Casimir Force

Quantum Vacuum Fluctuations Between Conducting Plates

Parameters

Casimir Force

Separation d
Force F
Pressure P
Thermal correction
Mode cutoff λ_min

F vs. Distance (log scale)

Theory

F = −(π²ℏc A)/(240 d⁴)

≈ −(1.3×10⁻²⁷ N·m⁴) × A/d⁴

Only modes fitting nλ/2 = d survive between plates. Outside: full vacuum spectrum → net inward pressure.

Thermal correction (Lifshitz): δF/F ≈ (16π²/3)(k_B T d / ℏc)³