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Chapter 12 : Heisenberg's uncertainty relation

史郎石川

It may be usually considered that the (12.2) is the mathematical representation of the (12.3).However, it is not true.In fact, in [84], J. von Neumann pointed out the difference between Robertson's uncertainty relation (= (12.2)) and Heisenberg's uncertainty relation (= (12.3)).

Jan 1, 20060 citations

Bell's Theorem: A Critique

M. R. Clover

By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.

arXiv:quant-ph/0502016Feb 1, 20059 citations

How I got to understand Heisenberg's Uncertainty Principle

Eli Maor

(2009). How I got to understand Heisenberg's Uncertainty Principle. Math Horizons: Vol. 16, No. 4, pp. 5-33.

Math HorizonsApr 1, 20090 citations

Aspects of universally valid Heisenberg uncertainty relation

Kazuo Fujikawa, Koichiro Umetsu

A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart et al. [Nat. Phys. 8, 185 (2012)]. This uncertainty relation is closely related to a modified form of the Arthurs–Kelly uncertainty relation, which is also tested by the spin-measurements. The universally valid Heisenberg uncertainty relation always holds, but both the modified Arthurs–Kelly uncertainty relation and the Heisenberg error–disturbance relation proposed by Ozawa, which was analyzed in the original experiment, fail in the present context of spin-measurements, and the cause of their failure is identified with the assumptions of unbiased measurement and disturbance. It is also shown that all the universally valid uncertainty relations are derived from Robertson's relation and thus the essence of the uncertainty relation is exhausted by Robertson's relation, as is widely accepted.A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart et al. [Nat. Phys. 8, 185 (2012)]. This uncertainty relation is closely related to a modified form of the Arthurs–Kelly uncertainty relation, which is also tested by the spin-measurements. The universally valid Heisenberg uncertainty relation always holds, but both the modified Arthurs–Kelly uncertainty relation and the Heisenberg error–disturbance relation proposed by Ozawa, which was analyzed in the original experiment, fail in the present context of spin-measurements, and the cause of their failure is identified with the assumptions of unbiased measurement and disturbance. It is also shown that all the universally valid uncertainty relations are derived from Robertson's relation and thus the essence of the uncertainty relation is exhausted by Robertson's relation, as is widely accepted.

arXiv:1211.1828Progress of Theoretical and Experimental PhysicsJan 1, 20139 citations

29.7 Probability: The Heisenberg Uncertainty Principle

OpenStaxCollege

Aug 22, 20161 citation

Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations

J. A. Mendoza-Fierro, L. M. Arévalo Aguilar, Víctor Manuel Velázquez Aguilar

arXiv:2109.00581The European Physical Journal PlusSep 1, 20214 citations

Chapter 12 : Heisenberg's uncertainty relation

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Chapter 12 : Heisenberg's uncertainty relation

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