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Foundations of Physics

On the Gravitization of Quantum Mechanics 1: Quantum State Reduction

Roger Penrose

Published Jan 10, 2014• 343 citations
Publisher

Abstract

This paper argues that the case for “gravitizing” quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change , the very formalism of quantum mechanics. Most particularly, an “Einsteinian”, rather than a “Newtonian” treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author.

DOI
10.1007/s10701-013-9770-0

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This paper argues that the case for “gravitizing” quantum theory is at least as strong as that for quantizing gravity. Accordingly, the principles of general relativity must influence, and actually change , the very formalism of quantum mechanics. Most particularly, an “Einsteinian”, rather than a “Newtonian” treatment of the gravitational field should be adopted, in a quantum system, in order that the principle of equivalence be fully respected. This leads to an expectation that quantum superpositions of states involving a significant mass displacement should have a finite lifetime, in accordance with a proposal previously put forward by Diósi and the author.
“Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using the Dirac–Pauli representation of free Dirac equation to search for the clues. In particular, we study how the double-slit diffraction experiment, when only one Dirac particle (‘say’ electron) at a time is in the apparatus, could test a gravitizing QT proposal in which the wavefunction collapse emerges on the detector screen from the Dirac–Pauli representation, as an objective process, resolving the measurement problem of QT.” [1] We found that the Dirac–Pauli representation is inherently a unified theory embodying a gravitizing QT proposal that Dirac–Pauli representation as wave nature is manifestation of inertial mass and the Foldy-Wouthuysen representation as particle nature is manifestation of gravitational mass such that the fact, that same physics is involved in these two representations, is simply the validity and exhibition of the principle of equivalence, of GR, in QT. [1] Richard Howl et al 2019 New J. Phys. 21 043047 DOI 10.1088/1367-2630/ab104a
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
We analyze Penrose's ideas concerning the role of gravity in the quantum-mechanical state reduction from the perspective of analogue-gravity models. We first review a line of work which argues that it is not enough to find a satisfactory quantization scheme for gravity in the description of a matter-gravity system. Instead of that; the standard rules of quantum mechanics as they are actually applied to matter systems need to be modified when the gravitational interaction is relevant. Among these ideas we focus on Penrose's argument for the absence of macroscopic quantum superpositions. He argues that such phenomenon has its roots in the idiosyncratic aspects of gravity, which become relevant just when the system is macroscopic and hence able to generate a sufficiently strong gravitational field, and not in the environmental decoherence. We then present an analogue model consisting of a Bose-Einstein condensate in a double well potential, where it is possible to build states that would correspond to putative superpositions of spacetimes. Such configurations are unstable and the source of instability from a microscopic point of view can be related to the abscence of a well-defined causal structure in the effective geometric description. We also discuss some additional lessons that can be taken from these instabilities.
Although the standard viewpoint in theoretical physics is that the unification of quantum theory and general relativity requires the quantization of gravity and spacetime, there is not consensus about whether spacetime must fundamentally have any quantum features. Here we show a theorem stating that spacetime degrees of freedom and a quantum system violate a Bell inequality in a background Minkowski spacetime if a few properties of general relativity and quantum theory have a broad range of validity, and if the quantum state reduction upon measurement is a real physical process that is completed superluminally when acting on distant quantum particles in a quantum entangled state. We argue that this implies that spacetime cannot be sensibly called classical if the assumptions in our theorem hold. In contrast to the Eppley-Hannah argument for the necessity of quantizing the gravitational field, we discuss the validity of our assumptions, our thought experiment does not require to manipulate or detect gravitational waves, and our theorem does not rely on the conservation of momentum or on the uncertainty principle.
The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.