Quantum superposition of spacetimes obeys Einstein's Equivalence Principle

Abstract

We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity, and in particular the fact that a superposition of massive bodies would lead to a violation of the Equivalence Principle. It has been argued that this violation implies that such a superposition must inevitably spontaneously collapse (like in the Diósi-Penrose model). We identify the origin of such an assertion in the impossibility of finding a local, classical reference frame in which Einstein's Equivalence Principle would hold. In contrast, we argue that the formulation of the Equivalence Principle can be generalised so that it holds for reference frames that are associated to quantum systems in a superposition of spacetimes. The core of this new formulation is the introduction of a quantum diffeomorphism to such Quantum Reference Frames (QRFs). This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity. Hence, it is not necessary to invoke a gravity-induced spontaneous state reduction when a massive body is prepared in a spatial superposition.

Falling through masses in superposition: quantum reference frames for indefinite metrics

“…The general idea employed here is to use the relativity of superpositions [23] under QRF transformations to make an indefinite metric definite. This aspect is similar to the one in previous works on QRFs for indefinite metrics [42,48], however there are important differences between the approaches. In [42,48], a local quantum inertial frame is introduced, which can be associated with a frame attached to a quantum particle falling freely in a superposition of gravitational fields.…”

“…This aspect is similar to the one in previous works on QRFs for indefinite metrics [42,48], however there are important differences between the approaches. In [42,48], a local quantum inertial frame is introduced, which can be associated with a frame attached to a quantum particle falling freely in a superposition of gravitational fields. It was shown that in the transition to the local quantum inertial frame, the metric becomes Minkowskian, extending the validity of Einstein's equivalence principle to quantum reference frames and spacetimes in general superpositions.…”

“…In particular, we can consider superpositions of gravitational fields (in the above sense) which are significantly different at a given spacetime point, as opposed to being related by a perturbative contribution. Moreover, under the restricted set of mass configurations studied here, our approach allows to transform to a frame in which the spacetime becomes globally definite, contrary to recent constructions of a local quantum inertial frame in which the metric becomes definite only in the origin of the reference frame [42,48]. This feature of our transformation allows us to describe the entire spacetime trajectories of probe particles within spacetimes in superposition, which is one of the paradigmatic problems of quantum gravity and the one most likely to be first implemented experimentally in the future.…”

“…These states |x (i) M , g can be linearly superposed and are orthogonal for different x (i) , given the classical distinguishability of the mass distributions. Thus, in future work, the argument provided in this work can be used to justify the assignment of orthogonal quantum states to classically distinguishable gravitational fields [42,48] -keeping in mind the condition that the superposed mass configurations are related by relative-distance-preserving transformations. It also vindicates a short-cut for determining the dynamics in the presence of massive objects in superposition by assuming a superposition of gravitational fields in the above sense from the start.…”

Entanglement/Asymmetry correspondence for internal quantum reference frames

“…Recently, it has led to a surge of interest in the quantum foundations community on the behavior of quantum systems under transformations between such "internal" quantum reference frames [30][31][32][33][34][35][36][37][38][39]. Among other results, this has led to proposals for quantum formulations of Einstein's equivalence principle [40][41][42][43][44] and to insights into the relativity of the notion of subsystem [45][46][47].…”