photon_massless
plain-language theorem explainer
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.
Claim. Unbroken $U(1)_{EM}$ 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
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.
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