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arXiv:1310.5308

The GRW flash theory: a relativistic quantum ontology of matter in space-time?

Michaël Esfeld, Nicolas Gisin

Published Oct 20, 2013• 2 citations
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Abstract

John Bell proposed an ontology for the GRW modification of quantum mechanics in terms of flashes occurring at space-time points. The paper spells out the motivation for this ontology, enquires into the status of the wave-function in it, critically examines the claim of its being Lorentz-invariant and considers whether it is a parsimonious, but nevertheless physically adequate ontology.

DOI
10.48550/arxiv.1310.5308

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John Bell proposed an ontology for the GRW modification of quantum mechanics in terms of flashes occurring at space-time points. The paper spells out the motivation for this ontology, enquires into the status of the wave-function in it, critically examines the claim of its being Lorentz-invariant and considers whether it is a parsimonious, but nevertheless physically adequate ontology.
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.
Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi–Rimini–Weber (GRW) model of spon-taneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As sug-gested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times. PACS numbers: 03.65.Ta; 03.65.Ud; 03.30.+p. Key words: spontaneous wave-function collapse; relativity; quantum theory without observers. 1
By means of the GRW flash theory and Bohmian mechanics, the paper shows how quantum mechanics accommodates a classical ontology of localised objects with a dynamics that describes the evolution of these objects. That dynamics is non-classical due to the entanglement of the wave function; but it can be entirely deterministic as illustrated by Bohmian mechanics. The wave function is a nomological parameter that can be construed according to any of the major philosophical stances with respect to laws. Against this background, the paper argues that quantum mechanics fits into the paradigm of modern physics as set out by Descartes. The far-reaching claims that call for receiving quantum mechanics as opening up a new paradigm of science are based on a confusion between science and scientism.
In Bell inequality tests, the evolution of the wavefunction is not covariant, i.e. not invariant under velocity boost that change the time ordering of events, but the laws that govern the probability distribution of possible results are. In this note I investigate what this could mean and whether there could be some covariant "real quantum stuff". This clarifies the implication of the Free Will Theorem and of relativistic spontaneous localization models based on the flash ontology (rGRWf). Some implications for the concept of time(s) are spelled out.