vacuumEnergyScale
plain-language theorem explainer
vacuumEnergyScale defines the characteristic energy scale of vacuum fluctuations as ħ divided by the fundamental tick duration τ₀. Researchers deriving zero-point energy from discrete time in Recognition Science would cite this when linking temporal discreteness to QFT vacuum activity. The definition follows directly from applying the energy-time uncertainty relation at the minimal interval τ₀.
Claim. The characteristic energy scale of vacuum fluctuations is $E_0 = ħ / τ_0$, where $ħ$ denotes the reduced Planck constant in RS-native units and $τ_0$ is the fundamental tick duration.
background
The QFT.VacuumFluctuations module derives vacuum fluctuations from τ₀ discreteness. Its module doc states: 'In Recognition Science, vacuum fluctuations arise from τ₀ discreteness: Time is discrete at scale τ₀. Uncertainty principle: ΔE·Δt ≥ ℏ/2. At Δt = τ₀, energy fluctuations are inevitable. These ARE the vacuum fluctuations.' Upstream, tau0 is the fundamental time unit (duration of one tick) in RS-native units, while hbar is defined as the reduced Planck constant ħ = E_coh · τ₀ = φ^{-5} · 1 in those units.
proof idea
This is a one-line definition that applies the division of hbar by tau0, implementing the energy scale from the uncertainty relation evaluated at the minimal time interval τ₀.
why it matters
This definition supplies the base energy scale for vacuum fluctuations, supporting the paper proposition 'The Origin of Zero-Point Energy from Temporal Discreteness'. It anchors the module's results on virtual particles, Casimir pressure, and the RS resolution of the cosmological constant problem. The construction rests on the Recognition Science constants and the eight-tick structure of τ₀.
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