THE_TEST // Static vs Dynamic // Emergent Gravity

The Question

Does gravity decohere a particle that isn't moving?

Put a particle in superposition of two positions. Don't let it oscillate. Don't let it move. Just let it sit there — existing in two places at once.

THE STATIC SUPERPOSITION

|ψ⟩ = |left⟩ + |right⟩

No oscillation. No dynamics. Just quantum position uncertainty.

Wait. Measure how long the superposition lasts. Subtract all known decoherence sources — thermal, electromagnetic, collisional.

Is there a residual? Does gravity itself destroy the superposition?

THE QUESTION

Γ_gravity(static) = ?

Two Predictions

Penrose-Diósi vs Bath-TT. Opposite answers.

Penrose-Diósi

Gravity couples to the full metric. The Newtonian potential differs between |left⟩ and |right⟩. This difference causes decoherence.

Γ ≠ 0

Static superpositions decohere.

VS

Bath-TT

The Bath couples to TT (transverse-traceless) stress-energy. Static sources have TT = 0. The Bath sees no difference between |left⟩ and |right⟩.

Γ = 0

Static superpositions don't decohere gravitationally.

Why They Differ

Penrose-Diósi Logic

Mass at position A creates potential φ_A
Mass at position B creates potential φ_B
Superposition means superposition of potentials
Energy difference E_G = ∫|φ_A - φ_B|² causes decoherence
Γ ~ E_G/ℏ ~ Gm²/(ℏΔx)

Bath-TT Logic

The Bath measures TT stress-energy
Static mass has T^TT = 0
|left⟩ and |right⟩ look identical to TT measurement
No information → no decoherence
Γ = 0 for static superposition

The Key Insight

Both theories agree on dynamic superpositions — oscillating masses decohere.

They disagree on static superpositions — mass just sitting in two places.

This is a qualitative difference, not a quantitative one. Zero vs non-zero. Binary. Decisive.

The Experiment

Create static superposition. Measure decoherence. Subtract known sources.

Protocol

t = 0

Prepare mass in spatial superposition |left⟩ + |right⟩

t = 0 → T

Hold superposition static. No driving. No oscillation. Isolate from environment.

t = T

Measure coherence. Interference visibility V(T).

Repeat

Vary T. Map V(T). Extract decoherence rate Γ from exponential decay.

The Subtraction

Total measured decoherence:

Γ_total = Γ_thermal + Γ_EM + Γ_collision + Γ_gravity

We know how to calculate Γ_thermal, Γ_EM, Γ_collision from standard physics.

The residual is:

Γ_gravity = Γ_total - Γ_known

The Numbers

Penrose-Diósi: Γ = Gm²/(ℏΔx)

For a 10 pg mass (10^-14 kg), separation 1 μm:

Γ_DP ~ 60 s^-1 → τ ~ 16 milliseconds

For a 10 fg mass (10^-17 kg), separation 1 μm:

Γ_DP ~ 6×10^-5 s^-1 → τ ~ 4 hours

Bath-TT predicts:

Γ_TT = 0 → τ = ∞ (limited only by other sources)

Key insight: larger masses → faster DP decoherence → easier to detect.

What The Result Means

One measurement. Two possible futures.

If Γ_gravity = 0

Static superpositions don't decohere gravitationally.

Bath-TT is confirmed
Penrose-Diósi is falsified
Gravity couples to TT, not full metric
Geometry-dependent decoherence is real
The framework stands

Everything changes.

If Γ_gravity = Γ_DP

Static superpositions decohere at the Penrose-Diósi rate.

Penrose-Diósi is confirmed
Bath-TT is falsified
Gravity couples to full metric
No geometry-dependent decoherence
The framework falls

Back to the drawing board.

Why This Is Science

A theory that cannot be falsified is not science.

We have stated our falsification criterion:

If static superpositions show gravitational decoherence at the Penrose-Diósi rate, the Bath-TT framework is wrong.

This is not hedging. This is not "consistent with." This is a binary test.

We have placed our bet. The universe will call.

Current Status

Where we are. What's needed.

2026: The Gap

Two paths to the test:

Path A: Large mass (10 pg)
DP prediction	τ ~ 16 ms
Current coherence at this mass	~ 0.1 ms (approaching)
Gap	~2 orders of magnitude
Path B: Small mass (10 fg)
DP prediction	τ ~ 4 hours
Current coherence at this mass	~ 1 second
Gap	~4 orders of magnitude

Path A is more promising: larger masses give faster DP rates.

The test is closer than it appears.

What Would Accelerate It

Larger masses in superposition — Γ_DP ∝ m², so 10× mass = 100× faster signal
Better isolation — reduces Γ_known, makes gravitational residual detectable
Cryogenic optomechanics — picogram masses approaching ground state, superposition next
Levitated nanoparticles — no mechanical contact, extreme isolation possible
Space-based experiments — removes seismic noise, enables longer coherence

The Bet

We predict that static superpositions will show zero gravitational decoherence.

Not "small." Not "below current detection." Zero.

Penrose predicts non-zero. One of us is wrong.

Static vs Dynamic.

This is the test. This is the bet. This is science.

Continue

The test is identified. Now build the machine.

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