In LFM, time dilation emerges from χ field depression rather than spacetime curvature. Clocks run slower where the χ field is depressed — giving identical predictions to General Relativity.
Sea level on Earth
The χ field approaches χ₀ = 19 (normalized to 1) far from mass, and decreases toward 0 at the event horizon (r = rₛ).
GPS is a real-world application where relativistic time dilation MUST be corrected, or position errors would accumulate to ~10 km/day!
Key insight: LFM and GR give identical predictions for time dilation. The difference is explanatory: LFM says clocks slow because particle masses change, while GR says spacetime geometry determines proper time. Both are mathematically equivalent descriptions of the same physical phenomenon.
Weak field (r >> rₛ):
χ/χ₀ ≈ 1 - GM/(rc²χ₀)
Exact (all r > rₛ):
χ/χ₀ = √(1 - rₛ/r)
where rₛ = 2GM/c² (Schwarzschild radius)
LFM formula:
dt'/dt = χ/χ₀
GR formula:
dt'/dt = √(1 - 2GM/rc²)
Clock difference per day:
Δt = (1 - χ/χ₀) × 86400 s