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Quantum Information and Measurement (QIM)

On the physical conclusion of the Heisenberg- Uncertainty-Relation

Jascha Zander, Roman Schnabel

Published Jan 1, 2019• 0 citations
Publisher
DOI
10.1364/qim.2019.t5a.25

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•Oct 16, 2023•1 citation
Heisenberg guessed, after he established the matrix quantum mechanics, that the non-commutativity of the matrices of position and momentum implied that the position and momentum of a particle could not be precisely simultaneously determined. He consequently conjectured that time and energy should also have a similar relationship. Soon after, Robertson derived an inequality concerning the space coordinate and momentum, which was thought to be the mathematical expression of the uncertainty relation guessed by Heisenberg. Since then, people have tried various devices to prove the correctness of these two relations. However, no one conducted a careful analysis of Heisenberg’s primary paper. In this work, we point out some serious problems in Heisenberg’s paper and the literature talking about the uncertainty relationships: the physical concepts involved in the uncertainty relations are not clear; one physical concept had more than one explanation, i.e., switching concepts; there has never been measurement experiment to support the relations. The conclusions are that the so-called coordinate–momentum uncertainty relation has never been related to actual measurement and there does not exist a time–energy uncertainty relation.
Recently, violation of Heisenberg's uncertainty relation in spin measurements is discussed [J.Erhart et al., Nature Physics 8, 185 (2012)] and [G.Sulyok et al., Phys.Rev. A 88, 022110 (2013)].We derive the optimal limitation of Heisenberg's uncertainty principle in a specific two-level system (e.g., electron spin, photon polarizations, and so on).Some physical situation is that we would measure x σ and y σ , simultaneously.The optimality is certified by the Bloch sphere.We show that a violation of Heisenberg's uncertainty principle means a violation of the Bloch sphere in the specific case.Thus, the above experiments show a violation of the Bloch sphere when we use ±1 as measurement outcome.This conclusion agrees with recent researches [K.
The Heisenberg equation may not be as well-known as Einstein’s e=mc^2. But the Heisenberg equation’s implications that there is an irreducible uncertainty with regard to the position of an object are no less intriguing than the implications of Einstein’s relativity equation that time slows to a stop when the relative velocity of an object approaches the speed of light. Using elementary mathematics and science, this paper begins by examining the physics of motion of an everyday object such as a tennis ball. The paper shows that the same physics that applies to everyday objects in fact also applies when it comes to subatomic particles, such as an electron in motion. And by taking gradual incremental steps in developing the mathematics of the underlying physics, the paper leads to the conclusion that the universe is inherently uncertain, that it is impossible to know the exact position of any object.