Why the Quantum Must Yield to Gravity

TL;DR

This paper critically examines Penrose's gravitationally induced quantum state reduction proposal, highlighting its limitations in the Newtonian regime and proposing alternative experiments involving superposed mass distributions to empirically test the theory.

Contribution

It critiques Penrose's collapse time formula, demonstrates its limitations in the Newtonian limit, and suggests new experimental setups involving superposed rotations for empirical validation.

Findings

Penrose's collapse time diverges in the Newtonian limit

Non-rotating mass distribution experiments are inadequate

Leggett-type SQUID or BEC experiments can test Penrose's theory

Abstract

After providing an extensive overview of the conceptual elements -- such as Einstein's `hole argument' -- that underpin Penrose's proposal for gravitationally induced quantum state reduction, the proposal is constructively criticised. Penrose has suggested a mechanism for objective reduction of quantum states with postulated collapse time T = h/E, where E is an ill-definedness in the gravitational self-energy stemming from the profound conflict between the principles of superposition and general covariance. Here it is argued that, even if Penrose's overall conceptual scheme for the breakdown of quantum mechanics is unreservedly accepted, his formula for the collapse time of superpositions reduces to T --> oo (E --> 0) in the strictly Newtonian regime, which is the domain of his proposed experiment to corroborate the effect. A suggestion is made to rectify this situation. In particular, recognising the cogency of Penrose's reasoning in the domain of full `quantum gravity', it is demonstrated that an appropriate experiment which could in principle corroborate his argued `macroscopic' breakdown of superpositions is not the one involving non-rotating mass distributions as he has suggested, but a Leggett-type SQUID or BEC experiment involving superposed mass distributions in relative rotation. The demonstration thereby brings out one of the distinctive characteristics of Penrose's scheme, rendering it empirically distinguishable from other state reduction theories involving gravity. As an aside, a new geometrical measure of gravity-induced deviation from quantum mechanics in the manner of Penrose is proposed, but now for the canonical commutation relations [Q, P] = ih.