Clear evasion of the uncertainty relation with very small probability

TL;DR

This paper argues that the uncertainty relation is a probabilistic consequence of quantum mechanics and can be evaded in processes with very small probability, especially through indirect measurements.

Contribution

It demonstrates that the uncertainty relation can be evaded in specific scenarios with tiny phase space sectors, challenging its interpretation as a fundamental principle.

Findings

Evasion occurs in diffraction processes with small probability

Standard Kennard's relation remains valid overall

No evasion observed in finite two-spin systems with entanglement

Abstract

We entertain the idea that the uncertainty relation is not a principle, but rather it is a consequence of quantum mechanics. The uncertainty relation is then a probabilistic statement and can be clearly evaded in processes which occur with a very small probability in a tiny sector of the phase space. This clear evasion is typically realized when one utilizes indirect measurements, and some examples of the clear evasion appear in the system with entanglement though the entanglement by itself is not essential for the evasion. The standard Kennard's relation and its interpretation remain intact in our analysis. As an explicit example, we show that the clear evasion of the uncertainty relation for coordinate and momentum in the diffraction process discussed by Ballentine is realized in a tiny sector of the phase space with a very small probability. We also examine the uncertainty relation for a two-spin system with the EPR entanglement and show that no clear evasion takes place in this system with the finite discrete degrees of freedom.