Interferometry, Decoherence, and Entanglement Proposals

Mesoscopic interferometry can test gravitational phases, unexplained decoherence, and the information-carrying capacity of a mediator. These are different targets. A Newtonian phase is compatible with several classical and quantum descriptions; loss of visibility is not automatically fundamental decoherence; and entanglement is evidence against a specified class of classical mediation models only under explicit locality and subsystem assumptions.

Required background. Quantum-Gravity Observables and Test Taxonomy fixes the inference chain, while Witnesses for Entanglement, Scrambling, and Recoverability supplies witness logic. Helpful background. Localized Probe and Detector Models develops operational probes, and Validity, Decoherence, and What Stochastic Gravity Does Not Capture separates stochastic metric effects from microscopic quantum gravity.

Branch-dependent gravitational phase

Let each of two masses occupy a superposition of locations $L$ and $R$. In the Newtonian regime, branch $ij$ accumulates

$$\phi_{ij}=-\frac{1}{\hbar} \int_0^t V(r_{ij}(t'))\,dt' \simeq \frac{Gm_1m_2t}{\hbar r_{ij}}.$$

Local phases can be removed. The entangling invariant is

$$\Phi=\phi_{LL}+\phi_{RR}-\phi_{LR}-\phi_{RL}.$$

For an initially separable equal superposition, $\Phi\ne0$ generically produces entanglement. Spin-dependent path preparation can map this phase to correlations such as $\langle\sigma_x\otimes\sigma_z\rangle$, allowing an entanglement witness after the paths recombine Bose et al. 2017.

The derivation assumes controlled trajectories, negligible retardation, a valid Newtonian potential, and a tensor-product assignment of the two masses. The experiment measures correlations among matter degrees of freedom. The statement about the mediator follows only after excluding direct interactions and specifying what classical channels are allowed.

First application: phase, witness, and noise budget

For equal masses with mean separation $d$ and path displacement $\Delta x\ll d$, a symmetric geometry gives the scaling

$$\Phi\sim \frac{Gm^2t}{\hbar} \frac{(\Delta x)^2}{d^3}.$$

The first application is to choose $(m,d,\Delta x,t)$, compute all four branch distances rather than relying on this scaling, evolve the density matrix, and evaluate a witness $W$ with a separable bound $W\le W_{\mathrm{sep}}$. Environmental decoherence multiplies off-diagonal terms approximately by

$$\mathcal{V}(t)= \exp\!\left[-\int_0^t (\Gamma_{\mathrm{gas}}+\Gamma_{\mathrm{bb}} +\Gamma_{\mathrm{vib}}+\cdots)dt'\right].$$

A forecast must propagate pressure, temperature, internal heating, trapping-field noise, vibration spectra, path calibration, and readout errors into the distribution of $W$. Residual electrostatic, magnetic, Casimir–Polder, and patch-potential interactions need measured upper bounds at the relevant separation. A conducting screen changes both backgrounds and gravitational geometry and must enter the forward model.

In the empirical sources reviewed here through the cutoff, gravity-mediated entanglement between mesoscopic masses has not been detected; the cited work consists of proposals, feasibility studies, and conceptual tests.

What would entanglement establish?

The influential local-mediation argument says that two systems cannot become entangled through only local operations and classical communication. Under that assumption, observing entanglement implies that the mediator carries noncommuting observables Marletto and Vedral 2017. This is a mediator-quantumness witness, not a measurement of gravitons, ultraviolet dynamics, or a particular quantum-gravity program.

The premise must now be stated especially carefully. A full-QFT matter treatment can allow local models with a classical gravitational field to generate entanglement through quantum matter exchange; Aziz and Howl exhibit such a countermodel and a different parameter scaling Aziz and Howl 2025. Whether that construction is ultimately viable is a separate question. Its immediate methodological force is decisive: entanglement alone is not interpretation-free. A robust experiment should vary mass, duration, separation, and geometry so that competing mechanisms with different scalings can be distinguished.

Likewise, an observed visibility loss is not evidence for gravity-induced collapse until gas collisions, blackbody emission, vibrations, electromagnetic gradients, timing jitter, and technical averaging are quantitatively excluded. A master equation such as

$$\dot\rho=-\frac{i}{\hbar}[H,\rho] -\Lambda[\hat x,[\hat x,\rho]]$$

defines a testable decoherence coefficient $\Lambda$. It does not by itself identify whether the underlying noise is environmental, stochastic-gravitational, or fundamental.

Adversarial control: a classical force with hidden noise

Inject a branch-dependent electrostatic potential adjusted to reproduce the predicted $\Phi$, together with correlated phase noise that matches the observed visibility. Blind the analysis to injection status. The pipeline must distinguish the force through charge reversal, shielding, separation scaling, and independent field sensing. Then simulate the classical-gravity-plus-quantum-matter countermodel and ask whether mass and time scans separate it from the mediator model.

If only a phase is recovered, the conclusion is a force measurement. If a witness violates its separable bound after all direct channels are excluded, the conclusion is incompatibility with the stated classical-channel class. Only a pattern of scaling tests can sharpen the interpretation. No such result by itself selects a UV completion.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Aziz, J., and R. Howl. “Classical Theories of Gravity Produce Entanglement.” Nature 646, 813–817 (2025). DOI.
• Bose, S., et al. “Spin Entanglement Witness for Quantum Gravity.” Physical Review Letters 119, 240401 (2017). DOI.
• Marletto, C., and V. Vedral. “Gravitationally Induced Entanglement between Two Massive Particles Is Sufficient Evidence of Quantum Effects in Gravity.” Physical Review Letters 119, 240402 (2017). DOI.