The Unimodular Bath

A Theoretical Synthesis

Gravity as Feedback, Spacetime as Equilibrium

Executive Summary

"Gravity is not fundamental, but rather the unique feedback mechanism required to preserve energy conservation in a system subject to continuous weak measurement."

The Core Thesis

This document synthesizes the Bath Framework for emergent gravity. Recent theoretical stress-testing has refined the model's prediction:

The framework does not reproduce standard General Relativity, but rather Unimodular Gravity.

This is a theoretical advantage: it naturally decouples the massive vacuum energy of the Bath from the emergent geometry, solving the cosmological constant problem without fine-tuning.

Microscopic Foundations

The ontology and operational equivalence of the Bath.

The Bath Ontology

The universe is permeated by a "Bath": a large-N, Lorentz-invariant Quantum Field Theory in its vacuum state.

  • Scale: N ~ 1019 degrees of freedom
  • Statistical suppression: Fluctuations vanish in classical limit
  • Coupling: Universal via Transverse-Traceless sector only
TTTij = radiative shape changes

Operational Equivalence

The coupling is operationally equivalent to a continuous weak measurement of the system's shape.

Hint = λ ∫ TTTΞ
  • Noise: Measurement induces decoherence
  • Heating: Suppresses shape superpositions
  • Without compensation: Energy injection (momentum diffusion)

Emergent Dynamics

Gravity as Feedback

Empirically, the universe does not undergo runaway heating. Therefore, the open-system dynamics must include a "Drift" or "Feedback" Hamiltonian that cancels the measurement-induced heating.

Continuous Measurement Energy Injection Feedback Required Gravity Emerges

Uniqueness

The unique feedback law consistent with no-signaling and statistical conservation is a long-range attractive interaction.

Gravity is not chosen — it is forced by consistency requirements.

Newton's Constant

The coupling strength emerges from microscopic parameters:

G ~ 4π / (λ²N²)

The weakness of gravity is linked to the large size of the Bath.

The Spectral Requirement

To recover a 1/r Newtonian potential from this feedback, the Bath's retarded TT correlator must possess a massless pole (1/k²) in the infrared.

Massless Pole → Static "TT Shadow" → Long-Range Force

The mechanism: mass suppresses vacuum fluctuations, generating a force even though coupling is purely radiative.

The Unimodular Pivot

The most significant update to the framework.

The Trace Obstruction

Standard General Relativity requires the exchange propagator to couple to both:

TμνTμν

Shear term

Trace term

The Derivation

A rigorous derivation proves that a Bath coupled only to TTT cannot generate the trace term necessary for full GR.

While temporal components (T00) are recovered via current conservation, the scalar trace (T) remains decoupled.

Emergent Field Equations
Rμν − ¼gμνR = 8πG (Tμν − ¼gμνT)

Unimodular Gravity: A theory invariant only under volume-preserving diffeomorphisms.

Why This Is a Success

This apparent limitation resolves a fatal flaw in emergent gravity approaches:

The Problem (Standard GR)

The vacuum energy of the Bath would act as a massive Cosmological Constant, curving the universe into a singularity.

The Solution (Unimodular)

Vacuum energy (pure trace: Tμν ∝ ημν) decouples completely from equations of motion.

The framework naturally explains why the huge energy of the Bath does not gravitate.

Predictions & Observable Consequences

The framework is falsifiable through two distinct channels.

Interferometry (Noise Spectroscopy)

The model predicts a specific TT-decoherence functional.

Signature: A floor of "shape noise" (correlated strain noise) that scales with mass distribution geometry.

Distinct from standard environmental noise or Penrose/Diósi collapse models.

Cosmological Deviations

Because the theory is Unimodular:

  • Dark Energy: Λ appears as integration constant, not fundamental parameter
  • Trace Anomaly: Subtle deviations in cosmology or strong-field regimes

The −½T² coupling becomes dynamically relevant in extreme conditions.

Conclusion

The corpus presents a self-consistent derivation of gravity as the hydrodynamics of a "Shape Measurement" Bath.

By strictly adhering to TT coupling, the framework:

1/r Force G from N Λ Problem Solved

The Three Achievements

  1. Derives the 1/r attractive force as a feedback requirement
  2. Explains the weakness of gravity via large-N scaling
  3. Automatically resolves the Cosmological Constant Problem by predicting Unimodular Gravity instead of standard GR
"Spacetime is not fundamental; it is the equilibrium state of a system minimizing information leakage to its environment."

Continue the Journey

Can this framework be tested in the laboratory?

The Experimental Test

A concrete proposal using Eöt-Wash class torsion balances to detect geometry-correlated force noise — the signature prediction that distinguishes Bath-TT from standard GR.

Explore the Experiment →