The Experiment That Almost Proves Quantum Gravity — And Why Gravity Might Spoil It

Tabletop quantum gravity — Quantum-Geometric Correspondence series

The most exciting tabletop idea in quantum gravity

For a century, quantum gravity has been a theory in search of an experiment. Planck-scale energies are hopelessly out of reach. Black-hole analogues are clever but indirect. Cosmology is noisy.

Then came a proposal that sounded almost too good: put two tiny masses in spatial superposition, let them gravitationally interact, and check whether they become entangled. If they do, gravity must be carrying quantum information — because classical fields, under standard assumptions, cannot create entanglement. The experiment is known as BMV or QGEM. Designs involving silica microspheres, laser traps, and separations of tens to hundreds of microns are now under serious experimental discussion.

If it works, it would be the first laboratory witness that gravity is quantum.

Our framework predicts something awkward: the witness may be suppressed by the very gravitational physics the experiment is trying to see.

Self-decoherence of the source

In our picture, a mass in spatial superposition decoheres because its gravitational field differs between branches. The energy scale is the one Diósi and Penrose identified. For a point mass that energy grows as you pull the arms apart. For a real solid sphere, when the arm separation is much larger than the particle size, the self-energy saturates:

$E_{\mathrm{sat}} \approx 1.2\,\frac{G m^2}{R}$

fixed by particle size, not by how far apart the arms are. That is the experimentally relevant regime for micron-sized spheres with tens-to-hundreds-of-microns arms.

While the two masses are trying to entangle each other through gravity, each mass is also decohering itself through gravity. The entanglement witness rides on residual quantum coherence. If self-decoherence wins, the witness goes dark.

A square law, not a cube law

When the experiment reaches the point where entanglement should appear, the residual visibility follows a square-law form:

$V \sim \exp\!\Bigl[-\mathcal{O}(1)\,\Bigl(\frac{d}{\Delta}\Bigr)^2\Bigl(\frac{d}{R}\Bigr)\Bigr]$

with a weak residual mass trend that falls as mass increases — opposite in sign to collapse models, which grow with mass squared.

Orientation matters. Parallel arms, perpendicular arms, and a special "magic" angle near 55° give different laws. That angular structure is itself a fingerprint.

What the numbers say

Take silica spheres around 10⁻¹⁴ kilograms, about 150 microns apart, with arm separations half that — a nominal design point. In all geometries the predicted residual visibility is essentially zero. The finite-size self-energy is so large at micron radii that coherence is gone. Standard analyses that ignore self-decoherence predict perfect visibility.

The window where an experiment can actually see a curve — visibility between roughly 5% and 95% — requires pushing the arms much farther apart than the particles. There the square law becomes measurable, and the weak inverse mass trend becomes a discriminator against collapse models.

So the prediction is not "the experiment will fail." It is sharper:

1. At the nominal design geometry, expect a null entanglement witness if this kind of self-decoherence is real.
2. At stretched arm ratios, expect a specific visibility curve — square or quartic, with a weak inverse-cube-root mass trend.
3. Collapse models and "no decoherence" quantum gravity make different curves. Experiment can tell them apart.

Why this is not special pleading

It would be cheap to invent a mechanism that conveniently kills the experiment you don't like. That is not what is happening here.

The same self-energy that sets gravitational decoherence for a single interferometer — a classical, rigorous, uncontroversial energy scale — is being applied consistently to the masses inside the entanglement witness. If gravity decoheres a one-particle superposition, it decoheres each arm of a two-particle setup. You cannot have the first prediction without the second.

The open question is the one the whole programme lives on: does that energy become a rate linear in Newton's constant, or only at second order? Standard quantum field theory says second order — thirty-four orders of magnitude slower, utterly negligible for this experiment. Our framework says linear. Nature can decide.

How to read a null result

A null entanglement witness would not, by itself, prove our framework. Classical noise, imperfect isolation, or a collapse model could also kill entanglement. What would be powerful is a shaped null — or a shaped partial visibility — that tracks the square law and the weak mass trend as mass, size, and arm geometry vary.

Conversely, a clean entanglement signal at the nominal design point, with no sign of the saturated self-energy suppression, would be serious trouble for the linear-rate story. That is a feature. Theories that cannot lose should not be trusted.

The upshot

This remains one of the most important proposed experiments in fundamental physics. Our contribution is a warning label written as a formula: gravity may be quantum and may still spoil the witness, because the same interaction that entangles also decoheres.

The interesting question is no longer only "do the masses entangle?" It is "does the visibility follow the saturated square law?" That is a sharper target — and a fairer one.

Related: Three Axioms, One Decoherence Rate.