A Relativistic Dynamical Collapse Model

Abstract

A model is discussed where all operators are constructed from a quantum scalar field whose energy spectrum takes on all real values. The Schrödinger picture wave function depends upon space and time coordinates for each particle, as well as an inexorably increasing evolution parameter $s$ which labels a foliation of space-like hypersurfaces. The model is constructed to be manifestly Lorentz invariant in the interaction picture. Free particle states and interactions are discussed in this framework. Then, the formalism of the CSL (Continuous Spontaneous Localization) theory of dynamical collapse is applied. The collapse-generating operator is chosen to to be the particle number space-time density. Unlike previous relativistically invariant models, the vacuum state is not excited. The collapse dynamics depends upon two parameters, a parameter $\Lambda$ which represents the collapse rate/volume and a scale factor $\ell$. A common example of collapse dynamics, involving a clump of matter in a superposition of two locations, is analyzed. The collapse rate is shown to be identical to that of non-relativistic CSL when the GRW-CSL choice of $\ell =a=10^{-5}$cm, is made, along with $\Lambda =\lambda /a^3$ (GRW-CSL choice $\lambda =10^{-16}{s}^{-1}$). However, it is also shown that the change of mass of a nucleon over the age of the universe is then unacceptably large. The case where $\ell$ is the size of the universe is then considered. It is shown that the collapse behavior is satisfactory and the change of mass over the age of the universe is acceptably small, when $\Lambda =\lambda /\ell a^2$.

25 pages, 1 figure

References in corpus (10)

• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Dynamical Reduction Models
• Relativistic state reduction dynamics
• Matter Density and Relativistic Models of Wave Function Collapse
• CSL Wave Function Collapse Model as a Mechanism for the Emergence of Cosmological Asymmetries in Inflation
• Parameter Diagrams of the GRW and CSL Theories of Wave Function Collapse
• Relativistic Collapse Model With Tachyonic Features
• Completely Quantized Collapse and Consequences
• How Stands Collapse II
• Multi-Time Equations, Classical and Quantum

Cited by in corpus (28)

• Non-Paradoxical Loss of Information in Black Hole Evaporation in a Quantum Collapse Model
• Black Holes: Eliminating Information or Illuminating New Physics?
• Relativistically Invariant Markovian Dynamical Collapse Theories Must Employ Nonstandard Degrees of Freedom
• Principle of least decoherence for Newtonian semi-classical gravity
• Impact of dynamical collapse models on inflationary cosmology
• Neutron star heating constraints on wave-function collapse models
• Relativistic collapse dynamics and black hole information loss
• Emergence of inflationary perturbations in the CSL model
• Generally covariant dynamical reduction models and the Hadamard condition
• Discussions about the landscape of possibilities for treatments of cosmic inflation involving continuous spontaneous localization models
• Constraining quantum collapse inflationary models with CMB data
• A Relativistic GRW Flash Process With Interaction
• Inflation including collapse of the wave function: The quasi-de Sitter case
• On the initial value problem for semiclassical gravity without and with quantum state collapses
• Semiclassical Self Consistent Treatment of the Emergence of Seeds of Cosmic Structure. The second order construction
• Eternal inflation and the quantum birth of cosmic structure
• Wave Function Collapse and the No-Superluminal-Signaling Principle
• Quasi-matter bounce and inflation in the light of the CSL model
• A (not so?) novel explanation for the very special initial state of the universe
• Generation of inflationary perturbations in the continuous spontaneous localization model: The second order power spectrum
• Enlightening the CSL model landscape in inflation
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space
• Reduced dynamics with Poincaré symmetry in an open quantum system
• Collapse of the wavefunction, the information paradox and backreaction
• Particle mixing and the emergence of classicality: A spontaneous-collapse-model view
• A dialog on the fate of information in black hole evaporation
• What happens once an accelerating observer has detected a Rindler particle?
• Hybrid Classical-Quantum Newtonian Gravity with stable vacuum