Exploring the implications of the uncertainty relationships in quantum mechanics - Wang, Huai-Yu (Frontiers in Physics, 2022)
Heisenberg guessed, after he established the matrix quantum mechanics, that the noncommutativity 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 similar relationship. Soon after, Robertson derived an inequality concerning the space coordinate and momentum, which was thought 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 did careful analysis of Heisenberg’s primary paper. In this work, we point out some serious problems in Heisenberg’s paper and in 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 explanations, i.e., switching concepts; there has actually never been measurement experiment to support the relations. The conclusions are that the so-called coordinate-momentum uncertainty relation has never related to actual measurement, and there does not exist time-energy uncertainty relation.