Constants Codata C Ne Zero

The speed of light constant

The speed of light in a vacuum, denoted c, is one of the most precisely known numbers in physics. Since 1983, the meter has been defined as the distance light travels in 1/299,792,458 of a second, making c exactly 299,792,458 meters per second. This is not a measured value with uncertainty; it is a fixed definition that anchors the entire SI system of units. The number is positive, which is physically necessary: light does travel, and it does so at a finite, positive speed.

The declaration c_ne_zero in the Recognition Science framework's machine-checked library of formal theorems establishes a simple but foundational fact: the speed of light constant is not equal to zero. The proof is immediate from the positivity lemma, which states that 0 < c. Since a positive number cannot be zero, the nonzero property follows directly. This is a trivial consequence of the definition, not a new physical discovery, but it matters for formal reasoning. Many mathematical operations, such as division, require a nonzero denominator, and this lemma provides that guarantee within the framework.

In Recognition Science, this constant is quarantined from the certified surface. It lives in a separate namespace alongside the reduced Planck constant and Newton's gravitational constant, all marked as empirical values from CODATA 2018. The framework's own derived constants, such as hbar = φ⁻⁵ and G = φ⁵/π, are distinct from these empirical counterparts. The quarantine exists because the certified chain of theorems should not depend on measured numbers; it relies only on the forcing chain that derives constants from the cost function. The empirical constants are available for numeric comparisons and reports, but they are not part of the proof surface.

What c_ne_zero does not claim is worth stating plainly. It does not assert that the speed of light is constant in all media or reference frames. It does not claim that the value 299,792,458 is derived from the framework's principles; it is an empirical input, not an output of the forcing chain. The lemma merely states that the defined number is nonzero, a purely formal fact about the definition. It carries no physical content beyond what the definition already implies, and it makes no statement about the nature of light or the structure of spacetime.

lemma c_ne_zero : c ≠ 0 := ne_of_gt c_pos

/-- Speed of light (exact SI definition). -/
@[simp] noncomputable def c : ℝ := 299792458

lemma c_pos : 0 < c := by unfold c; norm_num

What this page does not claim

The speed of light is constant in all media or reference frames. The value 299,792,458 is derived from the framework's principles rather than taken as an empirical input. The lemma makes any statement about the nature of light or the structure of spacetime.

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/Codata.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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