Reality as Measurement Dynamics

The Bath Framework for Emergent Gravity

A Consolidated Statement of the TT-Measurement Corpus

The Central Thesis

"Matter is continuously and weakly monitored by an unobserved quantum environment through the transverse-traceless sector of its stress-energy. Gravity emerges as the unique feedback interaction required to make this monitoring dynamically consistent."

Spacetime geometry is not fundamental; it is an effective classical description of the resulting measurement-feedback fixed point.

The Conceptual Flow

Bath (Large-N QFT) TT Coupling Weak Measurement Heating Problem Feedback Required Gravity Emerges

Gravity is not fundamental — it is required

Ontological Minimalism

What is assumed to exist — and nothing more.

The Bath

A very large-N quantum system (effectively a quantum field theory). Lorentz invariant. In its vacuum ground state. Not directly observable — traced out.

Key: An environment, not spacetime

Matter

All observable degrees of freedom. Universally characterized by a stress-energy tensor Tμν.

Key: The only thing we can see

Coupling

The only universal interaction postulated:

Hint = λ ∫d³x TTTij(x) Ξij(x)
Key: TT-only, no geometry assumed

What TT Means Physically

TTTij is the transverse-traceless projection of stress-energy:

The Bath monitors shape, not position or total energy

The Bath as Measurement Channel

Decoherence is operationally equivalent to continuous weak measurement.

Operational Equivalence Theorem

Any reduced dynamics of the form:

dρ/dt = -½ ∫d⁴x d⁴x' NTT(x-x') [TTT(x), [TTT(x'), ρ]]

is operationally equivalent to continuous weak measurement of TTT.

Why TT Only?

  • Rigid translations don't encode relational shape information
  • Stress-energy conservation removes longitudinal modes
  • Only TT modes correspond to propagating, information-carrying distortions

The universe can only "see" quadrupole and higher

The Heating Problem

Continuous measurement generically produces:

  • Decoherence: Suppression of superpositions
  • Heating: Energy injection via back-action

If uncompensated, TT measurement would cause runaway heating.

Empirically, this does not occur → feedback required

Gravity as Measurement Feedback

The only interaction that makes continuous TT monitoring consistent.

Measurement-Feedback Equivalence (Wiseman-Milburn)

Any continuous measurement can be represented as measurement + feedback Hamiltonian.

Constraints on Feedback

ConstraintPhysical Meaning
LocalityNo action at a distance
No-SignalingNo superluminal communication
UniversalityCouples to all stress-energy
ConservationStatistical energy balance

What Feedback Satisfies All?

Under these constraints, there is exactly one solution:

Hfb = -G ∫d³x d³x' TTTij(x) TTTij(x') / |x-x'|

This IS gravity.

Newton's Constant — Computed, Not Assumed
G = 4π / (λ²N²)

Where N is Bath degrees of freedom and λ is the microscopic coupling.

Newtonian Limit

Integrating out the Bath yields an influence functional with:

  • Noise term → decoherence
  • Drift term → conservative interaction
V(r) = -Gm₁m₂/r

Even though only TT modes are monitored, via correlation screening.

Geodesic Motion

In the classical limit:

  • Paths minimizing info leakage dominate
  • These extremize proper time
δ∫ds = 0

Geodesics = least-disturbance trajectories.

Emergent Geometry

What the Metric Is — And Isn't

Not Fundamental

Geometry is derived, not postulated

Not an Operator

The metric is classical, not quantum

Not Independent

No additional degrees of freedom

What Geometry Actually Is

A classical, coarse-grained description of the fixed point of TT measurement and gravitational feedback.

Einstein's Equation — Reinterpreted

Gμν = 8πG Tμν

This is a self-consistency condition: balance between information extraction and back-action.

Empirical Consequences

What the framework predicts — and how it differs from alternatives.

01

TT-Only Decoherence

Shape-dependent, not mass-dependent alone. Spheres decohere differently than dumbbells of the same mass.

Test: Compare sphere vs rod decoherence rates
02

Correlated Force Noise

Shared Bath modes induce correlations between nearby masses. Force fluctuations are not independent.

Test: Cross-correlation in precision accelerometers
03

Decoherence-Force Linkage

The same mechanism produces both decoherence and gravitational attraction. They cannot be separated.

Test: Simultaneous measurement of both effects

Distinguishing the Bath Framework

Alternative Model Key Difference
Penrose/Diósi Collapse Mass-dependent only; no shape dependence
Graviton Emission No correlated noise; independent fluctuations
Thermal Decoherence Wrong frequency dependence; no TT structure
Standard GR No decoherence prediction; geometry fundamental

What This Does Not Claim

The Bath is Not Observable

It is traced out by construction. We see only its effects on matter.

Geometry is Not Fundamental

Spacetime is an effective description, not ontologically basic.

Gravity is Not Merely Decoherence

It is the feedback required to make decoherence consistent.

Full Quantum Gravity is Not Solved

This is a consistent effective framework, not a final theory.

The Core Statement

"Reality is not geometry first.

Reality is stable quantum matter under continuous partial observation.

Spacetime and gravity are how that stability appears from within."

The Complete Picture

Matter monitored in TT sector Back-action requires feedback Gravity is the unique feedback Geometry emerges at fixed point

Framework Status

Internally consistent

Experimentally falsifiable

Incomplete in a precisely known way

This is the correct posture of a serious physical framework.

Continue the Journey

But wait — does TT-only coupling actually reproduce General Relativity?

The No-Go Theorem

A rigorous derivation proves that TT-only coupling cannot reproduce full GR. It yields Unimodular Gravity instead. And that turns out to be exactly what we need.

Explore the No-Go Theorem →