dorsal/arxiv
View SchemaBell's Theorem: a new Derivation that Preserves Heisenberg and Locality
| Authors | Michael Clover |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409058 |
| URL | https://arxiv.org/abs/quant-ph/0409058 |
Abstract
By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an extra term related to the time-ordering of actual measurements is found to augment (i.e. weaken) the upper bound of the inequality. Since the same locality assumptions hold for this rederivation as for the original, we conclude that only {\em classical} measurement-order independent local hidden variable theories are constrained by Bell's inequality; time dependent, non-classical local theories (i.e. theories respecting Heisenberg's Uncertainty Principle) can satisfy this new bound while exceeding Bell's limit. Unconditional nonlocality is only expected to occur with Bell parameters between $2\sqrt{2}$ and 4. This weakening of Bell's inequality is seen for the quantum Bell operator (squared) as an extra term involving the commutators of {\em local} measurement operators. We note that a factorizable second-quantized wavefunction can reproduce experimental measurements; because such wavefunctions allow local de Broglie-Bohm hidden variable modelling, we have another indication that violation of {\em Bell's} inequality does not require an acceptance of non-locality.
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"abstract": "By implicitly assuming that all measurements occur simultaneously, Bell\u0027s\nTheorem only applied to local theories that violated Heisenberg\u0027s Uncertainty\nPrinciple. By explicitly introducing time into our derivation of Bell\u0027s\ntheorem, an extra term related to the time-ordering of actual measurements is\nfound to augment (i.e. weaken) the upper bound of the inequality. Since the\nsame locality assumptions hold for this rederivation as for the original, we\nconclude that only {\\em classical} measurement-order independent local hidden\nvariable theories are constrained by Bell\u0027s inequality; time dependent,\nnon-classical local theories (i.e. theories respecting Heisenberg\u0027s Uncertainty\nPrinciple) can satisfy this new bound while exceeding Bell\u0027s limit.\nUnconditional nonlocality is only expected to occur with Bell parameters\nbetween $2\\sqrt{2}$ and 4. This weakening of Bell\u0027s inequality is seen for the\nquantum Bell operator (squared) as an extra term involving the commutators of\n{\\em local} measurement operators. We note that a factorizable second-quantized\nwavefunction can reproduce experimental measurements; because such\nwavefunctions allow local de Broglie-Bohm hidden variable modelling, we have\nanother indication that violation of {\\em Bell\u0027s} inequality does not require\nan acceptance of non-locality.",
"arxiv_id": "quant-ph/0409058",
"authors": [
"Michael Clover"
],
"categories": [
"quant-ph"
],
"title": "Bell\u0027s Theorem: a new Derivation that Preserves Heisenberg and Locality",
"url": "https://arxiv.org/abs/quant-ph/0409058"
},
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