We present a falsifiable framework for generating and detecting path entanglement mediatedby Newtonian gravity between two mesoscopic masses using pure motional interferometry. Eachmass is prepared in a spatial superposition of two paths with separation ∆x, the pair is heldfor an interaction time T at mean separation r, and then recombined locally. The gravita-tional interaction imprints branch-dependent phases ϕij = (Gm1m2T /ℏ) r−1ij on the four branches(i, j) ∈ {+, −}2, yielding a two-qubit controlled-phase operation whose gauge-invariant nonlocalphase is ∆ϕ = ϕ++ + ϕ−− − ϕ+− − ϕ−+ = (Gm1m2T /ℏ)(r−1++ + r−1−− − r−1+− − r−1−+). For a symmet-ric r ± ∆x geometry, ∆ϕ = (Gm2T /ℏ)(2/r − 1/(r + ∆x) − 1/(r − ∆x)) ≈ −2Gm2T ∆x2/(ℏr3) for∆x ≪ r. We show how ∆ϕ(r, ∆x, T ) appears as a geometry-modulated template in joint outputstatistics after recombination, and we formulate an inference protocol based on (i) template regres-sion across controlled modulations of r, ∆x, T and (ii) independent bounds and control experimentsthat constrain nongravitational interactions below the fitted template amplitude. Because the oper-ating point of interest can lie in the weak-phase regime (|∆ϕ| ≪ 1), we treat Bell-inequality violationas optional rather than primary; the escalation to an entanglement claim is framed in terms of ex-perimentally accessible two-qubit witnesses obtained from multi-basis correlation measurements onthe path degrees of freedom, together with a quantitative “no-template-match” falsifier.
We present a falsifiable framework for generating and detecting path entanglement mediatedby Newtonian gravity between two mesoscopic masses using pure motional interferometry. Eachmass is prepared in a spatial superposition of two paths with separation ∆x, the pair is heldfor an interaction time T at mean separation r, and then recombined locally. The gravita-tional interaction imprints branch-dependent phases ϕij = (Gm1m2T /ℏ) r−1ij on the four branches(i, j) ∈ {+, −}2, yielding a two-qubit controlled-phase operation whose gauge-invariant nonlocalphase is ∆ϕ = ϕ++ + ϕ−− − ϕ+− − ϕ−+ = (Gm1m2T /ℏ)(r−1++ + r−1−− − r−1+− − r−1−+). For a symmet-ric r ± ∆x geometry, ∆ϕ = (Gm2T /ℏ)(2/r − 1/(r + ∆x) − 1/(r − ∆x)) ≈ −2Gm2T ∆x2/(ℏr3) for∆x ≪ r. We show how ∆ϕ(r, ∆x, T ) appears as a geometry-modulated template in joint outputstatistics after recombination, and we formulate an inference protocol based on (i) template regres-sion across controlled modulations of r, ∆x, T and (ii) independent bounds and control experimentsthat constrain nongravitational interactions below the fitted template amplitude. Because the oper-ating point of interest can lie in the weak-phase regime (|∆ϕ| ≪ 1), we treat Bell-inequality violationas optional rather than primary; the escalation to an entanglement claim is framed in terms of ex-perimentally accessible two-qubit witnesses obtained from multi-basis correlation measurements onthe path degrees of freedom, together with a quantitative “no-template-match” falsifier.
ABSTRACT Background The gravity–quantum interface lacks a minimal, operational theory for the weak-field, non-relativistic, mesoscopic regime. Semiclassical gravity (SCG), which sources the classical Einstein equations from the quantum expectation value of stress–energy, is the dominant approximation but was designed for cosmological and astrophysical contexts, not for two-body entanglement experiments in the laboratory. A structural silence exists: no framework specifies how gravity couples to quantum matter when entanglement between spatially delocalised mesoscopic masses is at stake. Gap The Named Binary distinguishing Semiclassical Gravity Interface (SCGI) from Quantum-Mediator Gravity Interface (QMGI) does not appear in the literature as a formal operational distinction with computable consequences. No framework simultaneously satisfies: standard quantum mechanics for matter, no-signalling, reduction to Newtonian gravity for classical configurations, and entanglement-generation capability. This four-constraint conjunction defines the structural gap. Approach We formalise the two-body BMV (Bose–Marletto–Vedral) configuration using Hilbert-space language and quantum channels, derive the effective entangling Hamiltonian, prove that C(t) = |sin(Δφ(t)/2)| where Δφ(t) is the entangling phase determined by geometry and interaction time, and derive the design inequality τ_ent ≪ τ_dec as the admissibility condition for entanglement detection. We establish the Strongest Formulation in the five-part programme template, specify a pre-registerable CCS with quantitative decision rule, confirm structural invariance across three independent physics domains, ground the framework in IGT theory, and provide a complete Weil Protocol practitioner review pack. Results Under the four-constraint conjunction (standard QM + no-signalling + Newtonian reduction + entanglement capability), gravity in the mesoscopic weak-field regime must be modelled as a quantum channel: SCGI fails because classical channels cannot increase entanglement between initially separable systems. The entangling phase scales as Δφ(t) ~ Gm²dt/(ℏD²); detectable entanglement requires τ_ent/τ_dec < 1. Three independent distinguishing predictions follow that SCGI cannot make. Structural invariance is confirmed in quantum electrodynamics (photon-mediated entanglement), nuclear physics (exchange-mediated forces), and quantum optics (cavity-mediated entanglement). Implications Any tabletop detection of gravitationally induced entanglement between two mesoscopic masses in a BMV-type experiment would constitute a direct, model-independent, low-energy signature of the quantum nature of gravity. Any confirmed null result provides the strongest direct evidence for SCGI-type models and bounds the parameter space of quantum mediator theories. Weil Protocol practitioner review is required before policy adoption of experimental specifications; status INCOMPLETE. Human-stakes level: L2 · Weil Protocol: INCOMPLETE
We analytically solve the entangling quantum dynamics of two interacting Stern-Gerlach Interferometers~(SGI). Each SGI exploits an operator-valued force applied by a qubit to create and recombine a non-Gaussian state of matter. The entangling phase between the two qubits generated by the leading-order gravitational interaction of the massive degrees of freedom is found to be mass-independent, both for unitary and open dynamics, irrespective of the temperature and squeezing of the initial states. Further, we show that the solution of the four interferometric paths reveals that the mere presence of the interaction does not allow for a perfect recombination of the centre of mass. This second-order effect, alongside higher-order interaction terms, can be used to bound the mass from above and below, thus restricting the experiment's regime to mesoscopic masses. By solving the open dynamics which includes diffusion and dephasing with initial squeezed thermal states, the bounds are tightened by the inclusion of realistic experimental noise. We discuss diamagnetic levitated masses with embedded NV-centres as a specific physical implementation.
