Quantum stresses in the hydrogen atom

TL;DR

This paper investigates the interpretation of gravitational form factors as stress distributions inside the hydrogen atom, using the pilot wave interpretation to clarify their physical meaning and revealing that ar c measures the binding force.

Contribution

It provides a novel interpretation of gravitational form factors in quantum systems, specifically clarifying the physical meaning of ar c and D in the hydrogen atom context.

Findings

ar c quantifies the binding force in the hydrogen atom.

The interpretation of form factors as stress distributions is validated.

The pilot wave interpretation aids in understanding quantum stress distributions.

Abstract

Gravitational form factors are often interpreted as providing access to stresses inside hadrons, in particular through Fourier transforms of the form factors $D$ and $\bar{c}$. Some researchers, however, have expressed skepticism of this interpretation. I revisit the question, and argue that it is indeed appropriate to interpret these quantities as stress distributions. I consider the hydrogen atom's ground state as a familiar example, and use the pilot wave interpretation of quantum mechanics to give the distributions a clear meaning. A striking result is that $\bar{c}$ -- rather than $D$ -- quantifies the force law binding the system, which can be understood through Cauchy's first law of motion.