Heisenberg, uncertainty, and the scanning tunneling microscope

TL;DR

This paper analyzes high-resolution STM experiments and finds that interpreting electron charge density as a statistical quantity conflicts with the Heisenberg uncertainty principle, suggesting charge density is physically real and precisely measurable.

Contribution

It demonstrates that the electron charge density cannot be purely statistical, challenging conventional interpretations and reconciling experimental precision with quantum principles.

Findings

Charge density interpretation conflicts with Heisenberg uncertainty

Experimental precision implies charge density is measurable

Uncertainty principle would be violated if charge density were statistical

Abstract

We show by a statistical analysis of high-resolution scanning tunneling microscopy (STM) experiments, that the interpretation of the density of electron charge as a statistical quantity leads to a conflict with the Heisenberg uncertainty principle. Given the precision in these experiments we find that the uncertainty principle would be violated by close to two orders of magnitude, if this interpretation were correct. We are thus forced to conclude that the density of electron charge is a physically real, i.e., in principle precisely measurable quantity.