Gravitational which-path thought experiments often treat the mass and spatial separation of coherent alternatives as independently prescribed, so that at fixed separation Newtonian field contrast grows linearly with mass. In a physical realization, however, the usable separation is constrained by the coherent preparation-and-readout protocol, while the detector stand-off can also vary with mass. We derive the resulting protocol-dependent scaling of the gravitational field contrast and compare it with the mass scalings of two related observables arising in massive-superposition settings. Writing the mass dependence of the accessible separation and detector stand-off as d ∝ M−α and R ∝ Mβ, respectively, the field contrast scales as Δg ∝ M1−α−3β. A finite-density double-slit family gives Δgmax ∝ M−1/3 at fixed R, while a relative momentum transfer held fixed as M varies gives a mass-independent field contrast, and fixed relative velocity restores linear growth with mass. There is therefore no universal mass advantage for gravitational field contrast: whether increasing the mass helps depends on how the accessible separation and detector stand-off scale with mass. Finally, we show that gravity-mediated-entanglement phases and causality-bounded probe responses inherit different mass exponents from the same preparation-dependent separation resources, indicating that closely related massive-superposition settings can exhibit qualitatively different mass scalings depending on the observable being targeted.
Gravitational which-path thought experiments often treat the mass and spatial separation of coherent alternatives as independently prescribed, so that at fixed separation Newtonian field contrast grows linearly with mass. In a physical realization, however, the usable separation is constrained by the coherent preparation-and-readout protocol, while the detector stand-off can also vary with mass. We derive the resulting protocol-dependent scaling of the gravitational field contrast and compare it with the mass scalings of two related observables arising in massive-superposition settings. Writing the mass dependence of the accessible separation and detector stand-off as d ∝ M−α and R ∝ Mβ, respectively, the field contrast scales as Δg ∝ M1−α−3β. A finite-density double-slit family gives Δgmax ∝ M−1/3 at fixed R, while a relative momentum transfer held fixed as M varies gives a mass-independent field contrast, and fixed relative velocity restores linear growth with mass. There is therefore no universal mass advantage for gravitational field contrast: whether increasing the mass helps depends on how the accessible separation and detector stand-off scale with mass. Finally, we show that gravity-mediated-entanglement phases and causality-bounded probe responses inherit different mass exponents from the same preparation-dependent separation resources, indicating that closely related massive-superposition settings can exhibit qualitatively different mass scalings depending on the observable being targeted.
Matter-wave interferometry has confirmed the superposition principle for objects as large as fullerenes and, most recently, nanoparticles of thousands of atoms. Because every massive object sources a gravitational field, a long-standing question follows: does the gravitational field of a delocalized quantum system track the realized quantum state, or the probability-weighted expectation value of its mass distribution (semiclassical gravity)? We first revisit a distant-observer thought experiment in which gravitational which-path information appears to threaten complementarity, and summarize its modern resolution, which turns the apparent paradox into an argument for the quantization of the gravitational field. We then propose a variant of the 1981 Page–Geilker experiment that generalizes a protocol of Kent: the position of a macroscopic source mass is controlled by a quantum random trigger whose firing probability p is continuously tunable, a precision gravimeter monitors the local field, and an otherwise identical run with a classical pseudo-random trigger serves as a control. For no-collapse semiclassical gravity we derive, for a repeated protocol with reset, the field offset in intervals without a release and the suppression of the gravimeter step at quantum-triggered releases; both depend on p, whereas every event-sourced theory predicts a p-independent, event-following field, and the control run cancels systematics that scale with the release rate. Order-of-magnitude estimates indicate that a superconducting gravimeter and a 100–1000 kg source can bound the fraction of “counterfactual” mass that gravitates at the 10−3 level as a function of p. We state which hypotheses the experiment can falsify, why decoherence restricts its scope to no-collapse semiclassical theories, and how the design could be migrated to mesoscopic masses, where the question remains open. Version 2 (September 2026) of a manuscript first written in June 2026. 10 pages, 1 table, 44 references. Also submitted to arXiv (quant-ph, cross-list gr-qc).
