Masses Mass Genesis Open Propagation

Open propagation and zero rest mass

In classical physics, a particle with zero rest mass, like the photon, does not sit still; it moves at the speed of light in vacuum. The framework of Recognition Science models physical structure through a discrete record of events, and in that ledger, closed matter patterns repeat in a fixed eight-tick cycle. But a zero-rest-mass particle cannot be a closed pattern, because it never settles into a finite loop. The module OpenPropagation supplies the missing carrier: an open null light mode, which is a zero-cost propagating recognition mode carried by an injective infinite ray.

The classical definition of rest mass is the mass of a particle as measured in a frame where it is at rest. For a photon, this is zero. In the framework, rest mass reads directly from the recognition cost of the propagating mode. The module defines a structure OpenNullLightMode that bundles a propagating mode, a proof that its total cost is zero, and an injective ray, meaning a sequence of natural numbers where each step moves to a new position and never repeats. The injective ray is what distinguishes this carrier from a finite closed matter pattern, which would eventually cycle back to a previous state.

The module proves three things. First, the theorem openNullRestMass_zero shows that any open null light mode has rest mass exactly zero, by definition of the structure. Second, the theorem openNullLightMode_nonempty shows that such a mode actually exists, by constructing the canonical example: the canonical zero-cost propagating mode on the identity ray, where each step simply moves to the next natural number. Third, the theorem openNull_not_finite_closed shows that no open null light mode can have a positive period; the ray never repeats a position, so it cannot close into a finite loop. These three results are packaged into a certificate structure OpenNullLightCert that bundles the existence, the zero rest mass, and the non-periodicity into a single object.

What this establishes in plain language is that the framework can represent a massless particle as a genuine carrier, not as a degenerate or empty case. The zero-cost mode is not a closed pattern, so it does not get mistaken for a massive particle. Polarization and photon momentum are deliberately separate physics layers, not part of this recognition-level carrier. The module fills a gap in the framework's account of mass generation: it provides the missing carrier for the null side, where rest mass is zero, and proves that this carrier is consistent and nonempty.

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

theorem openNullLightMode_nonempty :
    ∃ γ : OpenNullLightMode, openNullRestMass γ = 0 :=
  ⟨canonicalOpenNullMode, openNullRestMass_zero canonicalOpenNullMode⟩

theorem openNull_not_finite_closed (γ : OpenNullLightMode) :
    OpenNullNotFiniteClosed γ := by
  intro n p hp
  exact openNullRay_no_positive_period γ n p hp

What this page does not claim

This module does not derive the speed of light or any other property of photons beyond zero rest mass. The open null carrier is not claimed to be a complete model of the photon; polarization and momentum are separate layers. The framework does not claim that zero rest mass is the only property needed to define a massless particle.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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