Quantum stresses in the hydrogen atom

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.