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A Collapse Mechanism Without Heating

Felix Finster, Claudio F. Paganini

TL;DR

The paper addresses the quantum measurement problem by deriving a collapse mechanism from causal fermion systems and shows it avoids heating the probe via a stochastic background. It develops an equal-time formalism and derives a Lindblad-type evolution for the statistical operator, while energy is conserved on average due to surface-layer integrals. It clarifies connections to CSL and ETH formulations and discusses experimental implications, notably the absence of probe radiation. The work provides a self-contained framework linking nonlocal Dirac dynamics to stochastic collapse phenomena with distinct physical predictions.

Abstract

It is shown that the collapse model derived from the theory of causal fermion systems does not give rise to a heating of the probe. Experimental consequences are worked out. The connections to the continuous spontaneous localization (CSL) model and the events-trees-histories (ETH) formulation of quantum theory are discussed.

A Collapse Mechanism Without Heating

TL;DR

The paper addresses the quantum measurement problem by deriving a collapse mechanism from causal fermion systems and shows it avoids heating the probe via a stochastic background. It develops an equal-time formalism and derives a Lindblad-type evolution for the statistical operator, while energy is conserved on average due to surface-layer integrals. It clarifies connections to CSL and ETH formulations and discusses experimental implications, notably the absence of probe radiation. The work provides a self-contained framework linking nonlocal Dirac dynamics to stochastic collapse phenomena with distinct physical predictions.

Abstract

It is shown that the collapse model derived from the theory of causal fermion systems does not give rise to a heating of the probe. Experimental consequences are worked out. The connections to the continuous spontaneous localization (CSL) model and the events-trees-histories (ETH) formulation of quantum theory are discussed.

Paper Structure

This paper contains 13 sections, 4 theorems, 70 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The Nonlocal Dirac Equation
  4. Hamiltonian Formulation
  5. The Equal Time Formalism
  6. The Equal Time Hamiltonian
  7. Expansion in Powers of $\ell_{\min}\,\|{\mathscr{B}}\|$
  8. Taking the Statistical Mean
  9. The Lindblad Dynamics
  10. Energy Conservation
  11. Wave Function Collapse
  12. Comparison with the CSL Model
  13. Comparison with the ETH Formulation

Key Result

Lemma 3.1

In the equal time formalism,

Figures (1)

  • Figure 1: The collapse mechanism.

Theorems & Definitions (8)

  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof : Proof of Lemma \ref{['lemmaWtil']}
  • Proposition 3.3
  • proof
  • Theorem 3.4
  • proof