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arXiv:2103.04805

Epistemological remarks about the Ghirardi-Rimini-Weber quantum theory

de Stefano, Francesco

Published Mar 8, 2021• 0 citations
arXivHTMLPDF

Abstract

We discuss the epistemological features of the Ghirardi, Rimini and Weber proposal to modify quantum mechanics in order to overcome the objectification problem, that means the transition between the quantum and the classical level of description of natural phenomena. We shall show that the GRW is a realistic theory, but in a way quite different from Einstein realism or other kinds of realism proposed in the past, such as the Many World Interpretation or the Bohmian Mechanics.

DOI
10.48550/arxiv.2103.04805

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We discuss the epistemological features of the Ghirardi, Rimini and Weber proposal to modify quantum mechanics in order to overcome the objectification problem, that means the transition between the quantum and the classical level of description of natural phenomena. We shall show that the GRW is a realistic theory, but in a way quite different from Einstein realism or other kinds of realism proposed in the past, such as the Many World Interpretation or the Bohmian Mechanics.
One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini & Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focusing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way.
Abstract I examine G.B. Baga’s arguments for the Ghirardi-Rimini-Weber (GRW) interpretation of non-relativistic quantum mechanics as ideally suited for Whitehead’s philosophy. Much of Bagci’s claims are in response to Michael Epperson, who argues in the same vein in favor of decoherence accounts (Omnès; Zureck). Pace Epperson, I do not think that decoherence is the final arbiter here, and instead I contrast GRW with several other accounts addressing foundational problems of quantum theory (Finkehtein; Green; Peres and Temo; etc.), which aho account for relativistic covariance, while GRW does not. I argue that such latter research programs align themselves in a more convincing manner with Whitehead’s scheme, in epistemic as well as metaphysical senses, than GRW.
The existence of multiple interpretations of quantum mechanics appears to pose a serious challenge for knowledge claims about the quantum domain. Hoefer argues that a scientific realist epistemology must be abandoned in this context, while Callender argues that the realist’s only option is to break the underdetermination between rival interpretations by appealing to extra-empirical virtues. We develop a different response to the quantum underdetermination problem based on identifying statements about the unobservable that all the major ontic interpretations of quantum mechanics agree on. It is commonly believed that Everettian, Bohmian, and GRW (Ghirardi–Rimini–Weber) quantum mechanics share nothing but empirical content. We argue that while they say very different things about the fundamental nature of quantum systems, they can be understood as agreeing on a plethora of more abstract theoretical claims. In our view, focusing on this descriptive overlap represents the most promising strategy for defending knowledge claims in the quantum domain. We close by considering how this overlap strategy relates to working posits formulations of scientific realism.
Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about ‘matter’ moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter. 1. Introduction2. Bohmian Mechanics3. Ghirardi, Rimini, and Weber3.1. GRWm3.2. GRWf3.3. Empirical equivalence between GRWm and GRWf4. Primitive Ontology4.1. Primitive ontology and physical equivalence4.2. Primitive ontology and symmetry4.3. Without primitive ontology4.4. Primitive ontology and quantum state5. Differences between BM and GRW5.1. Primitive ontology and quadratic functionals5.2. Primitive ontology and equivariance6. A Plethora of Theories6.1. Particles, fields, and flashes6.2. Schrödinger wave functions and many-worlds7. The Flexible Wave Function7.1. GRWf without collapse7.2. Bohmian mechanics with collapse7.3. Empirical equivalence and equivariance8. What is a Quantum Theory without Observers?
This work presents a historical-epistemological analysis of the foundations of quantum mechanics. From a philosophical point of view, the relationships between quantum mechanics and scientific realism are highlighted, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of measurement in the context of quantum mechanics is underlined, as an essential element in providing a coherent description of reality moving from the microcosm to the macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the ontological problem, the problem of the objectification of the wave function and the problem of the definition of discernibility. This is followed by an overview of the most important alternative proposals to the standard interpretation (Copenhagen interpretation), with particular reference to hidden variable theories, and other alternatives to standard quantum mechanics that profoundly modify the vision of reality, such as the Everett’s many-worlds theory, the QBism, the unified holistic approach.
Bohmian mechanics and Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of the Schr\\"odinger equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about matter moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to guide the motion of the matter.