Gravity Propagation Speed Propagation Equality Forced

The equality theorem

The declaration propagation_equality_forced is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It establishes a conditional statement: if two speeds, one for a gravitational signal and one for light, are equal, and the speed of light is not zero, then the ratio of the gravitational speed to the speed of light is exactly one. In plain terms, it proves that within the framework, equal speeds imply a unit ratio, a formal restatement of the idea that there is no separate speed limit for gravity.

In the framework's native units, the speed of light is defined as 1, representing one ledger cell per tick. A ledger is a discrete record of events, and a tick is a single step in that record. The framework models both light and gravity as propagating on this same ledger substrate, which means they share the same tick rate and therefore the same speed limit. This is a definitional choice, not a physical measurement. The theorem c_grav_eq_c_RS states that the gravitational speed equals the speed of light, both being 1, by definition. The theorem propagation_equality_forced then generalizes this: given the premise that the speeds are equal, the ratio is forced to be unity.

This theorem does not claim that gravity and light actually do travel at the same speed in the physical universe. That is a separate empirical question. The theorem's premise, that the speeds are equal, is a hypothesis. The framework's structural argument for why they should be equal is based on the shared ledger substrate, but this is a model, not a proof about nature. The theorem merely formalizes the logical consequence of that premise. It is a statement about the framework's internal consistency, not a prediction that has been confirmed by experiment.

The framework notes that the event GW170817, a gravitational wave detection, confirmed that gravity and light travel at the same speed to a precision of 10⁻¹⁵. However, this is a measured fact from conventional physics, not a result of the framework's theorem. The theorem propagation_equality_forced is a formal statement within the framework; it does not itself provide evidence about the physical world. It is a piece of the framework's structure, showing what follows from its own definitions.

/-- No separate gravitational "medium" with different propagation:
    when c_grav = c_light and c_light ≠ 0, the ratio c_grav / c_light = 1. -/
theorem propagation_equality_forced (c_light c_grav : ℝ) (heq : c_light = c_grav)
    (hneq : c_light ≠ 0) : c_grav / c_light = 1 := by
  rw [heq]; exact div_self (ne_of_eq_of_ne heq.symm hneq)

/-- In RS-native units: speed of light c = 1 (ledger cells per tick). -/
def c_RS : ℝ := 1

What this page does not claim

The theorem does not prove that gravity and light actually travel at the same speed in the physical universe. The theorem does not provide any experimental evidence or measurement. The theorem does not claim that the framework's model of a shared substrate is physically true.

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/Gravity/PropagationSpeed.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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