A new uncertainty Relation (revised version)

TL;DR

This paper introduces a revised quantum uncertainty relation linking electromagnetic potential and position uncertainty, and demonstrates its validation through observed potential drops in quantum Hall effect samples.

Contribution

It formulates a new quantum electrodynamical uncertainty relation and connects it to experimental observations in quantum Hall systems.

Findings

The new relation is consistent with observed potential drops at quantum Hall edges.

Potential drops can be interpreted as quantum uncertainties in the electromagnetic potential.

The relation bridges quantum electrodynamics and condensed matter phenomena.

Abstract

We formulate according to the quantum mechanical uncertainty relation a new quantum electrodynamical uncertainty relation $\Delta \breve{A} . \Delta l \sim \hbar/e$ where $\breve{A}$ and $\Delta l \geq l_B$ are the electromagnetic pure gauge potential, the position uncertainty and the magnetic length, respectively. Then, we show that the observed potential drops on the edge of QHE samples are varifications of this uncertainty relation, where the quantum potential drop of the relevant component of potential can be considered as its quantum uncertainty $\Delta \breve{A}$.