Pikovski et al. showed that gravitational time dilation couples the internal energy of a composite quantum system to its center-of-mass position, producing dephasing without modifying quantum mechanics. The resulting decoherence rate depends on the energy variance of internal degrees of freedom and yields a Gaussian temporal profile. Building on the thermodynamic identity Var(H)=k_B T^2 C_V, we evaluate this effect for macroscopic objects modeled as Debye solids in Earth's gravitational field. We demonstrate that the decoherence rate scales as a universal T^{5/2} power law at cryogenic temperatures, providing a unique phenomenological signature distinguishing it from spontaneous collapse models (e.g., CSL) which predict temperature-independent rates. Furthermore, we expand the Pikovski mechanism to structurally disordered materials (fractons) and analytically show that the scaling modifies to T^{(d_s/2)+1}, acting as highly sensitive gravitational noise receptors.
Pikovski et al. showed that gravitational time dilation couples the internal energy of a composite quantum system to its center-of-mass position, producing dephasing without modifying quantum mechanics. The resulting decoherence rate depends on the energy variance of internal degrees of freedom and yields a Gaussian temporal profile. Building on the thermodynamic identity Var(H)=k_B T^2 C_V, we evaluate this effect for macroscopic objects modeled as Debye solids in Earth's gravitational field. We demonstrate that the decoherence rate scales as a universal T^{5/2} power law at cryogenic temperatures, providing a unique phenomenological signature distinguishing it from spontaneous collapse models (e.g., CSL) which predict temperature-independent rates. Furthermore, we expand the Pikovski mechanism to structurally disordered materials (fractons) and analytically show that the scaling modifies to T^{(d_s/2)+1}, acting as highly sensitive gravitational noise receptors.
We evaluate the macroscopic entanglement-loss implications of gravitational time dilation, first identified by Pikovski et al. (2015). By moving beyond the idealized zero-temperature single-mode approximation to a continuous Debye model in the canonical ensemble, we derive the explicit phononic heat-capacity limits for spontaneous gravitational decoherence. We find that the decoherence rate driven by internal time-dilation variance strongly scales with σ∝T5/2 at ultra-low experimental temperatures (T≪ΘD), vanishing strictly at absolute zero. Furthermore, we demonstrate mathematically that translational invariance renders proper-time differences between spatially distinct branches of an identical matter distribution identically zero. Thus, contrary to the Diósi-Penrose approach, an isolated mass in a pure superposition cannot undergo solely self-gravitational state-collapse. Decoherence requires either an external gravitational potential gradient or internal structural asymmetry. Lastly, we prove that the topological spectral dimension ds of the macroscopic test mass determines the decoherence rate scaling, creating a new class of ultra-sensitive 'fracton-gravity sensors'.
The recently proposed centre-of-mass decoherence of composite objects due to gravitational time-dilation [Pikovski et al , Nat.Phys. 11, 668 (2015)] is confronted with the principle of equivalence between gravity and observer's acceleration. In the laboratory frame, a positional superposition | x 1 〉 + | x 2 〉 can quickly decohere whereas in the free-falling frame, as I argue, the superposition can survive for almost arbitrary long times. The paradoxical result is explained by the so far unappreciated feature of the proposed model: the centre-of-mass canonical subsystem is ambiguous, it is di˙erent in the laboratory and the free-falling frames, respectively. As long as the centre-of-mass motion of the composite object is non-relativistic, a simple Galilean-covariant Hamiltonian represents the Pikovski et al theory with exactly the same physical predictions. We emphasize the power of this Hamiltonian to understand essential features of the Pikovski et al theory and to moderate a few divergent statements in recent works.
Levitated optomechanical systems are approaching the regime where macroscopic quantum superpositions become experimentally accessible. A central question is whether gravity itself, through its unavoidable coupling to material quantum fluctuations, imposes a fundamental decoherence channel on such superpositions. Starting from two independently well-tested physical elements—the quantum vacuum fluctuations of the material energy-momentum tensor, and the weak-field linear response kernel of classical general relativity—we derive a structurally rigid scaling law for the gravitational decoherence rate: \Gamma \propto G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L). The exponents and dependence on mass M, superposition separation d, and object size L are fixed entirely by dimensional analysis and the semiclassical field equations, without tunable parameters. The overall amplitude is set by a single phenomenological input—the ultraviolet cutoff scale l_* of the effective geometric noise. Identifying l_* with the Planck length yields \Phi \sim \mathcal{O}(1) and a decoherence rate of order 1\,\text{Hz} for nanoparticles with M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, and L \sim 10^{-6}\,\text{m}, placing the prediction within the foreseeable sensitivity window of next-generation levitated optomechanical setups. We provide explicit falsification conditions, a three-path staged verification strategy that does not require simultaneous optimisation of all parameters, and operational signatures—including a distinctive pure-dephasing channel without energy relaxation—that distinguish this mechanism from environmental noise, zero-temperature electromagnetic vacuum fluctuations, and the Diósi-Penrose model.
A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we show how the center-of-mass motion of a quantum system subject to gravity can be derived more rigorously, addressing the ambiguous definition of relativistic center-of-mass coordinates. We further demonstrate that, contrary to the prediction by Pikovski et al., external forces play a crucial role in the relativistic coupling of internal and external degrees of freedom, resulting in a complete cancellation of the alleged coupling in Earth-bound laboratories for systems supported against gravity by an external force. We conclude that the proposed decoherence effect is an effect of relative acceleration between quantum system and measurement device, rather than a universal effect in gravitational fields.
Pikovski et al. [Nat. Phys. 11, 668 (2015)] show that a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field undergoes a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's equivalence principle to be valid, we analyze a physical realization of the (1+1)D thought experiment of Pikovski et al. to demonstrate that the dephasing between the different internal states arises not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Pikovski et al., where we propose that gravity plays a kinematic role by providing a relative velocity to the detector frame with respect to the particle; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We then apply this insight to their thought experiment in (1+1)D to draw a direct correspondence, and obtain the same mathematical result for dephasing. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the equivalence principle is 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.