Gravity-induced entanglement has been proposed as a method for testing the non-classical nature of gravity via tabletop experiments. While most existing proposals are restricted to the Newtonian limit, the frame dragging effect offers access to genuinely post-Newtonian features of the gravitational interaction and remains comparatively less explored. Here, we study gravity-induced entanglement generated by frame dragging in an interferometric setting and compute the entanglement phase between the rotational degrees of freedom of a source mass and the paths of a particle in two complementary ways: (i) via Schrödinger evolution with a quantized Lense-Thirring Hamiltonian in the large angular momentum limit, and (ii) via the on-shell action of linearized quantum gravity within the stationary phase approximation. Both approaches yield the same entanglement phase, consistent with the proper time difference between the interferometer arms. The path integral derivation further reveals how gravitational retardation modifies the entanglement phase, thereby making the local, relativistically causal linearized-gravity description explicit. Under the standard locality/mediator assumptions used in existing arguments, the resulting entanglement would witness non-classicality of the gravitational interaction.
This work presents numerical and theoretical evidence for a testable regime in which semiclassical Schrödinger–Newton dynamics predict a state-dependent gravitational self-interaction in mesoscopic quantum systems. Using large-scale Split-Step Fourier Method (SSFM) simulations, we identify a mass window (≈10⁻¹¹–10⁻¹⁰ kg) where quantum coherence and gravitational self-interaction coexist without immediate decoherence. In this regime, the gravitational self-energy depends smoothly on the spatial structure of the quantum state, leading to a differential phase evolution between superposition states with identical external potentials but different mass-density distributions. The predicted phase signal scales as m² and reaches experimentally relevant magnitudes (Δφ ≈ 10⁻³ rad) for millisecond evolution times, making the effect accessible to next-generation matter-wave and optomechanical interferometry. The work systematically validates the numerical approach, demonstrates energy conservation and convergence of the nonlinear dynamics, identifies a stable “breathing-mode” regime near 10⁻¹⁰ kg, and isolates the gravitational origin of the effect via null tests with the Schrödinger–Newton term removed. This preprint makes no claim regarding spacetime engineering, geometry manipulation, or violations of the equivalence principle. It is explicitly framed as a falsifiable test of semiclassical gravity in a previously inaccessible experimental regime. Confirmation or null detection would provide strong constraints on Schrödinger–Newton–type models and inform the ongoing search for the correct quantum–gravity interface.
This work presents a model-independent analysis of gravity-mediated entanglement based on the geometric structure of interaction-induced phase evolution. Using a minimal two-body phase model inspired by recent gravity-mediated entanglement proposals, it is shown that quantum entanglement between initially separable systems arises if and only if the induced phase structure is non-factorable. The central result identifies a gauge-invariant plaquette phase as a necessary and sufficient operational condition for entanglement generation. When this plaquette invariant is nonzero, standard quantum information diagnostics—such as negativity, concurrence, and Bell–CHSH correlations—confirm the presence of entanglement. When the invariant is eliminated, entanglement vanishes identically, even when individual phase magnitudes remain nonzero. A comprehensive suite of falsification tests is applied, including local phase factorization, plaquette removal, deterministic and stochastic phase scrambling, permutation symmetry tests, LOCC protocols, causal reordering, and controlled noise injection. Across all tests, entanglement survives exclusively in the presence of non-factorable phase structure. Scaling analyses further demonstrate consistent dependencies on mass, interaction time, separation distance, and superposition size, yielding a distinctive interaction fingerprint incompatible with classical or semiclassical channels. The framework is fully operational and does not assume a specific theory of quantum gravity. Instead, it provides a concrete, experimentally accessible criterion for probing nonclassical aspects of gravity using near-term interferometric platforms. The results sharpen the interpretational foundations of gravity-mediated entanglement proposals by isolating the minimal structural feature responsible for entanglement generation.
This work presents an explicit Newtonian gravitational phase model for two masses placed in spatial superposition and demonstrates that the resulting phase structure produces a non-zero plaquette invariant. Numerical simulations show that the plaquette phase scales with branch separation, generates entanglement according to analytic mappings, and vanishes under loop-removal kill tests. These results provide a fully operational demonstration that Newtonian gravitational phase accumulation produces the non-factorable loop structure required for gravity-mediated entanglement.