Quantum equivalence principle without mass superselection

TL;DR

This paper demonstrates that the Einstein equivalence principle remains valid in non-relativistic quantum mechanics without requiring a mass superselection rule by using an extended Galileo group where mass is an operator.

Contribution

It shows that the compatibility of the equivalence principle with quantum mechanics does not depend on the mass superselection rule, using an extended Galileo group framework.

Findings

Superpositions of different masses obey the equivalence principle.

The extended Galileo group treats mass as an operator.

Compatibility with the equivalence principle does not require superselection rules.

Abstract

The standard argument for the validity of Einstein's equivalence principle in a non-relativistic quantum context involves the application of a mass superselection rule. It is surprising that the consistency between such an important principle and quantum mechanics depends crucially on the imposition of a non-fundamental restriction. The objective of this work is show that, contrary to what the standard account holds, the compatibility between the principle of equivalence and quantum mechanics does not depend on the introduction of such a superselection rule. For this purpose, we consider the extended Galileo group, in which mass is treated as an operator, and show that within this scheme superpositions of different masses behave as they should in order to obey the equivalence principle.