A Theoretical Synthesis
Gravity as Feedback, Spacetime as Equilibrium
// CLASSIFICATION: SYNTHESIS_COMPLETE
// ORIGIN: SECTOR 7G (2045)
// CONTEXT: The pivot document. Shows how TT-only measurement yields Unimodular Gravity — solving the Λ problem without fine-tuning. Considered the "lucky constraint" of 2039.
"Gravity is not fundamental, but rather the unique feedback mechanism required to preserve energy conservation in a system subject to continuous weak measurement."
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.
The ontology and operational equivalence of the Bath.
The universe is permeated by a "Bath": a large-N, Lorentz-invariant Quantum Field Theory in its vacuum state.
The coupling is operationally equivalent to a continuous weak measurement of the system's shape.
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.
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.
The coupling strength emerges from microscopic parameters:
The weakness of gravity is linked to the large size of the Bath.
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.
The mechanism: mass suppresses vacuum fluctuations, generating a force even though coupling is purely radiative.
The most significant update to the framework.
Standard General Relativity requires the exchange propagator to couple to both:
Shear term
Trace term
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.
Unimodular Gravity: A theory invariant only under volume-preserving diffeomorphisms.
This apparent limitation resolves a fatal flaw in emergent gravity approaches:
The vacuum energy of the Bath would act as a massive Cosmological Constant, curving the universe into a singularity.
Vacuum energy (pure trace: Tμν ∝ ημν) decouples completely from equations of motion.
How the constraint sector completes the theory.
The no-go theorem shows TT coupling produces traceless field equations. A skeptic asks: where is Newton's law? A sphere has TTT = 0. If the Bath only sees TT content, how does a sphere gravitate?
The answer: the same way charges attract in QED — through the constraint sector, not through propagating modes.
A photon has two transverse polarizations. No longitudinal mode. No timelike mode. And yet two static charges attract via Coulomb's law — an interaction carried by zero photons.
The Coulomb potential is not a photon. It is a constraint — forced by Gauss's law, which itself follows from charge conservation:
Gravity has identical structure. The graviton has two TT polarizations. The Newtonian potential Φ = −GM/r is not carried by gravitational waves — it is determined by the Hamiltonian constraint:
Start from the UG field equations (the dynamical sector):
Take the covariant divergence of both sides. The left side, by the contracted Bianchi identity (a geometric identity, not an assumption):
The right side, using matter conservation ∇μTμν = 0 (Assumption A1):
Equating gives:
Λ appears as an integration constant — not sourced by vacuum energy.
Substitute R = −κT − 4Λ back into the traceless equations:
The full Einstein equation with cosmological constant. Recovered from the traceless equations alone.
The Newtonian limit: ∇²Φ = 4πGρ − Λc². For anything smaller than cosmological scales, the Λ term is negligible (~10⁻³⁵ m/s²). Spheres gravitate.
The Fierz-Pauli theorem (1939) shows that the unique Lagrangian for a free massless spin-2 field is linearized GR. But Bath-TT has no Lagrangian — it is Lindblad dynamics. So a deeper argument is needed.
Weinberg's soft graviton theorem (1964) requires only three inputs:
It does not require a Lagrangian, an action principle, or a fundamental gravitational field.
Weinberg's theorem forces the full exchange amplitude between any two sources:
This decomposes into two sectors:
What the Lindblad dynamics generates
What the Bianchi identity forces
The constraint sector is not an additional coupling. It is not put in by hand. It is forced by the spin-2 nature of the emergent graviton. This is how QED works: nobody adds the Coulomb potential by hand — it follows from U(1) gauge invariance, forced by spin-1. The gravitational constraint follows from diffeomorphism invariance, forced by spin-2.
The direct TT amplitude differs from GR by (1/d − 1/2)(Tr T)². This gap is exactly compensated by the constraint contribution, leaving only one physical difference:
Λ is an integration constant, not sourced by vacuum energy.
The 120-orders-of-magnitude cosmological constant problem dissolves — not by fine-tuning, but by architecture.
The full derivation with all equations, the Aharonov-Bohm analogy, and the BMV entanglement test is in Entry 034: And Still, Spheres Gravitate.
The framework is falsifiable through two distinct channels.
The model predicts a specific TT-decoherence functional.
Distinct from standard environmental noise or Penrose/Diósi collapse models.
Because the theory is Unimodular:
The −½T² coupling becomes dynamically relevant in extreme conditions.
The corpus presents a self-consistent derivation of gravity as the hydrodynamics of a "Shape Measurement" Bath.
"Spacetime is not fundamental; it is the equilibrium state of a system minimizing information leakage to its environment."
But there is a missing piece. The interaction Hint is symmetric...