virtualParticleLifetime
Virtual particle lifetime in Recognition Science is the duration a mass-m fluctuation can persist before the ledger corrects it, expressed as ħ/(2 m c²). Physicists modeling vacuum energy, Casimir forces, or QFT interpretations from discrete time would cite this. The definition is a direct algebraic reduction using the imported RS-native ħ.
claimThe lifetime of a virtual particle of mass $m$ is given by $Δt = ħ / (2 m c²)$.
background
The QFT module derives vacuum fluctuations from τ₀ discreteness: time is discrete at the fundamental scale, so the uncertainty relation forces energy fluctuations of order ħ/τ₀ that appear as virtual pairs. Upstream, ħ is supplied as the RS-native constant ħ = φ^{-5} (with c = 1) from Constants, while sibling declarations handle the related energy-time uncertainty and zero-point energy. The module setting treats these fluctuations as ledger corrections rather than quantized field modes.
proof idea
One-line definition that applies the imported hbar constant and divides by twice the rest energy term.
why it matters in Recognition Science
This definition supplies the explicit lifetime formula required by the QFT-010 target of obtaining vacuum activity from τ₀ discreteness. It supports the module's derivations of Casimir pressure and zero-point energy in sibling declarations and connects directly to the energy-time uncertainty relation. It leaves open the question of how the full QFT vacuum structure emerges without introducing field operators.
scope and limits
- Does not derive the uncertainty principle itself.
- Does not compute numerical values for specific particles.
- Does not address renormalization of the vacuum energy sum.
formal statement (Lean)
137noncomputable def virtualParticleLifetime (mass : ℝ) : ℝ :=
proof body
Definition body.
138 hbar / (2 * mass * c^2)
139
140/-- In RS, virtual particles are ledger fluctuations:
141
142 The ledger can briefly contain "extra" entries
143 that don't persist. These are virtual particles. -/