Puzzling out the mass-superselection rule

Abstract

Mass-superselection rule (MSR) states that in the non-relativistic quantum theory superpositions of states with different masses are unphysical. While MSR features even in textbooks, its validity, physical content and consequences remain debated. Its original derivation is known to be inconsistent, while a consistent approach does not yield a superselection rule. Yet, superpositions of masses do not seem to be present in Newtonian physics. Here we offer a resolution of the MSR puzzle. Crucial for the result is the understanding of two issues: how the notion of a mass parameter arises from the fundamentally dynamical relativistic notion of mass-energy, and what is the correct Newtonian limit of relativistic dynamics of composite particles. The result explains the physical content of the MSR without invoking any non-standard physics and clarifies the relation between MSR and a formalism describing relativistic composite particles, developed for studying relativistic effects in table top experiments.

Quantized mass-energy effects in an Unruh-DeWitt detector

“…As expected in non-relativistic physics, the above is simply a sum of the internal energy (acting only on the internal DoF) and the kinetic energy (acting only on the CoM) which features one mass parameter m g for all internal states. See refs [37,38] for detailed discussions of the non-relativistic limit of dynamics for composite particles.…”