# Puzzling out the mass-superselection rule

## TL;DR

This paper resolves the longstanding puzzle of the mass-superselection rule by clarifying its physical meaning and relation to relativistic mass-energy and the Newtonian limit, without invoking non-standard physics.

## Contribution

It provides a consistent explanation of the mass-superselection rule by analyzing the emergence of mass from relativistic energy and its Newtonian limit, clarifying its physical content.

## Key findings

- Superpositions of different masses are unphysical in non-relativistic quantum theory.
- The mass-superselection rule can be explained without non-standard physics.
- Relativistic mass-energy concepts clarify the rule's physical meaning.

## 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.