Physics Gravitational Wave Interferometry From Jcost

Gravitational wave interferometry

Gravitational wave interferometry is the technique that detects ripples in spacetime. Facilities like LIGO and Virgo use lasers to measure the stretching and squeezing of space itself. When a gravitational wave passes, it changes the distance between mirrors by a tiny fraction. The best detectors measure strains around 10^(-21), which is like measuring a distance smaller than a proton over a kilometer. This is the classical definition and the baseline sensitivity.

The technique works by splitting a laser beam and sending it down two long arms. A passing wave changes the length of one arm relative to the other, causing the beams to recombine with a slightly different phase. The resulting interference pattern reveals the wave's signature. LIGO first detected gravitational waves in 2015, confirming a prediction made by Albert Einstein in 1916. The detectors are essentially the most precise rulers ever built.

In Recognition Science, the framework models this sensitivity through its central cost function. The framework's ledger, a discrete record of recognition events, forces a specific cost function J(x) = (x + 1/x)/2 - 1. The gravitational wave strain h is modeled as this cost applied to a metric perturbation ratio. The detection threshold is set by the golden ratio: the strain must satisfy J(r) < J(φ), which lands in the interval (0.11, 0.13). This is a definitional choice within the framework, not a derived physical law.

The framework also organizes the five canonical source types for gravitational waves. These are black hole mergers, neutron star mergers, black hole neutron star mergers, continuous waves, and the stochastic background. The framework's machine-checked library of formal theorems proves that this count equals five. The library also verifies that the detection threshold is consistent with its canonical certificate. These are formal statements about the framework's own structures.

The practical consequence is that the framework provides a single unifying language for talking about both the sensitivity and the source taxonomy of gravitational wave detectors. It does not predict a new detection method or a new physical effect. It re-describes known experimental facts in terms of its cost function. The formal library shows the internal consistency of this description, but the experimental facts remain measured facts.

structure GWInterferometryCert where
  five_sources : Fintype.card GWSourceType = 5
  detection_threshold : CanonicalCert

structure GWInterferometryCert where
  five_sources : Fintype.card GWSourceType = 5
  detection_threshold : CanonicalCert

structure GWInterferometryCert where
  five_sources : Fintype.card GWSourceType = 5
  detection_threshold : CanonicalCert

structure GWInterferometryCert where
  five_sources : Fintype.card GWSourceType = 5
  detection_threshold : CanonicalCert

theorem gwSourceCount : Fintype.card GWSourceType = 5 := by decide

What this page does not claim

The framework does not derive the 10^(-21) sensitivity from first principles; it models the strain using its cost function. The framework does not predict a new type of gravitational wave source beyond the five canonical types. The framework does not claim that its detection threshold interval (0.11, 0.13) is a measured physical constant.

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/Physics/GravitationalWaveInterferometryFromJCost.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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