Physics Wien Law Rs

Wien's displacement law

Wien's displacement law is a rule from classical physics about the color of hot, glowing objects. It states that the wavelength at which a black body emits the most light is inversely proportional to its temperature. A hotter object, like a blue star, peaks at a shorter wavelength; a cooler one, like a red star, peaks at a longer one. The constant of proportionality, called the Wien displacement constant, is measured to be about 2.898 times 10 to the minus 3 meter-kelvin. Wilhelm Wien first derived this relationship in 1893 using thermodynamic arguments, and Max Planck's 1900 quantum theory of black-body radiation later explained it fully.

The Recognition Science (RS) module named physics-wien-law-rs does not derive or prove Wien's law. Its formal content is a small set of general statements about a cost function, which is a way of assigning a penalty to a mismatch. The module defines a cost as the function J applied to the ratio of two numbers, m over e. It then proves three facts about this cost: it is zero when m equals e, it is never negative when both inputs are positive, and the number phi minus 1.5 is positive, where phi is the golden ratio. These are true statements, but they are true for any two positive numbers, not for anything specific to heat, light, or temperature.

The module also bundles these three facts into a structure called a certificate, which simply records that the facts hold. The docstring inside the module is explicit about the situation. It calls the paragraph about the Wien constant a research note, a record of where the idea was meant to go, not a result. The same body of text is shared verbatim with 2383 sibling modules, each one a template waiting for a subject-specific definition of its two key quantities.

In Recognition Science, the framework models a discrete record of events, called a ledger, and the cost of a recognition event is forced by a proved theorem. The framework's machine-checked library of formal theorems proves that any cost function satisfying five plain conditions must equal J(x) = (x + 1/x)/2 - 1. The physics-wien-law-rs module plugs the ratio m/e into that forced cost. What is missing is a physical definition of m and e in terms of wavelength, temperature, or energy. Without that, the module remains a template, not a theorem about Wien's law.

What the module does establish is a small, clean example of the framework's tools. It shows how a cost function behaves at equality and on positive inputs, and it packages those facts into a reusable certificate. The honest takeaway is that this page is a placeholder. The path to a real RS statement about Wien's law would require defining the two quantities in the physics of black-body radiation, a step the module itself does not take.

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

What this page does not claim

The module does not prove or derive Wien's displacement law. The module does not establish a value for the Wien displacement constant. The module does not connect the cost function to any specific physical quantity without a further definition.

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/Wien_Law_RS.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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