Quantum equivalence principle without mass superselection

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

Galilei covariance and Einstein's equivalence principle in quantum reference frames

“…The framework devised by Bargmann constrains the compatibility of quantum mechanics with both GC and EEP to the nonexistence of mass superpositions. While Bargmann's formal construction is widely accepted in the literature and already figures as textbook content [2,3], his conclusion has been recurrently debated [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In particular, some authors interpreted the massdependent phase as a residue of the twin-paradox effect in nonrelativistic quantum mechanics [4,17], thus attributing deeper physical meaning to it.…”

“…On the other hand, there are some works defending that quantum mechanics is compatible with EEP [18][19][20]. In consonance with a program initiated long ago [7][8][9][10], it was recently suggested that the mass-superselection rule can be avoided if mass is taken as a dynamical variable [5]. Regardless of their conclusions, all of the aforementioned works stick to traditional ingredients, namely, the reference frames are fundamentally classical and the analysis is focused on the wave function.…”

Puzzling out the mass-superselection rule

“…Finally, proposals were put forward to simulate dynamics of mass-superpositions with quantum optical setups in order to test MSR experimentally [6]. On the other hand a fully consistent formalism has been developed where mass and proper time are conjugate dynamical variables [7][8][9][10][11]. This challenges the above approaches and shows that neither physical meaning nor validity of MSR are fully understood.…”

“…( 7)). We usually do not think of time dilation effects as demonstrating masssuperpositions -nor as effects violating MSR -although H le with H r → M c 2 is operationally the same as H dm , with the added rest mass term, as in refs [7][8][9][10][11].…”

“…In fact, mass-energy equivalence has been used by Einstein to derive the gravitational time dilation [41]. The symmetry of the dynamical-mass framework comprises Galilean transformations for spacetime coordinates and translations along a new coordinate associated with the dynamical mass [4,11,23]. The lowenergy relativistic theory is instead invariant under central extension of the Galilei group with mass-energy as the central element, which is the Lorentz symmetry up to 1/c 2 [27], and proper time takes the role of the additional coordinate [7,8,10].…”