A Smoking Gun for Gravitational Decoherence: Watching Entanglement Disappear

Entanglement Decay from Gravitational Decoherence — Quantum-Geometric Correspondence series

The Problem with Testing Gravity's Quantum Role

Suppose gravity really does cause quantum superpositions to collapse, as the Diosi-Penrose hypothesis predicts. How would you prove it?

The obvious approach---put a massive particle in superposition and watch it decohere---has a fatal weakness. Even in the best vacuum, at the lowest temperatures, there are always stray photons, residual gas molecules, and thermal vibrations that could explain any observed decoherence. How do you know it was gravity and not some mundane environmental effect?

This paper identifies a distinctive signature that only gravitational decoherence can produce: the decay of entanglement between distant particles.

The Key Insight: Monogamy of Entanglement

Entanglement is a jealous resource. One of the deepest results in quantum information theory is the monogamy of entanglement: if particle A becomes highly entangled with system C, its entanglement with particle B must decrease. There is only so much quantum correlation to go around.

Now consider this setup: two particles, A and B, are prepared in an entangled state. Then particle A is placed into a spatial superposition---shifted so its quantum wavefunction occupies two locations at once.

According to the Diosi-Penrose hypothesis, particle A's two positions correspond to distinguishable gravitational field configurations. The gravitational degrees of freedom become entangled with A's position:

$|L\rangle|g_0\rangle \rightarrow |L\rangle|g_L\rangle, \quad |R\rangle|g_0\rangle \rightarrow |R\rangle|g_R\rangle$

As the gravitational field "learns" which branch A is in, monogamy kicks in. A's growing entanglement with gravity comes at the expense of its entanglement with distant particle B.

The Prediction

The central result is precise and testable. The concurrence---a standard measure of entanglement---decays exponentially:

$C(t) = C(0) \exp\left(-\frac{GM^2 t}{\hbar d}\right)$

where $M$ is the mass of particle A and $d$ is the superposition separation. The entanglement decays at exactly the gravitational decoherence rate.

For a Bell inequality test, the state is a pure-dephasing state, whose exact CHSH maximum is $S_{max}(t) = 2\sqrt{1 + e^{-2\Gamma_{grav} t}}$. This exceeds the classical bound of 2 for all finite times, approaching 2 only asymptotically---so the experimental figure of merit is not a sharp cutoff but how far $S$ stays above 2. (Under a cruder Werner approximation, $S_{max}(t) = 2\sqrt{2}\exp(-\Gamma_{grav} t)$ and the violation would end at $t_{Bell} \approx 0.35 \tau_{dec}$, about a third of the decoherence time.)

What makes this prediction powerful is what it rules out.

Why Only Gravity Can Do This

Standard environmental decoherence---photons scattering off particle A, air molecules colliding with it---destroys A's local coherence. A's spatial superposition decays. But crucially, this does not directly affect A's pre-existing entanglement with distant particle B.

Why not? Because standard environmental interactions are local. Air molecules bounce off A, becoming entangled with A's position. But they have no connection to B, which could be across the room or across the continent. The environment "learns" about A's position without disturbing the A-B correlations.

Gravitational decoherence is fundamentally different. The gravitational field is not an external environment that A happens to interact with. It is intrinsic to A's spatial configuration. When A is in superposition, the gravitational field itself is in superposition---and it is this field that becomes entangled with A's position. Because the gravitational entanglement is with A's own degrees of freedom (its mass-energy configuration), monogamy directly reduces A's entanglement capacity with B.

Four frameworks give sharply different predictions:

Only Diosi-Penrose predicts correlated local decoherence and entanglement decay, both at exactly rate $GM^2/(\hbar d)$. This correlation is the smoking gun.

How to Do the Experiment

The proposed platform is levitated optomechanics: massive particles suspended in laser traps in ultra-high vacuum.

The protocol has five phases:

1. Prepare two silica microparticles (mass $\sim 20$ picograms, radius $\sim 1$ μm) and cool them to their motional ground state
2. Entangle the particles via Coulomb coupling
3. Superpose particle A by coherently displacing it into a spatial superposition ($d \sim 10$ μm)
4. Wait for a variable time, from zero up to several decoherence times
5. Measure the remaining entanglement via Bell-basis measurements

For these parameters ($M = 20$ pg, $d = 10$ μm), the predicted decoherence time is about 40 milliseconds. Reaching this regime, however, sits well beyond current quantum-superposition records and remains a long-term target.

The environmental decoherence budget is the central obstacle. At standard ultra-high vacuum ($10^{-8}$ Pa) and 100 mK, gas collisions overwhelm the gravitational rate by roughly four orders of magnitude. For this modest-mass configuration, only extreme high vacuum ($\sim 10^{-13}$ Pa)---currently projected only for space-based platforms such as MAQRO/DECIDE---pushes the collisional rate below the gravitational signal. Alternatively, operating at much larger (microgram) masses lifts the gravitational rate above the collisional floor at ground-based UHV, at the cost of requiring superpositions far beyond any current demonstration.

Four Control Experiments

Scientific rigor demands controls that could falsify the gravitational interpretation:

1. No superposition: Run the same protocol but skip the displacement step. No entanglement decay should be observed. If it is, something systematic is wrong.
2. Mass scaling: Repeat with particles of different mass. The decoherence time should scale as $M^{-2}$---doubling the mass should cut the time by a factor of four.
3. Separation scaling: Vary the superposition distance $d$ (e.g. 1, 5, 10 μm). The decoherence time should scale linearly with $d$---double the separation, double the coherence time. This is opposite to environmental decoherence, which gets worse with larger separations.
4. Temperature variation: Lower the temperature further. Gravitational decoherence should be completely temperature-independent, unlike any thermal mechanism.

The Timeline

The technology building blocks exist but need to be combined:

• Nanoparticle levitation and ground-state cooling: demonstrated
• Spatial superposition of levitated particles: achieved at $\sim 100$ femtometers (10 pg), needs $10^7$-$10^8\times$ improvement
• Two-particle entanglement: major gap, currently in development
• Extreme high vacuum ($\le 10^{-13}$ Pa): projected only for space platforms, some five orders below ground-based UHV

A realistic experimental timeline:

• 2030--2032: $\sim 10$ nm superposition with 10 pg particles
• 2030--2035: Two-particle Coulomb entanglement demonstrated
• mid-2030s: Cryogenic XHV in space (MAQRO/DECIDE class)
• late 2030s: Proof-of-principle entanglement decay measurement
• 2040--2045: Mass and separation scaling verified
• 2045--2050: Definitive test

What Is at Stake

If entanglement decay is observed at the predicted rate, it would be direct evidence that gravity plays a fundamental role in the quantum-to-classical transition---beyond any known environmental mechanism, and pointing to non-perturbative gravitational physics operating at laboratory scales.

If no decay is observed, the Diosi-Penrose hypothesis is falsified for the tested mass range, and standard quantum mechanics survives another challenge.

Either outcome would mark a milestone in our understanding of where quantum mechanics ends and the classical world begins.

This is the entanglement-decay paper of the Quantum-Geometric Correspondence series, identifying entanglement decay as a unique experimental signature of gravitational decoherence.