Compton Reconstruction

Introduction

This document marks the second formal step in the reconstruction of the Compton scattering experiment through the geometry of the Lilborn Framework. Having established the Triangle of Structural Encounter in Step 1, we now proceed to define the precise magnitudes of the three vectors within this geometric system.

Overview of the Triangle

The triangle consists of three vectors:
– Blue Vector: Represents the initial incident beam

– Green Vector: Represents the scattered coherence front

– Red Vector: Represents the recoil registry vector of the electron

Assigning Magnitudes to the Vectors

To move from a conceptual triangle to a testable model, we must define the physical lengths of these vectors based on observable quantities.

Blue Vector (Incident Coherence Front)

We define the length of the incident beam vector using its spatial frequency or inverse wavelength.
Let the incident wavelength be λ.

Then the vector magnitude is proportional to:
|Blue| = ℓ / λ

Where ℓ is the structural constant of the Lilborn Framework (commonly approximated as 299,792 km/s).

Green Vector (Scattered Coherence Front)

Similarly, let the final wavelength after scattering be λ′.

Then:
|Green| = ℓ / λ′

Red Vector (Electron Registry Recoil)

In the standard model, this vector is associated with momentum. In our framework, it represents a structural interaction involving the electron’s rest mass mₑ.

We define:
|Red| = mₑ · ℓ

This identifies the registry vector’s magnitude as a function of the electron’s mass and the coherence constant.

Summary of the Triangle’s Sides

With these definitions, the triangle is fully defined:
– Side A (Blue): ℓ / λ

– Side B (Green): ℓ / λ′

– Side C (Red): mₑ · ℓ

These vectors can now be inserted into the Law of Cosines to derive the full Compton wavelength shift equation from first geometric principles.

With the vectors now quantified, we are ready to proceed to Step 3: the full geometric derivation using the Law of Cosines.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams