casimirPressure
plain-language theorem explainer
The definition supplies the Casimir pressure P(d) = -π² ħ c / (240 d⁴) for separation d > 0, using the Recognition Science value of ħ. Researchers modeling vacuum forces in discrete-time QFT frameworks cite it when computing the attractive force between plates. The definition is a direct one-line encoding of the standard formula with the imported constants.
Claim. The Casimir pressure for plate separation $d > 0$ is $P(d) = -{π^2 ħ c}/(240 d^4)$, where ħ is the reduced Planck constant in Recognition Science native units.
background
The QFT.VacuumFluctuations module derives vacuum fluctuations from τ₀ discreteness. Zero-point energy arises because the uncertainty principle at the minimal time step τ₀ forces energy fluctuations; these are identified with the virtual pairs and mode restrictions that produce the Casimir effect. The upstream Constants.hbar supplies ħ = φ^{-5} in RS units (E_coh · τ₀), while c remains the speed of light (set to 1 in native units elsewhere in the framework).
proof idea
One-line definition that directly encodes the textbook Casimir formula using the imported ħ and c constants.
why it matters
The definition is invoked by the downstream theorem casimir_is_attractive to prove the pressure is negative. It implements the QFT-010 claim that vacuum fluctuations originate in τ₀ discreteness, connecting to the forcing chain (T5 J-uniqueness, T7 eight-tick octave) and the Recognition Composition Law that governs mode counting. The 240 coefficient is taken from standard QFT rather than re-derived inside Recognition Science.
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