[Paper Review] Towards a theory of wavefunction collapse Part 2: Collapse as abrupt reconfigurations of wavefunction's evolution in a dynamically expanding spacetime

Garrelt Quandt-Wiese|arXiv (Cornell University)|Jan 2, 2017

Quantum Mechanics and Applications68 references3 citations

TL;DR

This paper proposes a Dynamical Spacetime approach that explains wavefunction collapse as a self-reinforcing, quasi-abrupt reconfiguration of quantum evolution when spacetime reaches critical expansion. It unifies quantum collapse with general relativity by showing how spacetime geometry dynamically favors one quantum state, suppressing others via destructive interference, while reproducing Born's rule and predicting deviations in three-state superpositions.

ABSTRACT

A new approach to wavefunction collapse is proposed. The so-called Dynamical Spacetime approach enhances semiclassical gravity and enables it for an explanation of wavefunction collapse by postulating that the spacetime region on which quantum fields exist and on which the wavefunction's evolution can be regarded is bounded towards the future by a spacelike hypersurface, which is dynamically expanding towards the future. Collapse is displayed in the way that the wavefunction's evolution becomes unstable at certain critical expansions of spacetime, at which it reconfigures via a self-reinforcing mechanism quasi-abruptly to an evolution resembling a classical trajectory. Thereby, spacetime geometry changes in favour of the winning state, which causes the path of the other state to vanish by destructive interference. This mechanism for collapse can explain the quantum correlations in EPR experiments without coming into conflict with relativity and the Free Will theorem. The Dynamical Spacetime approach is mathematically formulated on basis of the Einstein-Hilbert action and predicts for the Newtonian limit the same lifetimes of superpositions as the gravity-based approaches of Diosi and Penrose. A second important feature of the Dynamical Spacetime approach is its capability to forecast reduction probabilities. It can explain why all experiments performed so-far confirm Born's rule, and predict deviations from it, when solids evolve into three-state superpositions. The basics needed for the derivations in this paper are developed in Part 1 by an analysis of semiclassical gravity.

Motivation & Objective

• To develop a relativistic, geometric explanation of wavefunction collapse that avoids conflict with relativity and the Free Will theorem.
• To unify quantum measurement with general relativity by modeling spacetime as dynamically expanding and causally bounded.
• To derive collapse probabilities consistent with Born's rule and predict deviations in higher-order superpositions.
• To provide a mechanism for collapse that is self-reinforcing and quasi-abrupt, emerging from spacetime geometry.

Proposed method

• The approach is grounded in the Einstein-Hilbert action, modeling spacetime as a dynamically expanding region bounded by a future spacelike hypersurface.
• Quantum field evolution is restricted to this expanding spacetime region, with collapse occurring when critical expansion thresholds are reached.
• The mechanism involves a self-reinforcing transition where the winning quantum state induces a geometric reconfiguration favoring its own trajectory.
• Destructive interference eliminates competing paths by altering spacetime geometry, effectively causing their paths to vanish.
• The model is formulated in a way that reduces to Newtonian gravity in the weak-field limit, matching Penrose and Diosi's predictions for superposition lifetimes.
• Reduction probabilities are derived from the geometric dynamics, enabling prediction of Born rule compliance and deviations in three-state systems.

Experimental results

Research questions

• RQ1 How can wavefunction collapse be consistently described within a relativistic spacetime framework without violating causality or the Free Will theorem?
• RQ2 What geometric mechanism in spacetime could trigger a quasi-abrupt transition from superposition to definite state?
• RQ3 Why do all current experiments confirm Born's rule, and under what conditions might deviations occur?
• RQ4 How does the dynamical expansion of spacetime lead to the suppression of competing quantum paths via destructive interference?
• RQ5 Can the model reproduce the predicted superposition decay times of gravity-based collapse models like those of Penrose and Diosi?

Key findings

• The model reproduces the same superposition lifetimes in the Newtonian limit as the gravity-based approaches of Penrose and Diosi.
• Collapse emerges as a self-reinforcing, quasi-abrupt reconfiguration of wavefunction evolution at critical spacetime expansions.
• The mechanism explains quantum correlations in EPR-type experiments without violating relativistic causality.
• The theory predicts that Born's rule will hold for two-state superpositions but may deviate when systems evolve into three-state superpositions.
• Spacetime geometry dynamically favors the winning quantum state, causing the paths of other states to vanish through destructive interference.
• The approach provides a geometric, relativistic foundation for wavefunction collapse that is mathematically consistent with the Einstein-Hilbert action.