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arXiv:1305.2450 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Testing the equivalence principle with unstable particles

Yuri Bonder, Ephraim Fischbach, H. Hernández-Coronado, D. E. Krause, Z.J. Rohrbach, Daniel Sudarsky

Published Jun 11, 2013• 12 citations
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Abstract

We develop a framework to test the equivalence principle under conditions where the quantum aspects of nature cannot be neglected, specifically in the context of interference phenomena with unstable particles. We derive the nonrelativistic quantum equation that describes the evolution of the wave function of unstable particles under the assumption of the validity of the equivalence principle and when small deviations are assumed to occur. As an example, we study the propagation of unstable particles in a COW experiment, and we briefly discuss the experimental implications of our formalism.

DOI
10.1103/physrevd.87.125021

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We develop a framework to test the equivalence principle under conditions where the quantum aspects of nature cannot be neglected, specifically in the context of interference phenomena with unstable particles. We derive the nonrelativistic quantum equation that describes the evolution of the wave function of unstable particles under the assumption of the validity of the equivalence principle and when small deviations are assumed to occur. As an example, we study the propagation of unstable particles in a COW experiment, and we briefly discuss the experimental implications of our formalism.
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the “classical” detector and the “quantum” system, must be relaxed. We argue, therefore, that if both the equivalence principle and quantum mechanics continue to survive experimental tests, then this favors “informational” interpretations of quantum mechanics (where formalism is built around relations between observables, defined as information that can be accessed by an observer of the system. In particular “collapse” is understood as a change of relative information as the detector interacts with the system) over “ontic ones” (assuming the physical reality of states and wave functions, which are assumed to be more than informational objects. In particular collapse is understood as a physical process). In particular, we show that relational-type interpretations can readily accommodate the equivalence principle via a minor modification of the assumptions used to justify the formalism. We qualitatively speculate what a full generally covariant quantum dynamics could look like, and comment on experimental investigations.
The covariance of the Schr\"odinger equation under Galilei boosts and the compatibility of nonrelativistic quantum mechanics with Einstein's equivalence principle have been constrained for so long to the existence of a superselection rule which would prevent a quantum particle from being found in superposition states of different masses. In an effort to avoid this expedient, and thus allow nonrelativistic quantum mechanics to account for unstable particles, recent works have suggested that the usual Galilean transformations are inconsistent with the nonrelativistic limit implied by the Lorentz transformation. Here we approach the issue in a fundamentally different way. Using a formalism of unitary transformations and employing quantum reference frames rather than immaterial coordinate systems, we show that the Schr\"odinger equation, although form variant, is fully compatible with the aforementioned principles of relativity.
I comment on the interpretation of a recent experiment showing quantum interference in time. It is pointed out that the standard nonrelativistic quantum theory, used by the authors in their analysis, cannot account for the results found, and therefore that this experiment has fundamental importance beyond the technical advances it represents. The recent experiment of Lindner, et al 1, clearly shows the effect of interference in time for a particle wave function. The results are discussed in that paper in terms of a very precise solution of the time-dependent nonrelativistic Schrödinger equation. In this Comment, I wish to point out that the nonrelativistic Schrödinger theory cannot predict interference phenomena in time, and therefore the very striking results of this beautiful experiment have a fundamental importance which goes beyond the technical advances which it represents. It is well known, in fact, that the nonrelativistic quantum theory cannot predict interference in time. For example, Ludwig 2 has pointed out that the time variable cannot be a quantum observable, a prerequisite for the development of interference phenomena, since
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In quantum theory we refer to the probability of finding a particle between positions xxx and x+dxx+dxx+dx at the instant ttt, although we have no capacity of predicting exactly when the detection occurs. In this work, we first present an extended nonrelativistic quantum formalism where space and time play equivalent roles. It leads to the probability of finding a particle between xxx and x+dxx+dxx+dx during [t,t+dtt,\phantom{\rule{0.16em}{0ex}}t+dtt,t+dt]. Then, we find a Schr\"odinger-like equation for a ``mirror'' wave function $\ensuremath{\phi}(t,x)$ associated with the probability of measuring the system between ttt and t+dtt+dtt+dt, given that detection occurs at xxx. In this framework, it is shown that energy measurements of a stationary state display a nonzero dispersion, and that energy-time uncertainty arises from first principles. We show that a central result on arrival time, obtained through approaches that resort to ad hoc assumptions, is a natural, built-in part of the formalism presented here.