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Bulletin of the American Physical Society

Universal Uncertainty Relations

Gilad Gour

Published Mar 3, 2014• 0 citations
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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.
The present paper is concerned with the derivation of the Einstein's formula of equivalence of mass and energy, E = mc^2 , from the universal uncertainty relations. These relations are a generalization of the original uncertainty relations developed by Werner Heisenberg in 1927. Thus, this approach unifies two of the most important laws of physics as provides the proof of a) the quantum mechanical nature of the above formula, and, b) the correctness of the universal uncertainty relations that I found in 2012.