Gravity Propagation Speed Propagation Implies Equal Speed

The shared substrate

In physics, the speed of gravity is a measured quantity. The 2017 neutron star merger GW170817 placed the gravitational wave speed equal to the speed of light to within about one part in 10¹⁵. That measurement is an empirical fact about our universe. The Recognition Science framework makes a stronger structural claim: in its own units, the two speeds are not merely close, they are identical by definition.

The framework's starting point is a ledger, a discrete record of recognition events. Every physical process, including the propagation of light and of gravity, advances one cell per tick of this ledger. Since both use the same tick rate and the same cell size, the speed limit they share is exactly one cell per tick. In these units the speed of light c_RS is defined as 1, and the gravitational signal speed c_grav_RS is also defined as 1. The theorem propagation_implies_equal_speed states this equality directly: if c_grav_RS equals c_RS, then c_grav_RS equals c_RS. It is a tautology in the formal sense, a restatement of the defining assumption rather than a derivation from deeper principles.

The framework's library also proves two supporting facts. The ratio c_grav_RS / c_RS equals 1, and more generally, whenever two speeds are equal and nonzero, their quotient is 1. These are simple consequences of the definitions. The library's docstring describes the situation plainly: there is no separate gravitational medium with a different tick rate. Light and gravity share one substrate, so their propagation speeds match exactly.

What the declaration does not claim is just as important. It does not prove that gravity in our universe travels at the measured speed of light. That remains an empirical result, confirmed by GW170817 to extraordinary precision but not derived from the framework. The framework's equality is a definitional consequence of its own model, not a prediction that could be falsified by a future measurement. If a future experiment found a mismatch, it would not refute the theorem; it would refute the framework's assumption that both processes share the same ledger substrate.

The practical upshot for a reader is this: Recognition Science offers a clean conceptual explanation for why gravity and light might travel at the same speed, namely that both are ripples in the same discrete substrate. The explanation is coherent and internally consistent, but it rests on a chosen model, not on a measured fact. The empirical equality remains a discovery about nature, not a consequence of the framework.

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

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

/-- Propagation-speed structural marker implies gravity/light equality in RS units. -/
theorem propagation_implies_equal_speed (h : c_grav_RS = c_RS) :
    c_grav_RS = c_RS :=
  h

/-- 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]

What this page does not claim

The declaration does not prove that gravity in our universe travels at the measured speed of light, a fact established by the GW170817 observation. The declaration does not derive the equality from deeper principles; it restates the defining assumption that both speeds equal 1. The declaration does not predict a numerical value for the speed of gravity in SI units.

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.

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