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arXiv:1404.6644 · New Journal of Physics

Gravity-related spontaneous wave function collapse in bulk matter

Lajos Diósi

Published Oct 9, 2014• 42 citations
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Abstract

In the DP-model, gravity-related spontaneous wave function collapses suppress Schrödinger cat states which are conceptually problematic especially for gravity and space-time. We derive the equations of the model for the hydrodynamic-elastic (acoustic) modes in a bulk. Two particular features are discussed: the universal dominance of spontaneous collapses at large wavelengths, and the reduction of spontaneous heating by a slight refinement of the DP-model.

DOI
10.1088/1367-2630/16/10/105006

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In the DP-model, gravity-related spontaneous wave function collapses suppress Schrödinger cat states which are conceptually problematic especially for gravity and space-time. We derive the equations of the model for the hydrodynamic-elastic (acoustic) modes in a bulk. Two particular features are discussed: the universal dominance of spontaneous collapses at large wavelengths, and the reduction of spontaneous heating by a slight refinement of the DP-model.
Selected issues of the concept of spontaneous collapse are discussed, with the emphasis on the gravity-related model. We point out that without spontaneous collapses the Schrödinger cat states would macroscopically violate the standard conservation laws even in the presence of environmental noise. We prove that the collapse time of condensed matter c.o.m. superpositions is not sensitive to the natural uncertainty of the nuclear locations whereas we formulate the conjecture that superfluid He may show an anomalous low rate of spontaneous collapse compared to common condensed matter. 1.
The possibility that the collapse of the wave function in quantum mechanics is real and ultimately connected to (classical) gravity has been debated for decades with main contributions by Diósi and Penrose (DP). In particular, Diósi proposed a noise-based dynamical reduction model, which captures the same order of magnitudes for the collapse time suggested by Penrose based on heuristic arguments. This is known in the literature as the DP model (Diósi–Penrose). A peculiarity of the DP model is the prediction of spontaneous heating of matter, which can be tested without the need for massive quantum superpositions. Notably, a very similar effect is predicted by recent theoretical approaches to gravity as a classical-only information channel. Here, we reconsider the current constraints on the DP model from spontaneous heating by analyzing experimental situations not properly considered before. We argue that the parameter-free version of the DP model is close to be ruled out by standard heat leak measurements at ultralow temperatures with a conclusive exclusion likely within reach with existing technology. This result would strengthen a recent claim of exclusion inferred by spontaneous x-ray emission experiments, which relies on the somewhat stronger assumption that the DP noise field is white up to x-ray frequencies.
Selected issues of the concept of spontaneous collapse are discussed, with the emphasis on the gravity-related model. We point out that without spontaneous collapses the Schrödinger cat states would macroscopically violate the standard conservation laws even in the presence of environmental noise. We prove that the collapse time of condensed matter c.o.m. superpositions is not sensitive to the natural uncertainty of the nuclear locations whereas we formulate the conjecture that superfluid. He may show an anomalous low rate of spontaneous collapse compared to common condensed matter.
Based on the assumption that the standard Schrödinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals have survived from the 1980s. The Schrödinger–Newton equation (1984) provides well-localized solitons for free macro-objects but lacks the mechanism of how extended wave functions collapse on solitons. The gravity-related stochastic Schrödinger equation (1989) provides the spontaneous collapse, but the resulting solitons undergo a tiny diffusion, leading to an inconvenient steady increase in the kinetic energy. We propose the stochastic Schrödinger–Newton equation, which contains the above two gravity-related modifications together. Then, the wave functions of free macroscopic bodies will gradually and stochastically collapse to solitons, which perform inertial motion without momentum diffusion: conservation of momentum and energy is restored.
Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength $\ensuremath{\xi}$ of the complex metric fluctuations with available experimental data. We show that $\ensuremath{\xi}\ensuremath{\ge}{10}^{\ensuremath{-}26}$ in order for the model to guarantee classicality of macro-objects, and at the same time $\ensuremath{\xi}\ensuremath{\le}{10}^{\ensuremath{-}20}$ in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of $\ensuremath{\xi}\ensuremath{\sim}{10}^{\ensuremath{-}21}$.
I impose the Newtonian criteria of inertial frames on the c.o.m.trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schrödinger equation eliminates the Brownian motion of the c.o.m., and restores the exact inertial motion for free masses. For the collapse of Schrödinger cat states the Born rule is satisfied invariably. The proposed machinery comes from the radical assumption that, in the vicinity of the spontaneously localized mass, the stochastic fluctuations of the c.o.m.—inevitable in the collapse process—would drag the physical inertial frame with themselves. The perspective of a general theory is presented where the spontaneous-collapse-caused breakdown of local energy-momentum conservation could be remedied by altering the metric, resulting in collapse-induced curvature of the space-time. My assumption of frame-drag by quantized masses is independent of the general relativistic frame-drag by classical masses.