The GRW Theory and the Foundations of Statistical Mechanics

Marco Baldovin, Giacomo Gradenigo, Angelo Vulpiani +1 more

Valia Allori, Sheldon Goldstein, Roderich Tumulka +1 more

A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a ‘primitive ontology’ (PO), i.e. variables describing the distribution of matter in four-dimensional space–time. In this article, we illustrate the value of having a PO. We do so by focussing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To this end, we investigate a number of examples based on toy models built from the elements of familiar interpretations of quantum theory.11 Introduction2 The GRWm and GRWf Theories 2.1 The GRW process 2.2 GRWm 2.3 GRWf3 Predictions and Primitive Ontology 3.1 Calibration functions 3.2 Taking the PO seriously 3.3 Examples from the literature 3.4 The main theorem about operators in the GRW formalism 3.5 The GRW formalism4 A Set of Examples 4.1 Bohmian mechanics 4.2 Bohmian trajectories and GRW collapses 4.2.1 Bohm’s law and GRW’s law 4.2.2 Bohm’s law and a modified GRW law 4.2.3 Trajectories from the GRW wave function 4.2.4 Configuration jumps and GRW law 4.2.5 Another way of configuration jumps and GRW law 4.3 MBM: Bohm-like trajectories from the master equation 4.3.1 Empirical equivalence of MBM with GRWm and GRWf4.4 Master equation and matter density4.5 Master equation and flashes5 Conclusions

Roderich Tumulka

Ever since we have been in the possession of quantum theories without observers, such as Bohmian mechanics or the Ghirardi‐Rimini‐Weber (GRW) theory of spontaneous wave function collapse, a major challenge in the foundations of quantum mechanics is to devise a relativistic quantum theory without observers. One of the difficulties is to reconcile nonlocality with relativity. I report about recent progress in this direction based on the GRW model: A relativistic version of the model has been devised for the case of N noninteracting (but entangled) particles. A key ingredient was to focus not on the evolution of the wave function but rather on the evolution of the matter in space‐time as determined by the wave function.

Sergei Vladimirovich Tyablikov

William Michael Kallfelz

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.

Vladimir V. Bazhanov, Conrad J. Burden