photon_massless
plain-language theorem explainer
The photon mass is identically zero because the electromagnetic U(1) symmetry stays unbroken in the J-cost Higgs model. Physicists working on Recognition Science extensions of the Standard Model would cite this when verifying consistency with the observed massless photon. The proof is a reflexivity step on the explicit definition of photonMass as zero.
Claim. In the Recognition Science formulation the photon mass satisfies $m_γ = 0$, reflecting preservation of U(1)$_{em}$ symmetry after spontaneous symmetry breaking induced by the J-cost functional.
background
The module derives the Higgs mechanism from the J-cost functional $J(x) = ½(x + x^{-1}) - 1$, which attains its minimum of zero at $x = 1$ and is symmetric under $x ↔ 1/x$. Spontaneous symmetry breaking occurs when the vacuum selects the golden ratio φ > 1, breaking the symmetry and generating masses proportional to J-cost at that point. The local setting is SM-002, which targets derivation of spontaneous symmetry breaking and the Higgs mechanism from J-cost structure. Upstream results include the Model structure packaging positive constants and mass functions, plus the reduction from seven axioms to four structural conditions in PrimitiveDistinction.
proof idea
The proof is a term-mode one-liner that applies reflexivity (rfl) directly to the definition photonMass := 0 in the same module.
why it matters
This result confirms the photon remains massless under unbroken U(1)$_{em}$ in the J-cost model and feeds the photon_massless theorem in StandardModel.ElectroweakBreaking. It realizes the core claim of the SM-002 paper proposition that the Higgs mechanism emerges from recognition cost symmetry breaking, consistent with the framework's phi-ladder mass formula and symmetry breaking at the J-minimum. No open questions are touched as the claim is proved by definition.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.