Masses Mass Genesis Open Propagation Open Null Rest Mass Zero

The null carrier

In physics, a particle with zero rest mass, like the photon, never sits still; it always moves at the speed of light. The Recognition Science framework needs a way to represent such an entity within its own terms. Its fundamental objects are recognition events, discrete records of occurrences, and the framework assigns each mode of propagation a cost, a measure of what it takes for that mode to exist. The theorem openNullRestMass_zero establishes that a specific kind of mode, one that propagates along an infinite, non-repeating ray at zero cost, has a rest mass of exactly zero.

The declaration defines an open null light mode as a structure with three parts: a propagating mode from the framework's null recognition physics, a proof that this mode has zero total cost, and an injective function from natural numbers to natural numbers, which serves as the ray. Injectivity means the ray never revisits a point; it stretches out endlessly without looping back. The theorem itself is a direct consequence of the mode's definition: since the rest mass is defined as the total cost of the mode, and the mode's cost is zero, the rest mass is zero. This is not a numerical approximation or a fitted parameter; it is a logical necessity within the framework's construction.

The framework's library also proves a companion fact: such an open ray cannot close with any positive period. This ensures that the zero-rest-mass carrier is not mistaken for a finite, localized matter pattern, which would have a closed, repeating structure. The framework explicitly provides a canonical example of this open null mode, using the identity ray, to demonstrate that the concept is not empty. These results are collected in a certificate structure, OpenNullLightCert, which bundles the existence of a zero-rest-mass mode, the canonical example's zero mass, and the non-periodicity of all such open rays.

What this theorem does not do is provide a complete theory of light. The declaration is a structural carrier: it establishes that a zero-rest-mass entity can exist within the framework's ontology. Polarization and photon momentum are explicitly noted as separate physics layers, not addressed by this result. The theorem does not derive the speed of light, nor does it explain why light has the properties it does beyond its zero rest mass. It is a foundational piece, ensuring the framework has a place for massless propagation, not a full account of electromagnetism.

theorem openNullRestMass_zero (γ : OpenNullLightMode) :
    openNullRestMass γ = 0 :=
  γ.zero_cost

/-- An injective ray cannot close with any positive period. -/
theorem openNullRay_no_positive_period
    (γ : OpenNullLightMode) (n p : ℕ) (hp : 0 < p) :
    γ.ray (n + p) ≠ γ.ray n := by
  intro h
  have hidx : n + p = n := γ.ray_injective h
  omega

/-- The canonical open null carrier: canonical zero-cost NRM on the identity
ray. -/
def canonicalOpenNullMode : OpenNullLightMode where
  mode := Physics.NullRecognitionMode.canonicalNRM
  zero_cost := Physics.NullRecognitionMode.nrm_totalCost_zero
  ray := fun n => n
  ray_injective := by
    intro a b h
    exact h

What this page does not claim

The theorem does not derive the speed of light or any other property of photons beyond zero rest mass. The theorem does not provide a full account of electromagnetism or light-matter interactions. The theorem does not claim that all zero-rest-mass particles must follow an open ray; it only establishes one valid carrier.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Masses/MassGenesis/OpenPropagation.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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