Cosmology Siconversion

The calibration seam

Cosmology siconversion is the part of the Recognition Science framework that translates its internal predictions into the units astronomers actually use. The framework derives physics in its own natural units, where the speed of light, a fundamental length, and a fundamental time are all set to 1. To check those predictions against observations, a single calibration anchor is needed. That anchor is the Planck scale.

The Planck length and Planck time are the bridge. In the framework's native units, the Planck length is proved to be 1/√π. Its value in meters, about 1.616255 × 10⁻³⁵ m, is an external fact, depending on the human-defined meter and second, not on Recognition Science theory. The module defines the SI values of the Planck length and time, along with the speed of light, a megaparsec, a light-year, and a gigayear, and provides conversion functions between these systems.

The module also records observed cosmological quantities in SI form: the age of the universe as 13.787 billion years, the Hubble constant from late-universe measurements as 73.04 km/s/Mpc, and from early-universe measurements as 67.36 km/s/Mpc. These are not predictions. They are the measured numbers against which the framework's own derived ratios, such as the age divided by the Planck time, are meant to be compared.

In Recognition Science, the theoretical content lives in the ratios, not in the SI values. The framework proves that the Planck length is 1/√π in native units, and it provides a certified consistency check that the SI Planck length divided by the speed of light agrees with the SI Planck time to within one percent. This certificate, SICalibrationCert, is a machine-checked theorem in the framework's library of formal proofs.

The practical consequence is that anyone working inside the framework can take a derived quantity in native units, multiply by the Planck length or time, and obtain a number in meters or seconds that can be compared directly with observational data. The siconversion module makes the framework's predictions testable in the units of the laboratory and the telescope.

theorem planck_length_SI_pos : 0 < planck_length_SI := by
  unfold planck_length_SI; norm_num

/-- Planck length in meters (CODATA 2018).
    ℓ_P = √(ℏG/c³) = 1.616255 × 10⁻³⁵ m.
    Uncertainty: ±0.000018 × 10⁻³⁵ m (relative: 1.1 × 10⁻⁵). -/
def planck_length_SI : ℝ := 1.616255e-35

/-- Convert a distance from Planck lengths to meters. -/
def planck_to_meters (r_planck : ℝ) : ℝ := r_planck * planck_length_SI

/-- Observed age in Gyr. -/
def obs_age_Gyr : ℝ := 13.787

What this page does not claim

This module does not derive the SI values of the Planck scale. This module does not resolve the Hubble tension between early and late universe measurements. This module does not predict the age of the universe in years.

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/Cosmology/SIConversion.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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