Gravity Propagation Speed Speed Ratio Unity

The speed ratio theorem

The speed of light in a vacuum, usually written c, is about 299,792,458 meters per second. General relativity predicts that gravitational waves also travel at c, and the 2017 event GW170817 confirmed this to within about one part in 10^15. The question of whether gravity and light propagate at exactly the same speed is therefore a physical one, settled by observation to extraordinary precision.

Within the Recognition Science framework, this equality is not merely empirical but structural. The framework models reality as a discrete ledger, a record of events advancing in uniform ticks. Both light and gravity propagate on this single substrate, so both share the same tick rate. In the framework's native units, where one tick equals one ledger cell, the speed of light is defined as c = 1. The gravitational signal speed is likewise defined as c_grav = 1.

The declaration speed_ratio_unity in the framework's machine-checked library states that the ratio c_grav / c equals 1. The argument is immediate: since both quantities are defined as 1, their quotient is 1 divided by 1, which is 1. A more general companion declaration, propagation_equality_forced, shows that whenever two speeds are equal and the reference speed is nonzero, their ratio must be 1. This is a formal restatement of a basic arithmetic fact, and the framework presents it as the structural marker for why no separate gravitational medium with a different tick rate can exist.

What the declaration does not claim is more significant than what it proves. The declaration assumes the equality of the two speeds as a premise; it does not derive that equality from deeper principles. The framework's docstring asserts that both speeds share the ledger substrate, but that assertion is a modeling choice, not a proved result. The declaration also says nothing about the measured value of c in physical units, nor about how the framework's native units translate to meters and seconds. It establishes only the conditional statement: if the speeds are equal, their ratio is one.

The consequence is that the framework's account of gravity and light propagation is internally consistent on this point. It does not add a new physical prediction about the speed of gravity; it formalizes the equality that observation already supports. A reader should take the declaration as a definitional scaffold, not as an independent derivation of a physical constant.

/-- When both speeds are defined from the same tick rate, their ratio is 1. -/
theorem speed_ratio_unity : c_grav_RS / c_RS = 1 := by
  simp only [c_grav_RS, c_RS, div_one]

/-- 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)

/-- Gravitational "signal" speed in RS-native units.
    Same as c: both use the ledger as substrate. -/
def c_grav_RS : ℝ := 1

/-- 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 declaration does not prove that gravity and light actually travel at the same speed; it assumes that equality as a premise. The declaration does not derive the numerical value of c in physical units. The framework's assertion that both speeds share the ledger substrate is a modeling choice, not a proved result.

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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: