A Relativistic Version of the Ghirardi-Rimini-Weber Model

Abstract

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 spontaneous 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 suggested 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.

arXiv comment19 pages LaTeX, no figures

References in corpus (11)

• Dynamical Reduction Models
• EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory
• Hypersurface Bohm-Dirac models
• Relativistic Collapse Model With Tachyonic Features
• Relativistic Spontaneous Localization: A Proposal
• Simple Proof for Global Existence of Bohmian Trajectories
• A non-local, Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories
• Opposite Arrows of Time Can Reconcile Relativity and Nonlocality
• Simulating causal collapse models
• A Stochastic Model of a Quantum Field Theory
• Flux-Across-Surfaces Theorem for a Dirac Particle

Cited by in corpus (93)

• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory
• Relativistic state reduction dynamics
• J.S. Bell's Concept of Local Causality
• Matter Density and Relativistic Models of Wave Function Collapse
• Can Bohmian mechanics be made relativistic?
• What Bell Did
• Predictions and Primitive Ontology in Quantum Foundations: A Study of Examples
• Parameter Diagrams of the GRW and CSL Theories of Wave Function Collapse
• Bell's Theorem and Locally-Mediated Reformulations of Quantum Mechanics
• Benefits of Objective Collapse Models for Cosmology and Quantum Gravity
• Non-Paradoxical Loss of Information in Black Hole Evaporation in a Quantum Collapse Model
• The Conway-Kochen argument and relativistic GRW models
• Non-Markovian continuous quantum measurement of retarded observables
• Quantum Theory and Determinism
• Many-Worlds and Schroedinger's First Quantum Theory
• Comment on "The Free Will Theorem"
• The "Unromantic Pictures" of Quantum Theory
• The Point Processes of the GRW Theory of Wave Function Collapse
• A Solution to the Lorentzian Quantum Reality Problem
• Relativistically Invariant Markovian Dynamical Collapse Theories Must Employ Nonstandard Degrees of Freedom
• Impact of dynamical collapse models on inflationary cosmology
• Quantum States as Ordinary Information
• Neutron star heating constraints on wave-function collapse models
• Collapse Models: a theoretical, experimental and philosophical review
• Bell's theorem and the issue of determinism and indeterminism
• The Quantum Formalism and the GRW Formalism
• The Status of the Wave Function in Dynamical Collapse Models
• Dynamical Reduction Models: present status and future developments
• Gravitational Decoherence: A Thematic Overview
• The Measurement Problem: Decoherence and Convivial Solipsism
• Events and the Ontology of Quantum Mechanics
• Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere
• Relativistic collapse dynamics and black hole information loss
• How Quantum Theory Helps us Explain
• Black Holes: Information Loss But No Paradox
• Emergence of inflationary perturbations in the CSL model
• Generally covariant dynamical reduction models and the Hadamard condition
• Lorentzian Quantum Reality: Postulates and Toy Models
• A relativistically interacting exactly solvable multi-time model for two mass-less Dirac particles in 1+1 dimensions
• On Bohmian Mechanics, Particle Creation, and Relativistic Space-Time: Happy 100th Birthday, David Bohm!
• Do We Have Any Viable Solution to the Measurement Problem?
• Mass-coupled relativistic spontaneous collapse models
• Beable-Guided Quantum Theories: Generalising Quantum Probability Laws
• Multi-Time Equations, Classical and Quantum
• Collapse models: main properties and the state of art of the experimental tests
• Epistemology of Wave Function Collapse in Quantum Physics
• A simple explicitly solvable interacting relativistic N-particle model
• A Relativistic GRW Flash Process With Interaction
• How to account for quantum non-locality: ontic structural realism and the primitive ontology of quantum physics
• Dynamical state reduction in an EPR experiment
• On the (im)possibility of extending the GRW model to relativistic particles
• Newtonian Semiclassical Gravity in the Ghirardi-Rimini-Weber Theory with Matter Density Ontology
• Semiclassical Self Consistent Treatment of the Emergence of Seeds of Cosmic Structure. The second order construction
• The effect of spontaneous collapses on neutrino oscillations
• Lorentz-invariant, retrocausal, and deterministic hidden variables
• Quasi-matter bounce and inflation in the light of the CSL model
• Particles, Fields, and the Measurement of Electron Spin
• A (not so?) novel explanation for the very special initial state of the universe
• A representation of the wave function on the three-dimensional space
• Enlightening the CSL model landscape in inflation
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space
• Boson-fermion unification, superstrings, and Bohmian mechanics
• Collapse of the wavefunction, the information paradox and backreaction
• Tabletop Experiments for Quantum Gravity Are Also Tests of the Interpretation of Quantum Mechanics
• On the question of current conservation for the Two-Body Dirac equations of constraint theory
• Extending quantum mechanics entails extending special relativity
• A dialog on the fate of information in black hole evaporation
• A Categorical Framework for Quantum Theory
• Particle mixing and the emergence of classicality: A spontaneous-collapse-model view
• Single particle energy diffusion from relativistic spontaneous localization
• On relativistic elements of reality
• The Operational Choi-Jamiolkowski Isomorphism
• Quantization in classical mechanics and reality of Bohm's psi-field
• From the measurement problem to the primitive ontology programme
• Quantization in relativistic classical mechanics: the Stueckelberg equation, neutrino oscillation and large-scale structure of the Universe
• Stochastic dark matter: Covariant Brownian motion from Planckian discreteness
• What happens once an accelerating observer has detected a Rindler particle?
• Ghostly action at a distance: a non-technical explanation of the Bell inequality
• The effect of time-dilation on Bell experiments in the retrocausal Brans model
• A proposal for a new kind of spontaneous collapse model
• Effects of the continuous spontaneous localization model in the regime of large localization length scale
• Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility
• Bell's nonlocality and gravity
• Hybrid Classical-Quantum Newtonian Gravity with stable vacuum
• Towards relativistic generalization of collapse models
• A proposal for a metaphysics of self-subsisting structures. II. Quantum physics
• What does it take to solve the measurement problem?
• Reality, No Matter How You Slice It
• Quantum Physics in Space
• On substantive Lorentz invariance and quantum theory
• New avenues for testing collapse models
• A New Derivation of the Propagator's Path Integral for Spinless Elementary Particles