Constants Rsnative Units C In Si

The speed of light in RS units

The speed of light in a vacuum, usually written c, is one of the most precisely measured numbers in physics. In SI units it is exactly 299,792,458 meters per second, a value fixed by the 1983 definition of the meter. That definition makes the speed of light a conversion factor between space and time rather than a quantity that needs experimental determination.

The Recognition Science framework takes the same step, but more radically. Its native unit system, defined in the machine-checked library of formal theorems, chooses the ledger primitives as the base standards. The ledger, a discrete record of recognition events, supplies two fundamental units: the tick, one atomic time quantum, and the voxel, the distance light traverses in one tick. In these units the declaration c = 1 is a definition, not a measurement. The speed of light is exactly one voxel per tick, by construction.

The framework then builds the rest of its unit system on this choice. Energy is measured in coherence quanta, where one quantum equals phi to the power minus five, phi being the golden ratio approximately 1.618. Action, the Planck constant equivalent, is one coherence quantum times one tick. Mass is measured as energy divided by c squared, which in these units is simply energy itself. Every ratio between these quantities is fixed by phi alone, with no reference to SI or any external standard.

This is a modeling choice, not a physical discovery. The framework defines c to be one in its native units; it does not derive the measured value of c in meters per second. The conversion to SI is optional and explicit, handled by a structure called ExternalCalibration. The framework's claim is that all physics can be expressed in these internal units without external anchoring, not that it predicts the meter's length from first principles.

What the declaration does not claim is equally important. It does not claim that the speed of light is variable or that special relativity is wrong; c remains a constant in all inertial frames. It does not claim that the voxel and tick correspond to known physical quanta; they are abstract units of the framework's ledger, not measured properties of nature. And it does not claim to have derived the SI value of c from the golden ratio or any other framework constant. The framework's contribution is a self-consistent unit system, not a new measurement of a known constant.

/-- Speed of light: c = ℓ₀/τ₀ = 1 voxel/tick. -/
@[simp] def c : Velocity := 1

/-- Coherence scaling: E_coh = φ⁻⁵. -/
noncomputable def E_coh_rs : ℝ := phiRung (-5)

/-- Action quantum: ħ = E_coh · τ₀ = E_coh in RS-native units. -/
@[simp] noncomputable def hbarQuantum : ℝ := cohQuantum * tick

/-- External calibration structure for mapping RS units to SI/other systems. -/
structure ExternalCalibration where
  /-- Seconds per tick (τ₀ in seconds). -/
  seconds_per_tick : ℝ
  /-- Meters per voxel (ℓ₀ in meters). -/
  meters_per_voxel : ℝ
  /-- Joules per coherence quantum. -/
  joules_per_coh : ℝ
  /-- All conversion factors are positive. -/
  seconds_pos : 0 < seconds_per_tick
  meters_pos : 0 < meters_per_voxel
  joules_pos : 0 < joules_per_coh
  /-- Consistency: c = ℓ₀/τ₀ must equal 299792458 m/s in SI. -/
  speed_consistent : meters_per_voxel / seconds_per_tick = 299792458

What this page does not claim

The declaration does not derive the SI value of c from the golden ratio or any framework constant. The declaration does not assert that the tick and voxel correspond to known physical quanta. The declaration does not imply that the speed of light is variable or that special relativity is violated.

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/Constants/RSNativeUnits.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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