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arXiv:quant-ph/0104052

Emergence of classicality in non relativistic quantum mechanics through gravitational self-interaction

Sergio De Filippo

Published Apr 10, 2001• 2 citations
arXivHTMLPDF

Abstract

An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary dynamics results from a unitary one in a space with twice as many degrees of freedom as the ordinary ones. It exhibits a threshold for the emergence of classical behavior for bodies of ordinary density on rather long times or instantaneously, respectively at around 10^11 or 10^20 proton masses.

DOI
10.48550/arxiv.quant-ph/0104052

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An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary dynamics results from a unitary one in a space with twice as many degrees of freedom as the ordinary ones. It exhibits a threshold for the emergence of classical behavior for bodies of ordinary density on rather long times or instantaneously, respectively at around 10^11 or 10^20 proton masses.
It is shown that a recently proposed model for the gravitational interaction in non relativistic quantum mechanics is the instantaneous action at a distance limit of a field theoretic model containing a negative energy field. It reduces to the Schroedinger-Newton theory in a suitable mean field approximation. While both the exact model and its approximation lead to estimates for localization lengths, only the former gives rise to an explicit non unitary dynamics accounting for the emergence of the classical behavior of macroscopic bodies.
One of the most significant debates of our time is whether our macroscopic world (i) naturally emerges from quantum mechanics or (ii) requires new physics. We argue for the latter and propose a simple gravitational self-decoherence mechanism. For this purpose, we postulate the existence of a Heisenberg cut such that particles with masses mmm much smaller and larger than a critical mass MC{M}_{\mathrm{C}}MC​ (of the order of the Planck mass MP{M}_{\mathrm{P}}MP​) would be necessarily treated according to quantum and classical rules, respectively. Our effective model is designed to capture the new physics that free quantum particles would experience as their masses approach MC{M}_{\mathrm{C}}MC​. The purity loss for free quantum particles is evaluated and shown to be highly inefficient for quantum particles with $m\ensuremath{\ll}{M}_{\mathrm{C}}$ but very effective for those with $m\ensuremath{\sim}{M}_{\mathrm{C}}$. The physical picture behind it is that coherence would (easily) leak from heavy enough particles to (nonobservable) spacetime quantum degrees of freedom. Finally, we contextualize our proposal with state-of-the-art experiments and show how it can be tested in a future Stern-Gerlach-like experiment.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.
The fact that gravitational environments cannot be shielded (since gravity is universal) makes them of great theoretical interest to decoherence mechanisms and to the quantum-to-classical transition. While past results seemed to indicate that graviton-induced decoherence of spatial superpositions happens only for macroscopic systems, recently it was shown that this mechanism can be enhanced through the system's own dynamical internal structure. In this work, we extend this analysis by including the interaction with a classical Newtonian potential. We show that, although the graviton bath alone dominates the mechanism for short times compared to a timescale established by the size of the quantum spatial superposition, the interaction between the gravitons and the internal degrees of freedom of the system renders decoherence inevitable in the long-time limit, even for microscopic masses. We also show that this mechanism is slightly slowed down by the interplay with the classical Newtonian potential, which, for systems without dynamical internal degrees of freedom, can even lead to recoherence-like behaviour, at least in principle.
We present a unified and minimal theoretical framework addressing the quantum-classical transition, the measurement problem, and the emergence of the arrow of time, grounded in gravitational physics. Building on the insight that quantum superpositions of mass distributions necessarily imply superpositions of gravitational potentials, we show that such states are unavoidably associated with superpositions of proper times due to gravitational time dilation. By extending the system Hilbert space to include a temporal degree of freedom, we demonstrate that matter-time entanglement leads naturally to effective decoherence when the time degree of freedom is traced out. The resulting reduced dynamics takes the form of a Lindblad master equation derived from an underlying unitary evolution. This framework reproduces the correct microscopic and macroscopic limits, clarifies the relation to Diósi-Penrose-type models, and provides a coherent account of classicality and temporal irreversibility without postulating observers, environmental decoherence as fundamental, or objective wavefunction collapse.
We propose a conservative theoretical framework addressing the emergence of classical time and the uniqueness of the past within quantum mechanics, without modifying its fundamental postulates or introducing objective collapse mechanisms. The central observation is that quantum superpositions of mass–energy distributions necessarily imply superpositions of gravitational potentials, and therefore superpositions of proper times. By treating time as an effective quantum degree of freedom and extending the system Hilbert space accordingly, we show that matter–time entanglement leads to an intrinsic dispersion of proper time. Gravitational fluctuations and irreversible memory formation dynamically suppress this dispersion, giving rise to an effective closure of temporal histories. The resulting dynamics admits stable fixed points corresponding to classical time and a unique past, while remaining fully compatible with global unitarity. We analyze the stability of this closure, its relation to decoherence and quantum Darwinism, and its implications for cosmology, including the interpretation of the Big Bang as a temporal closure process rather than a fundamental beginning of time. The framework clarifies the role of gravity in the quantum–classical transition and delineates the physical conditions under which a unique history can emerge.