was wrong to believe that quantum physics is local and deterministic, is challenged. A parametrised model, Q, for the state vector evolution of spin 1/2 particles during measurement is developed. Q draws on recent work on so-called riddled basins in dynamical systems theory, and is local, deterministic, nonlinear and time asymmetric. Moreover the evolution of the state vector to one of two chaotic attractors (taken to represent observed spin states) is effectively uncomputable. Motivation for this model arises from Penrose's speculations about the nature and role of quantum gravity. Although the evolution of Q's state vector is uncomputable, the probability that the system will evolve to one of the two attractors is computable. These probabilities correspond quantitatively to the statistics of spin 1/2 particles. In an ensemble sense the evolution of the state vector towards an attractor can be described by a diffusive random walk. Bell's theorem and a version of the Bell-Kochen_specker quantum entanglement paradox are discussed. It is shown that proving an inconsistency with locality demands the existence of definite truth values to certain counterfactual propositions. In Q these deterministic propositions are physically uncomputable and no non-algorithmic solution is either known or suspected. Adapting the mathematical formalist approach, the non-existence of definite truth values to such counterfactual propositions is posited. No inconsistency with experiment is found. Hence Q is not necessarily constrained by Bell's inequality.
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"abstract": "The conventional view, that Einstein was wrong to believe that quantum\nphysics is local and deterministic, is challenged. A parametrised model, Q, for\nthe state vector evolution of spin 1/2 particles during measurement is\ndeveloped. Q draws on recent work on so-called riddled basins in dynamical\nsystems theory, and is local, deterministic, nonlinear and time asymmetric.\nMoreover the evolution of the state vector to one of two chaotic attractors\n(taken to represent observed spin states) is effectively uncomputable.\nMotivation for this model arises from Penrose\u0027s speculations about the nature\nand role of quantum gravity. Although the evolution of Q\u0027s state vector is\nuncomputable, the probability that the system will evolve to one of the two\nattractors is computable. These probabilities correspond quantitatively to the\nstatistics of spin 1/2 particles. In an ensemble sense the evolution of the\nstate vector towards an attractor can be described by a diffusive random walk.\nBell\u0027s theorem and a version of the Bell-Kochen_specker quantum entanglement\nparadox are discussed. It is shown that proving an inconsistency with locality\ndemands the existence of definite truth values to certain counterfactual\npropositions. In Q these deterministic propositions are physically uncomputable\nand no non-algorithmic solution is either known or suspected. Adapting the\nmathematical formalist approach, the non-existence of definite truth values to\nsuch counterfactual propositions is posited. No inconsistency with experiment\nis found. Hence Q is not necessarily constrained by Bell\u0027s inequality.",
"arxiv_id": "quant-ph/9505025",
"authors": [
"T. N. Palmer"
],
"categories": [
"quant-ph",
"chao-dyn",
"gr-qc",
"nlin.CD"
],
"title": "A Local Deterministic Model of Quantum Spin Measurement",
"url": "https://arxiv.org/abs/quant-ph/9505025"
},
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