How can gravity and quantum theory be tested together?

The question in perspective

Quantum theory describes superpositions of matter configurations. General relativity describes a dynamical spacetime sourced by matter. Reconciling them requires more than adding a gravitational potential to a Schrödinger equation: one must specify which quantities are quantum, how matter sources geometry, and what an experiment can distinguish.

A manageable entry point is two masses, each coherently split between two locations. Can their gravitational interaction generate entanglement, and what would that establish?

A phase that cannot be removed locally

Label each mass’s paths by \(0,1\). Assume fixed separations \(d_{ij}\), weak fields, negligible motion during an interaction time \(t\), and no competing interaction. In a branch-dependent Newtonian interaction model, the energy \(V_{ij}=-Gm_1m_2/d_{ij}\) produces

\[\ket\Psi=\frac12\sum_{i,j=0}^1e^{i\phi_{ij}}\ket{ij},\qquad \phi_{ij}=\frac{Gm_1m_2t}{\hbar d_{ij}}.\]

The sign follows from \(e^{-iV_{ij}t/\hbar}\). This assumes an interaction acting on the joint path state; it is not a derivation of that interaction from every possible classical or quantum theory of gravity.

Independent phase changes on the two masses can remove three phase combinations. The invariant combination is

\[\Delta=\phi_{00}+\phi_{11}-\phi_{01}-\phi_{10}.\]

Write the coefficients as a two-by-two matrix \(M_{ij}=e^{i\phi_{ij}}/2\). A pure two-qubit state is a product exactly when this matrix has rank one. Here

\[|\det M|=\frac12\left|\sin\frac\Delta2\right|.\]

Thus the ideal state is entangled unless \(\Delta\) is a multiple of \(2\pi\). The result identifies a measurable nonlocal phase. It does not, by itself, identify a microscopic theory of spacetime.

What is established, and what is debated

Gravity-mediated entanglement proposals connect an entanglement witness to assumptions about a mediator’s information-carrying capabilities. Operations restricted to local quantum operations and classical communication cannot create entanglement from a separable input.

The inference from entanglement to quantum gravity depends on how that restriction models the interaction. Martín-Martínez and Perche examine locality assumptions. Aziz and Howl propose classical-gravity field-theoretic mechanisms, while Gundhi, Infantino, and Bassi contest the entanglement calculation in that scenario. These are competing claims, not a settled experimental verdict.

What remains unresolved

The broader task is a consistent, predictive account of quantum matter and gravity. For a tabletop test, the sharper task is to identify which observable distinguishes explicitly defined models after electromagnetic forces, environmental decoherence, and preparation errors are included. Entanglement evidence and evidence for quantized gravitational degrees of freedom must be connected by a stated argument.

A concrete next investigation

Reproduce: compute \(\Delta\) for a specified four-distance geometry, diagonalize either mass’s reduced state, and check the determinant criterion. At \(\Delta=\pi\), the ideal state has maximally mixed local states.

Check: add arbitrary single-mass phases and verify that \(\Delta\) and the entanglement are unchanged.

Extend: compare two fully specified interaction models at the same approximation order, retaining all required amplitudes. Derive a measurement and uncertainty budget that distinguish their predictions. Improving that discrimination is a research contribution; observing a phase alone does not settle quantum gravity.

Selected references

1. Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity

   Chiara Marletto, Vlatko Vedral. 2017. Research proposal

   A gravity-mediated entanglement proposal; interpret the conclusion with its mediator assumptions.

2. What gravity mediated entanglement can really tell us about quantum gravity

   Eduardo Martín-Martínez, T. Rick Perche. 2022. Research paper

   Examines the locality and modelling assumptions behind gravity-mediated entanglement tests.

3. Classical theories of gravity produce entanglement

   Joseph Aziz, Richard Howl. 2025. Research paper

   A proposed field-theoretic mechanism; its entanglement inference is disputed in subsequent work.

4. Can classical theories of gravity produce entanglement?

   Anirudh Gundhi, Giorgia Infantino, Angelo Bassi. 2026. Preprint

   Challenges the amplitude treatment in the Aziz–Howl proposal; read alongside the original claim.

Years refer to first arXiv submission. Publication details are available in the linked records.