dorsal/arxiv
View SchemaThe quantum measurement problem and physical reality: a computation theoretic perspective
| Authors | R. Srikanth |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602114 |
| URL | https://arxiv.org/abs/quant-ph/0602114 |
| DOI | 10.1063/1.2400889 |
| Journal | AIP Conference Proceedings 864, pp. 178-193 (2006) |
Abstract
Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub-physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.
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"abstract": "Is the universe computable? If yes, is it computationally a polynomial place?\nIn standard quantum mechanics, which permits infinite parallelism and the\ninfinitely precise specification of states, a negative answer to both questions\nis not ruled out. On the other hand, empirical evidence suggests that\nNP-complete problems are intractable in the physical world. Likewise,\ncomputational problems known to be algorithmically uncomputable do not seem to\nbe computable by any physical means. We suggest that this close correspondence\nbetween the efficiency and power of abstract algorithms on the one hand, and\nphysical computers on the other, finds a natural explanation if the universe is\nassumed to be algorithmic; that is, that physical reality is the product of\ndiscrete sub-physical information processing equivalent to the actions of a\nprobabilistic Turing machine. This assumption can be reconciled with the\nobserved exponentiality of quantum systems at microscopic scales, and the\nconsequent possibility of implementing Shor\u0027s quantum polynomial time algorithm\nat that scale, provided the degree of superposition is intrinsically, finitely\nupper-bounded. If this bound is associated with the quantum-classical divide\n(the Heisenberg cut), a natural resolution to the quantum measurement problem\narises. From this viewpoint, macroscopic classicality is an evidence that the\nuniverse is in BPP, and both questions raised above receive affirmative\nanswers. A recently proposed computational model of quantum measurement, which\nrelates the Heisenberg cut to the discreteness of Hilbert space, is briefly\ndiscussed. A connection to quantum gravity is noted. Our results are compatible\nwith the philosophy that mathematical truths are independent of the laws of\nphysics.",
"arxiv_id": "quant-ph/0602114",
"authors": [
"R. Srikanth"
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"doi": "10.1063/1.2400889",
"journal_ref": "AIP Conference Proceedings 864, pp. 178-193 (2006)",
"title": "The quantum measurement problem and physical reality: a computation theoretic perspective",
"url": "https://arxiv.org/abs/quant-ph/0602114"
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