Valia Allori

On the Common Structure of Bohmian Mechanics and the Ghirardi–Rimini–Weber Theory

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 Schrödingers 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? Introduction Bohmian Mechanics Ghirardi, Rimini, and Weber3.1. GRWm3.2. GRWf3.3. Empirical equivalence between GRWm and GRWf GRWm GRWf Empirical equivalence between GRWm and GRWf Primitive Ontology4.1. Primitive ontology and physical equivalence4.2. Primitive ontology and symmetry4.3. Without primitive ontology4.4. Primitive ontology and quantum state Primitive ontology and physical equivalence Primitive ontology and symmetry Without primitive ontology Primitive ontology and quantum state Differences between BM and GRW5.1. Primitive ontology and quadratic functionals5.2. Primitive ontology and equivariance Primitive ontology and quadratic functionals Primitive ontology and equivariance A Plethora of Theories6.1. Particles, fields, and flashes6.2. Schrödinger wave functions and many-worlds Particles, fields, and flashes Schrödinger wave functions and many-worlds The Flexible Wave Function7.1. GRWf without collapse7.2. Bohmian mechanics with collapse7.3. Empirical equivalence and equivariance GRWf without collapse Bohmian mechanics with collapse Empirical equivalence and equivariance What is a Quantum Theory without Observers?

Many Worlds and Schrödinger’s First Quantum Theory

Schrödinger’s first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schrödinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully, this theory is seen to be an empirically adequate many-worlds theory and not an empirically inadequate theory describing a single world. Moreover, this formulation—Schrödinger’s first quantum theory—can be regarded as a formulation of the many-worlds view of quantum mechanics that is ontologically clearer than Everett’s. 1. Monstrosity2. Duality3. Parallelity4. Reality5. Nonlocality6. Relativity7. Probability8. Typicality9. Uncertainty10. Summary Monstrosity Duality Parallelity Reality Nonlocality Relativity Probability Typicality Uncertainty Summary

Predictions and Primitive Ontology in Quantum Foundations: A Study of Examples

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.1 1 Introduction 2 The GRWm and GRWf Theories   2.1 The GRW process   2.2 GRWm   2.3 GRWf 3 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 formalism 4 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 GRWf 4.4 Master equation and matter density 4.5 Master equation and flashes 5 Conclusions 1 Introduction 2 The GRWm and GRWf Theories   2.1 The GRW process   2.2 GRWm   2.3 GRWf   2.1 The GRW process   2.2 GRWm   2.3 GRWf 3 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 formalism   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 formalism 4 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 GRWf 4.4 Master equation and matter density 4.5 Master equation and flashes   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     4.2.1 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 GRWf     4.3.1 Empirical equivalence of MBM with GRWm and GRWf 4.4 Master equation and matter density 4.5 Master equation and flashes 5 Conclusions

A New Argument for the Nomological Interpretation of the Wave Function: The Galilean Group and the Classical Limit of Nonrelativistic Quantum Mechanics.

ABSTRACT In this article I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non-Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement with many physicists, ensures that Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally, I show how this favours a nomological rather than an ontological view of the wave function.

The Road to Maxwell's Demon: Conceptual Foundations of Statistical Mechanics

test, and anticipated Mairan’s remark that the test was impracticable’ (148). The colour of the moons of the Jupiter was a topos already for the young Newton in the 1660s (see Bechler 1973; Pedersen 2000, both cited in the book). Darrigol highlights the significance of long-prevailing tenets of mechanical philosophies, like modificationist colour theories or theories of ether and matter, and neglecting many aspects of the experimental side of this development, an area where much innovative historical research has been done in the last few decades, is a reasonable price to pay for this. As an intellectual history the book is well researched, well written, and does an excellent job in showing the importance of optics (and the light–sound analogy) throughout the development of classical physics.

Space, Time, and (How They) Matter

This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach.