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arXiv:1709.03809 · Physical review. D/Physical review. D.

Ghirardi-Rimini-Weber model with massive flashes

Antoine Tilloy

Published Jan 23, 2018• 20 citations
arXivHTMLPDF

Abstract

I introduce a modification of the Ghirardi-Rimini-Weber (GRW) model in which the flashes (or space-time collapse events) source a classical gravitational field. The resulting semiclassical theory of Newtonian gravity preserves the statistical interpretation of quantum states of matter in contrast with mean field approaches. It can be seen as a discrete version of recent proposals of consistent hybrid quantum classical theories. The model is in agreement with known experimental data and introduces new falsifiable predictions: (1) single particles do not self-interact, (2) the $1/r$ gravitational potential of Newtonian gravity is cut off at short ($\ensuremath{\lesssim}{10}^{\ensuremath{-}7}\text{ }\text{ }\mathrm{m}$) distances, and (3) gravity makes spatial superpositions decohere at a rate inversely proportional to that coming from the vanilla GRW model. Together, the last two predictions make the model experimentally falsifiable for all values of its parameters.

DOI
10.1103/physrevd.97.021502

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I introduce a modification of the Ghirardi-Rimini-Weber (GRW) model in which the flashes (or space-time collapse events) source a classical gravitational field. The resulting semiclassical theory of Newtonian gravity preserves the statistical interpretation of quantum states of matter in contrast with mean field approaches. It can be seen as a discrete version of recent proposals of consistent hybrid quantum classical theories. The model is in agreement with known experimental data and introduces new falsifiable predictions: (1) single particles do not self-interact, (2) the 1/r1/r1/r gravitational potential of Newtonian gravity is cut off at short (\ensuremath≲10\ensuremath−7  m\ensuremath{\lesssim}{10}^{\ensuremath{-}7}\text{ }\text{ }\mathrm{m}\ensuremath≲10\ensuremath−7  m) distances, and (3) gravity makes spatial superpositions decohere at a rate inversely proportional to that coming from the vanilla GRW model. Together, the last two predictions make the model experimentally falsifiable for all values of its parameters.
Spontaneous collapse models are proposed modifications to quantum mechanics which aim to solve the measurement problem. In this article, we will consider models which attempt to extend a specific spontaneous collapse model, the Ghirardi-Rimini-Weber model (GRW), to be consistent with special relativity. We will present a condition that a relativistic GRW model must meet for three cases: for a single particle, for NNN distinguishable particles, and for indistinguishable particles. We will then show that this relativistic condition implies that one can have a relativistic GRW model for a single particles or for distinguishable noninteracting, nonentangled particles but not otherwise.
The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e., the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate theory. The standard semiclassical theory suffers from fundamental inconsistencies (e.g., Schr\"odinger cat sources, faster-than-light communication and violation of the Born rule) which can only be ignored in simple typical situations. We harness the power of spontaneous localization models, historically constructed to solve the measurement problem in quantum mechanics, to build a consistent theory of (stochastic) semiclassical gravity in the Newtonian limit. Our model makes quantitative and potentially testable predictions: we recover the Newtonian pair potential up to a short distance cutoff (hence, we predict no one-particle self-interaction) and uncover an additional gravitational decoherence term which depends on the specifics of the underlying spontaneous localization model considered. We hint at a possible program to go past the Newtonian limit, towards a consistent general relativistic semiclassical gravity.
Semiclassical gravity, in which a classical spacetime is sourced by the quantum expectation value of the stress-energy tensor, is a standard framework for describing the gravitational interaction of quantum matter. In the nonrelativistic limit this approach leads to the Schrödinger-Newton equation, which is often assumed to be consistent at least in the weak-field regime. In this work, we reexamine this assumption for spatial quantum superpositions of massive particles. We show that, when the quantum state is properly normalized, no modification of the Newtonian gravitational potential arises at leading order. However, at first post-Newtonian order the semiclassical coupling generically produces state-dependent contributions involving the mass density and the mass current of the superposition. These terms have a parametric scaling which is different from that of the corresponding relativistic corrections and which does not have Planck mass suppression. Our results therefore impose a strong post-Newtonian consistency constraint on deterministic semiclassical gravity, indicating that sourcing the metric solely by expectation values is insufficient to recover a consistent relativistic weak-field expansion.
The Ghirardi–Rimini–Weber (GRW) theory is a physical theory that, when combined with a suitable ontology, provides an explanation of quantum mechanics. The so-called collapse of the wave function is problematic in conventional quantum theory but not in the GRW theory, in which it is governed by a stochastic law. A possible ontology is the flash ontology, according to which matter consists of random points in space-time, called flashes. The joint distribution of these points, a point process in space-time, is the topic of this work. The mathematical results concern mainly the existence and uniqueness of this distribution for several variants of the theory. Particular attention is paid to the relativistic version of the GRW theory that was developed in 2004.
Continuing the development of the ZSM-Newton/Coulomb approach to semiclassical Newtonian gravity/electrodynamics [1], we formulate a ZSM-Newton/Coulomb version of the large N approximation scheme proposed by Oriols et al. [2]. We show that this new large N scheme makes it possible to self-consistently describe the center-of-mass evolution of a large number of gravitationally/electrostatically interacting, identical, \emph{zbw} particles, without assuming that the particles are weakly coupled, and without entailing the problematic macroscopic semiclassical gravitational/electrostatic cat states characteristic of the mean-field Schr{ö}dinger-Newton/Coulomb equations. We also show how to recover N-particle classical Newtonian gravity/electrodynamics for many gravitationally/electrostatically interacting macroscopic particles (composed of many interacting \emph{zbw} particles), as well as classical Vlasov-Poisson mean-field theory for macroscopic particles weakly interacting gravitationally/electrostatically. Finally, we outline an explicit model of environmental decoherence that can be incorporated into Oriols et al.'s scheme as applied to ZSM-Newton/Coulomb.