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arXiv:2509.22429 · Physical review. D/Physical review. D.

Quantum internal vibrations in macroscopic systems with classical centers of mass

Gabriel H. S. Aguiar, George E. A. Matsas

Published Dec 15, 2025• 1 citation
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Abstract

Harmonizing classical and quantum worlds is a major challenge for modern physics. A significant portion of the scientific community supports the notion that classical mechanics is an effective theory that arises from quantum mechanics. Recently, the present authors have argued that this should not be the case, as quantum mechanics is not trustworthy for describing the center of mass of systems with masses $m$ much larger than the Planck mass $M_\text{P}$. In this vein, a simple gravitational self-decoherence model was proposed, describing how the center of mass of quantum systems would classicalize for $m \sim M_\text{P}$. Here, we show that our model does not prevent macroscopic systems (with classical centers of mass) from harboring quantum internal vibrations (as has been observed in the laboratory).

DOI
10.1103/tvdy-9gl4

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Harmonizing classical and quantum worlds is a major challenge for modern physics. A significant portion of the scientific community supports the notion that classical mechanics is an effective theory that arises from quantum mechanics. Recently, the present authors have argued that this should not be the case, as quantum mechanics is not trustworthy for describing the center of mass of systems with masses mmm much larger than the Planck mass MPM_\text{P}MP​. In this vein, a simple gravitational self-decoherence model was proposed, describing how the center of mass of quantum systems would classicalize for m∼MPm \sim M_\text{P}m∼MP​. Here, we show that our model does not prevent macroscopic systems (with classical centers of mass) from harboring quantum internal vibrations (as has been observed in the laboratory).
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.
The quantum orthodoxy attests that all dynamical degrees of freedom should be quantized, including those associated with the centers of mass of composite/complex systems, such as protons/pebbles. By assuming that the centers of mass of protons/pebbles should be quantized, one implies the existence of a corresponding Fock space, since, according to the present lore, quantum mechanics is a consequence of quantum field theory. Despite the fabulous success of quantum mechanics, it is unreasonable to assume the existence of annihilation and creation operators for pebbles. Fortunately, there are strong reasons to doubt that wave mechanics can describe the centers of mass of systems at or above the Planck scale, thereby jeopardizing the construction of the corresponding Fock space. We argue that isolated (free) systems with masses exceeding the Planck mass would have their centers of mass governed by classical (rather than quantum) mechanics, despite harboring macroscopic quantum phenomena as observed in the laboratory. Here, we briefly revisit (i) the arguments for the need for a Heisenberg cut delimiting the boundary between the quantum and classical realms and (ii) the kind of new physics expected at (the uncharted region of) the Heisenberg cut.
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Newton’s force law [Formula: see text] is derived from the Schrödinger equation for isolated macroscopic bodies, composite states of e.g. [Formula: see text] atoms and molecules, at finite body temperatures. We first review three aspects of quantum mechanics (QM) in this context: (i) Heisenberg’s uncertainty relations for their center of mass (CM), (ii) the diffusion of the CM wave packet, and (iii) a finite body temperature which implies a metastable (mixed-) state of the body: photon emissions and self-decoherence. They explain the origin of the classical trajectory for a macroscopic body. The ratio between the range [Formula: see text] over which the quantum fluctuations of its CM are effective, and the body’s (linear) size [Formula: see text], [Formula: see text] or [Formula: see text], tells whether the body’s CM behaves classically or quantum mechanically, respectively. In the first case, Newton’s force law for its CM follows from the Ehrenfest theorem. We illustrate this for weak gravitational forces, a harmonic-oscillator potential, and for constant external electromagnetic fields slowly varying in space. The derivation of the canonical Hamilton equations for many-body systems is also discussed. Effects due to the body’s finite size such as the gravitational tidal forces appear in perturbation theory. Our work is consistent with the well-known idea that the emergence of classical physics in QM is due to the environment-induced decoherence, but complements and completes it, by clarifying the conditions under which Newton’s equations follow from QM, and by deriving them explicitly.
A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary framework for quantum gravity by assuming that the operators tied to the gravitational degrees of freedom are unobservable and equating physical entropy with matter - gravity entanglement entropy. Here we obtain preliminary results on the extent of decoherence this theory predicts. We treat first a static state which, if one were to ignore quantum gravitational effects, would be a quantum superposition of two spatially displaced states of a single classically well describable ball of uniform mass density in empty space. Estimating the quantum gravitational effects on this system within a simple Newtonian approximation, we obtain formulae which predict, for example, that as long as the mass of the ball is considerably larger than the Planck mass, such a would-be-coherent static superposition will actually be decohered whenever the separation of the centres of mass of the two ball-states exceeds a small fraction (which decreases as the mass of the ball increases) of the ball radius. We then obtain a formula for the quantum-gravitational correction to the would-be-pure density matrix of a non-relativistic many-body Schrödinger wavefunction and argue that this formula predicts decoherence between configurations which differ (at least) in the `relocation' of a cluster of particles of Planck mass. We estimate the entropy of some simple model closed systems, finding a tendency for it to increase with `matter-clumping' suggestive of a link with existing phenomenological discussions of cosmological entropy increase.
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.