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On the conjectured gravity-related collapse rate $E_\Delta/\hbar$ of massive quantum superpositions.

Lajos Diósi

Published Nov 8, 2021• 0 citations
OpenAlex

Abstract

Roger Penrose and the author share the proposal that the spatial superposition $|x_1\rangle+|x_2\rangle$ of a massive object collapses into its localized components $|x_1\rangle$ or $|x_2\rangle$ with the characteristic time $\hbar/E_\Delta$ where $E_\Delta$ is the gravitational self-energy excess of the superposition versus the localized states. Underlying arguments of such radical departure from standard quantum mechanics and different derivations of the rate equation are briefly recapitulated and discussed.

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On the conjectured gravity-related collapse rate EΔ/ℏE_\Delta/\hbarEΔ​/ℏ of massive quantum superpositions.
Roger Penrose and the author share the proposal that the spatial superposition ∣x1⟩+∣x2⟩|x_1\rangle+|x_2\rangle∣x1​⟩+∣x2​⟩ of a massive object collapses into its localized components ∣x1⟩|x_1\rangle∣x1​⟩ or ∣x2⟩|x_2\rangle∣x2​⟩ with the characteristic time ℏ/EΔ\hbar/E_\Deltaℏ/EΔ​ where EΔE_\DeltaEΔ​ is the gravitational self-energy excess of the superposition versus the localized states. Underlying arguments of such radical departure from standard quantum mechanics and different derivations of the rate equation are briefly recapitulated and discussed.
Inspired by an ontic view of the wavefunction in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates. We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states. Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
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 τ = ¯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 τ → ∞ (∆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
Abstract Inspired by an ontic view of the wave function in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state , depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates . We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states . Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
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.
According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the general covariance principle 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 collapse states are also problematic.