Cosmology Siconversion Planck To Seconds

The Planck Time Bridge

The Planck time, about 5.39 × 10⁻⁴⁴ seconds, is the smallest meaningful interval in modern physics, the time light takes to cross the Planck length. The Recognition Science framework works in its own native units where this interval is simply 1, and the declaration planck_to_seconds is the bridge that carries a time measured in those native units into the seconds of an SI stopwatch. The rule is a plain multiplication: multiply the native time by 5.391247 × 10⁻⁴⁴ to get seconds.

The framework's library proves that this conversion factor is positive, and it certifies that the Planck length divided by the speed of light is consistent with the Planck time to within one percent. That consistency check is a theorem about the definitions, not a measurement. The SI value itself, 5.391247 × 10⁻⁴⁴ seconds, is an external fact, sourced from CODATA experimental data. It depends on the human-chosen meter and second, so the framework does not derive it; it adopts it as the calibration seam through which its predictions are expressed in familiar units.

In Recognition Science, the theoretical content lives in ratios, not in the SI numbers. The framework can predict that the age of the universe in native units is some number, and the conversion factor turns that into 4.354 × 10¹⁷ seconds, the observed age. The same bridge converts the observed Hubble constant, about 73 km/s/Mpc from late-universe measurements, into the framework's native rate. The conversion is a definition, a chosen rule of translation, and the positivity and consistency theorems are the machine-checked guarantees that the rule is coherent.

What the declaration does not claim is that the framework predicts the numerical value of the Planck time in seconds. That number is a laboratory result, not a derivation. The framework's contribution is the bridge itself, the certified conversion that lets its native-unit predictions be compared with telescope data. Without this seam, a prediction in native units would be an orphan number; with it, the framework's ratios become testable against the measured age of the universe and the expansion rate.

/-- Convert a time from Planck times to seconds. -/
def planck_to_seconds (t_planck : ℝ) : ℝ := t_planck * planck_time_SI

theorem planck_time_SI_pos : 0 < planck_time_SI := by
  unfold planck_time_SI; norm_num

theorem si_calibration_cert : SICalibrationCert where
  planck_length_positive := planck_length_SI_pos
  planck_time_positive := planck_time_SI_pos
  consistency := by unfold planck_length_SI c_SI planck_time_SI; norm_num
  consistency2 := by unfold planck_length_SI c_SI planck_time_SI; norm_num

/-- Planck time in seconds (CODATA 2018).
    t_P = ℓ_P/c = 5.391247 × 10⁻⁴⁴ s. -/
def planck_time_SI : ℝ := 5.391247e-44

What this page does not claim

The framework does not predict the numerical value of the Planck time in seconds; that value is a CODATA-sourced measurement. The declaration does not establish any physical law or relation beyond the definition of the conversion factor. The one-percent consistency check between Planck length and time is a theorem about the chosen definitions, not a new physical measurement.

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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