The Quantum Origin of Classical Spacetime

Why has quantum gravity been so hard?

Decades of effort to quantize gravity have struggled because we've been looking at it backwards. Instead of asking "how do we make gravity quantum," this framework asks "why does quantum matter produce classical spacetime?" The answer: redundancy optimization. Matter arranges itself to maximize the capacity for storing quantum temporal records, and Einstein's equations emerge as the optimality conditions.

The redundancy principle

Matter minimizes a constrained variational functional. To avoid circular logic, we treat the coherence factor \(\Xi\) as an independent field during variation, with the coherence-time-potential (CTP) relation \(\Xi = C[\Phi]\) imposed as a separate constraint via Lagrange multiplier \(\Lambda(x)\).

• \(\rho(x)\): Matter density
• \(\omega(x)\): Local clock frequency
• \(\Xi(x)\): Coherence factor (independent field during variation)
• \(C[\Phi](x)\): CTP relation \(= \exp(-|\nabla\Phi|^2/\xi^2)\)

Quantum lapse fluctuations drive everything

In quantum gravity, the lapse \(N = e^{\Phi}\) fluctuates quantum-mechanically. The quantum thermal bath couples to proper time increments \(\delta\tau_c = N(x)dt\) rather than to \(\Phi\) itself, creating a noise environment that affects all clocks. The temporal potential \(\Phi\) mediates correlations between quantum clocks through the CTP relation \(C[\Phi] = \exp(-|\nabla\Phi|^2/\xi^2)\), and matter organizes to exploit these correlations for maximum information storage.

The flux law (time evolution)

While the Poisson equation gives equilibrium, time evolution follows the flux law from temporal geometry:

Only energy flux can change time curvature. This complements the redundancy-derived Poisson relation, giving us both statics and dynamics from optimization plus conservation.

Decoherence scaling: the smoking gun

The theory predicts a specific decoherence signature for quantum clocks in gravitational fields:

This linear mass scaling distinguishes it from collapse models like CSL/GRW, which predict \(M^2\) scaling. Current quantum experiments are approaching the sensitivity to test this prediction.

Clock networks reveal gravity's quantum nature

Slow lapse fluctuations create correlated noise across spatial scales. The correlation length is:

Cross-correlations between separated clocks decay as:

Revolutionary experimental opportunity

This suggests a direct measurement of \(G\) through clock correlations, independent of gravitational forces:

1. Deploy optical clock arrays at various separations
2. Measure cross-correlations in timing fluctuations
3. Extract correlation length \(\xi\) from decay
4. Directly infer \(G\) from \(\xi = c/\sqrt{8\pi G \rho_{\text{eff}}}\)

This would be the first measurement of gravity's quantum nature through information storage rather than force.

"Why does matter cluster?" answered

The age-old question of gravitational attraction gets a information-theoretic answer: matter clusters because clustered configurations maximize redundant record capacity. Dense regions can store more correlated temporal information in lapse fluctuations, driving the attractive force we observe.

Connection to measurement and flux laws

This framework unifies all previous papers:

• Scalar-flux law: The redundancy functional is another constraint equation
• Quantum measurement: Same information-theoretic optimization drives basis selection
• Temporal geometry: The lapse \(\Phi\) emerges as the optimal storage medium
• Energy flux: Conservation laws govern how stored information evolves

Special cases validate the framework

• 2+1 gravity: Redundancy extremization yields only boundary terms → no local degrees of freedom (correct)
• Cosmology: Setting \(a = e^{-\Phi}\) and \(H = -\dot{\Phi}\) recovers Friedmann equations exactly
• Black holes: Near horizons, \(\partial R/\partial r \to \infty\) makes local time indefinite while preserving global consistency

Wheeler-DeWitt connection

The redundancy functional emerges from quantum gravity itself through Born-Oppenheimer approximation:

1. Start with Wheeler-DeWitt equation: \(\hat{H}|\Psi\rangle = 0\)
2. Separate scales: Heavy geometry + light matter
3. Integrate out fast modes: Generates influence functional
4. Result: Lapse noise kernel \(C_{\Phi}\) and redundancy functional \(R\)

Classical Einstein equations emerge as the semiclassical limit of quantum redundancy optimization.

Why this changes everything

This framework explains three major mysteries:

1. Why quantum gravity is hard: We've been trying to quantize the emergent classical limit
2. Why Einstein's equations work: They optimize information storage capacity
3. Why matter attracts: Clustering maximizes temporal record redundancy

Experimental roadmap

The theory makes concrete testable predictions:

• Quantum decoherence: \(\Gamma \propto \omega^2 M\) scaling in interferometers
• Clock correlations: Exponential decay with characteristic length \(\xi\)
• Gravitational measurement of \(G\): Information-theoretic determination independent of forces
• Lapse noise spectroscopy: Direct detection of quantum spacetime fluctuations

Conceptual revolution

Instead of force-mediated spacetime curvature, we have information-optimized temporal structure. Matter bending space is only part of the picture. It arranges itself to maximize the universe's capacity for storing and correlating temporal records. Gravity becomes a manifestation of optimal information processing in quantum time.