Gravitational Time Dilation and Low-Acceleration Dynamics in the LFM Framework: From GPS Clocks to Galaxy Rotation Curves

Gravitational Time Dilation from Local Oscillator Dynamics in the Lattice Field Medium Framework

This paper shows that gravitational time dilation arises directly from the canonical Lattice Field Medium (LFM) governing equation:

d^2E/dt^2 = c^2 ∇^2E − χ(x)^2 E

without invoking spacetime curvature, metric tensors, or parameter fitting.

In the LFM framework, localized wave solutions exhibit harmonic temporal behavior with angular frequency equal to the local value of the chi field. As a result, clock rates scale with the local chi field, leading to the testable relation that the fractional frequency shift equals the fractional change in chi. The spatial chi field profile employed in this work is imported unchanged from prior, independent LFM gravity validations and is not derived or adjusted using time-dilation data.

The prediction is tested against three independent experiments using real observational data:

1. Precision optical atomic clock comparisons at small height separations (Chou et al., 2010),

2. Gravitational time dilation observed in Global Positioning System (GPS) satellite clocks (Ashby, 2003),

3. The Pound–Rebka gravitational redshift experiment (1960).

In all cases, LFM predictions are consistent with published measurements within reported experimental uncertainty. Additional theoretical consistency checks demonstrate agreement with general relativity in the weak-field regime, while clarifying the distinct physical interpretation offered by LFM: time dilation emerges from local oscillator dynamics in a variable dispersion field rather than from fundamental spacetime geometry.

The paper explicitly distinguishes observational validations from theoretical consistency checks, states falsifiability conditions, and provides reproducible analysis scripts. Strong-field regimes and low-acceleration behavior are identified as domains where future experiments may differentiate LFM from general relativity.