Gravitational Decoherence from Vacuum Synchronization Delay

Gravitational Decoherence from Vacuum Synchronization Delay: A Prediction of Field-Based Gravity

Author:
Jim Redgewell

Abstract

We propose a novel prediction arising from a field-based reinterpretation of the Einstein field equation, in which gravity results from phase synchronization delays in a quantum vacuum field \( \hat{\Phi} \). In this framework, gravitational effects do not arise from spacetime curvature but from vacuum coherence dynamics. We demonstrate that entangled quantum systems subjected to differing gravitational potentials accumulate measurable phase mismatches due to differential synchronization delay, leading to partial decoherence. This effect is not predicted by general relativity or standard QFT and offers a new avenue for experimental verification using high-precision clocks or entangled photon interferometry.

1. Introduction

Standard general relativity describes gravity as the curvature of spacetime, but this geometric framework is conceptually at odds with quantum field theory, which operates on a fixed background. In Tugboat Theory and related field-based gravity approaches, gravitational phenomena are reinterpreted as arising from delayed synchronization of quantum phases in the vacuum.

In this formulation, a scalar field \( \hat{\Phi}(x) \) encodes the local state of vacuum phase coherence. A massive object perturbs this field, and changes in \( \hat{\Phi} \) propagate at finite speed, leading to time dilation and curvature-like effects. When two entangled particles reside in different gravitational potentials, their respective \( \hat{\Phi} \) values evolve differently, introducing a relative phase shift that can degrade quantum coherence.

2. Synchronization Field Perturbation

In the weak-field limit, the synchronization field obeys:

\[ \nabla^2 \hat{\Phi}(r) = \frac{8\pi G}{c^4} T^0_0(r) \]

For a point mass \( M \), the solution is:

\[ \hat{\Phi}(r) \approx -\frac{GM}{rc^2} \]

Assume two entangled systems A and B at radii \( r_A \) and \( r_B \) (e.g., different altitudes). The difference in synchronization field leads to a phase accumulation difference over time.

3. Relative Phase Accumulation

The local clock rate is proportional to \( 1 / \partial_0 \hat{\Phi} \). The phase difference accumulated over time \( T \) is:

\[ \Delta \phi = \omega_0 \int_0^T \left( \frac{1}{\partial_0 \hat{\Phi}_A} - \frac{1}{\partial_0 \hat{\Phi}_B} \right) dt \]

For small gravitational potentials:

\[ \partial_0 \hat{\Phi}(x) \approx 1 + \epsilon(x), \quad \epsilon(x) \sim \frac{GM}{rc^2} \] \[ \Rightarrow \Delta \phi \approx -\omega_0 \int_0^T [\epsilon_A(t) - \epsilon_B(t)] dt \]

For small vertical separation \( h \) near Earth:

\[ \epsilon_B - \epsilon_A \sim \frac{g h}{c^2}, \quad \Rightarrow \Delta \phi \sim \omega_0 T \frac{g h}{c^2} \]

4. Decoherence Criterion

If \( |\Delta \phi| > \delta \phi_c \), the coherence bandwidth of the entangled system, decoherence will occur. For optical transitions \( \omega_0 \sim 10^{15} \) rad/s:

\[ \Delta \phi \sim 10^{15} \cdot 1 \cdot \frac{9.8 \cdot 1}{(3 \times 10^8)^2} \approx 1.1 \times 10^{-10} \text{ rad} \]

This small but detectable phase shift provides a testable signature.

5. Experimental Proposal

A terrestrial or space-based atom interferometer or photon entanglement experiment could test this effect:

• Two arms of the interferometer at different heights
• Entangled clocks or atoms exposed to differing \( \hat{\Phi} \)
• Recombination should show reduced fringe contrast or loss of entanglement

Candidate platforms: ACES (ISS), STE-QUEST, optical clock towers.

6. Conclusion

The prediction of gravitationally induced quantum decoherence due to vacuum synchronization delay is unique to field-based gravitational models such as Tugboat Theory. This effect does not arise in general relativity or standard QFT and offers a direct, testable window into quantum-gravitational coupling via coherence dynamics. Future experiments may detect this subtle but fundamental interaction, opening new frontiers in the search for a unified theory of matter and gravity.