A Universally Valid Uncertainty Relation Revisited

TL;DR

This paper revisits Ozawa's universally valid uncertainty relation, analyzing conditions for its violation and providing experimental evidence of its boundary condition effects through re-analysis of hydrogen molecule data.

Contribution

It offers a detailed theoretical analysis of conditions for violating the generalized uncertainty relation and presents experimental validation using molecular data.

Findings

Conditions for violation of the uncertainty relation are identified.

Experimental data shows boundary conditions can lessen the uncertainty bound.

Re-analysis confirms the theoretical predictions.

Abstract

A universally valid uncertainty relation proposed by Ozawa is re-investigated under for the generalized equation of motion with some boundary condition. Necessary conditions for violation (lessening) of the Heisenberg-type uncertainty relation is discussed in detail. An experimental test of lessening of the generalized uncertainty relation due to the boundary condition is shown by re-analyzing the data measuring electron densities of hydrogen molecule encapsulated in a cage of fullerene C60.