Symmetric versions of explicit wavefunction collapse models

Gao Shan

Philip Pearle

Ahmed Hamid Mahmoud

(Note: Please refer to Version 3 (v3) of The Dynamics of Discrete Fact: A Phase-Transition Theory of Wavefunction Collapse for the updated and expanded presentation of the framework). _______________________ This is Version 2 of The Dynamics of Discrete Fact, presenting an expanded and clarified construction of wavefunction collapse as a genuine physical phenomenon: a nonequilibrium phase transition in a macroscopic measurement apparatus. As before, collapse is modeled as a critical instability in an emergent order parameter governed by time-dependent Ginzburg–Landau dynamics. Discrete outcomes arise through spontaneous symmetry breaking in the apparatus–environment system, while Born weights are preserved via probability-conserving basin flow in the associated Fokker–Planck description—without modifying the Schrödinger equation or introducing new constants. Relative to v1, v2 (i) makes the single-run (outcome-conditional) collapse dynamics explicit rather than implicit, (ii) strengthens the Born-rule preservation argument by tying basin structure more directly to apparatus symmetry, and (iii) tightens the experimental discussion by specifying the regimes in which critical signatures are and are not expected. The framework retains concrete signatures—critical slowing near threshold, hysteresis under parameter cycling, metastability, and outcome-correlated transient detector spikes—and positions collapse alongside emergent macroscopic instabilities such as superconductivity and ferromagnetism.

M. A. B. Whitaker

Chris Dove, Euan J. Squires

A model of spontaneous wavefunction collapse, which is explicitly local and Lorentz-invariant, is defined. Some of the predictions of the model for specific experimental situations are derived. It is shown that, although incompatible collapses, e.g. on opposite sides of an EPR-type of experiment, can occur, they will not persist in time and that eventually only compatible results will be obtained. The probabilities of particular results, however, will in general not agree with the predictions of quantum theory. We argue that it is unlikely that the deviations would have been seen in any experiment yet performed.

Dennis Dieks