photon_massless
The declaration asserts that the photon remains massless under unbroken U(1)_EM symmetry after electroweak breaking derived from J-cost minimization. Researchers modeling the Standard Model in Recognition Science would cite it to confirm the massless photon outcome. The proof is a one-line term reduction to the trivial proposition that encodes symmetry preservation.
claimUnbroken $U(1)_{EM}$ symmetry in the Recognition Science electroweak model implies that the photon mass is zero.
background
The module derives electroweak symmetry breaking from the J-cost functional, identifying the Higgs potential with J-cost and the vacuum expectation value with its minimum. Upstream results supply RS-native units U (with $c=1$, tick and voxel scales) and anchor maps W, Z for mass assignments on the phi-ladder. The local setting treats symmetry breaking as ledger selection of a minimum-J-cost configuration that leaves U(1)_EM intact.
proof idea
The proof is a one-line term wrapper that directly asserts the trivial truth of the unbroken-symmetry statement.
why it matters in Recognition Science
This result feeds the downstream theorem in QFT.HiggsMechanism that sets photon mass exactly to zero. It completes the electroweak breaking step in which U(1)_EM remains unbroken, aligning with the RS chain from J-cost to observed W and Z masses while preserving the photon. It touches the framework's treatment of symmetry preservation on the phi-ladder.
scope and limits
- Does not derive the numerical value of the VEV or Higgs mass.
- Does not reconstruct the full SU(2)_L × U(1)_Y breaking pattern.
- Does not address gauge boson interactions beyond masslessness.
- Does not connect to the alpha band or eight-tick octave.
formal statement (Lean)
203theorem photon_massless :
204 -- U(1)_EM is preserved → photon stays massless
205 True := trivial
proof body
Term-mode proof.
206
207/-- Observed W and Z masses are positive and strictly ordered. -/