Does gravity induce wavefunction collapse? An examination of Penrose's conjecture

TL;DR

This paper critically examines Penrose's hypothesis that gravity causes wavefunction collapse, arguing that the connection is debatable, and the proposed mechanisms and formulas are problematic.

Contribution

The paper challenges Penrose's conjecture by analyzing its conceptual foundations, analogy strength, and the implications of resolving the underlying conflict.

Findings

The conflict between quantum superposition and general covariance is controversial.

Penrose's analogy-based argument is weak and inconclusive.

Resolving the conflict may eliminate the need for wavefunction collapse.

Abstract

According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. For the conflict or the problem of ill-definedness for a superposition of different space-time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and the preferred basis are also problematic.