Preparing massive particles in coherent spatial superpositions is a central objective of modern quantum science, motivated by applications ranging from fundamental tests of quantum mechanics and gravity to quantum-enhanced sensing. The experimental difficulty of realizing such superpositions is usually attributed to environmental decoherence mechanisms whose impact depends on the details of the experimental implementation. Here we identify a universal constraint arising from momentum conservation and the quantum nature of the preparation apparatus. Any protocol that places a particle of mass m in a spatial superposition with separation d necessarily entangles the particle with the center-of-mass degree of freedom of the apparatus responsible for the splitting. The resulting recoil displacement, fixed by conservation of the mass dipole moment, reduces the coherence of the particle when the apparatus is not included as part of the quantum system. For an apparatus of mass M, preserving coherence requires the recoil displacement to remain smaller than the coherence length of the apparatus center-of-mass state, leading to a quantitative bound expressible as a constraint on its temperature and on how rigidly the apparatus is anchored to the laboratory frame. We analyze the implications of this bound for current matter-wave interferometry experiments, proposals for gravitationally mediated entanglement, and tests of quantum mechanics near the Planck scale. Our main result, which may seem counterintuitive, is that the recoil of even heavy macroscopic apparatuses can pose a surprisingly strong constraint on the coherence of spatial superpositions of particles with masses well below the Planck mass. Finally, we discuss why the resulting limitation should be regarded as a conservative estimate and under which conditions it can be interpreted as an instance of false decoherence.
This thesis investigates the role of gravitational waves in quantum systems, motivated by advances in our understanding of the quantum–gravity interface and efforts to identify experimental signatures of quantum gravity. It focuses on gravitational decoherence and the interplay between internal energy and centre-of-mass dynamics in composite quantum systems, complemented by a study of internal-energy effects in gravitationally mediated entanglement. First, we develop relativistic Hamiltonian formulations showing that changes in a composite system’s internal energy increase its gravitational mass rather than alter its momentum. This removes earlier ad hoc arguments for eliminating “anomalous friction forces”. We show that gravitational waves act as a dynamical background, inducing curvature-dependent forces that modify total momentum. Second, we revisit a thought experiment in which tensions between causality and complementarity arise. We identify a scenario in which these tensions follow from energy–mass equivalence, making the effect specific to gravitational interactions. In a gravitationally mediated entanglement experiment using Newtonian gravity as mediator, we investigate whether decohering gravitational radiation can resolve the apparent conflict. Finally, we build upon a model of gravitational decoherence consistent with general relativity. This requires deriving a higher-derivative quantum Langevin equation and master equation. The resulting dynamics show that gravitational interactions induce decoherence in the canonical momentum basis of the quadrupole and generate acceleration- and jerk-dependent corrections absent in electrodynamics. Together, these results show that weak-field gravitational interactions leave distinct relativistic imprints on quantum systems, including effects unique to gravitational waves, providing potential signatures that distinguish gravity from other interactions.
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.
Gravity can both generate quantum entanglement and cause decoherence through time-dilation effects. This note studies the competition between these two effects by treating them as consequences of the same Newtonian mass–energy interaction. Using a solvable two-body model with a coupling between energy and geometry, the work shows that the position-dependent part of the interaction produces the entangling phases associated with gravitationally induced entanglement, while the energy-dependent part produces proper-time decoherence. The paper computes this race exactly and derives several results. First, the outcome is independent of the strength of gravity itself: the dynamics depends only on the combination of coupling strength and interaction time, meaning that gravity sets the timescale but does not determine the final verdict. The result is controlled by the structure of the interaction and the geometry of the quantum state. Second, a registered prediction that internal energy spread would eventually destroy gravitational entanglement is disproved by the exact calculation. Instead, the entanglement decreases but approaches a nonzero geometry-dependent floor. The mechanism is traced to the energy-product coupling, which produces a non-Gaussian characteristic function and prevents complete suppression of the entangling effect. Third, the work derives an exact separability boundary: two sources with spatial coherences v1 and v2 become entangled at the optimal phase precisely when (1 + v1)(1 + v2) > 2. Fully decohered sources cannot generate entanglement, while partial coherence can be sufficient. Finally, the paper verifies that the record–decoherence relation holds inside the same gravitational interaction: coherence lost by a system equals the information recorded by the rest of the universe, combining entanglement and proper-time decoherence into a single information budget. The results are obtained within finite exactly solvable models with declared limitations: static branches, Newtonian-form coupling, no graviton exchange, and no dynamical quantum gravity. The work provides a controlled theoretical framework for understanding the competition between gravitationally induced entanglement and gravitational decoherence.
When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no “gravitons” are emitted during the experiment.