Ralf Meelker · 2026

Precausal Substrate Theory

The Casimir discreteness correction

PST correction ξ(d₀/d)² vs plate separation — the d⁻⁶ signal that departs from standard QFT

detectable todaynext-gen experimentsbelow current sensitivity1% — current limit at d = 160 nm0.094% — PST signal at 160 nmd₀ = 4.92 nm50 nm5102050100200500plate separation d (nm)0.01%0.1%1%10%100%PST correction ξ(d₀/d)²PST d⁻⁶ correction (d₀ ≈ 4.92 nm)

Vacuum between the plates

d9 vacuum field modes
Plate separation d160.0 nm
PST correction0.0946%
d₀ / d ratio0.031
Below current sensitivity (<0.19%)
δP = −ξ π²ℏc d₀² / (240 d⁶)
correction = ξ(d₀/d)²
The d⁻⁶ scaling is a necessary signature (shared with other single-length-scale vacuum modifications); the parameter-free coefficient ξ = 90/π² fixes the diagnostic amplitude ξd₀² that selects PST. d₀ ≈ 4.92 nm is a representative value of the Landau-Ginzburg coherence length.
v19.13