Mode Counting Argument
Between the plates, only standing waves with λ = 2d/n are allowed. Outside, all modes exist. The energy difference — ∝ difference in mode density — gives a net inward pressure. The force scales as 1/d⁴: stronger for smaller gaps.
This has been measured to 1% precision. It matters for MEMS devices: at 10 nm separation, Casimir pressure is ~1 atm. Repulsive Casimir forces also exist with the right material combinations (used in frictionless bearings).