eV_to_J
The declaration supplies the exact numerical value of the electron-volt to joule conversion in SI units. Device physicists working on Recognition Science coherent light therapy cite it when scaling φ-ladder photon energies to joules for wavelength and power calculations. The definition consists of a single numeric literal assignment with no computation or lemmas.
claimThe conversion factor from electron volts to joules is defined to be $1.602176634 × 10^{-19}$.
background
The Photobiomodulation Device module formalizes a φ-energy ladder for light therapy, with E(n) = E_base · φ^n. Here E_base equals φ^{-5} eV converted to joules using the supplied factor, representing the recognition coherence quantum. The module imports Constants and applies this conversion to define E_PBM as φ eV in joules, which lies in the therapeutic red/near-IR band. Upstream results establish the positivity of the factor via norm_num and its use in bounding lemmas such as E_PBM_bounds.
proof idea
The declaration is a direct numeric definition. No lemmas are applied and no tactics are invoked.
why it matters in Recognition Science
This definition enables the φ-energy ladder to interface with physical units, feeding directly into E_base, E_PBM, and the theorem E_PBM_is_rung_6 that identifies rung 6 with the therapeutic energy. It supports the module's results on 8-beat neutrality and brainwave entrainment by providing the SI scaling for device parameters. The value aligns with the Recognition Science constants where energies are expressed relative to φ.
scope and limits
- Does not derive the numerical value from Recognition Science axioms.
- Does not include measurement uncertainty.
- Does not apply to other energy units.
- Does not reference the J-cost function or defect distance.
formal statement (Lean)
54def eV_to_J : ℝ := 1.602176634e-19
proof body
Definition body.
55