Geometry Of Interaction In A Coherence-Based Framework

Introduction

This document presents the formal reconstruction of the Ives–Stilwell experiment, focusing on the geometric structure of coherence interactions rather than relativistic time dilation. It initiates the next phase of theoretical deconstruction in the Lilborn Framework, allowing visitors to follow the process step-by-step as we reinterpret one of the most foundational experiments underpinning special relativity. This experiment includes not only a challenge to the concept of time dilation but also a direct reconstruction of how observed frequency shifts emerge without invoking any velocity-based temporal model.

What is the Geometry of Interaction?

Defining the spatial structure of signal registration in the absence of propagation and time dilation.

The Source (Emitter)

A source moves with constant velocity v in the laboratory frame. It is not emitting “light pulses” through space but rather interacting with a stationary field of coherent registration, a structural field that defines potential interactions based on spatial alignment.

The Observer (Receiver)

The observer is fixed in the lab frame. The observer does not receive propagated signals; rather, the observer encounters coherence fronts as they intersect with the observer’s detection geometry. These interactions register as frequency, based on how closely spaced the coherence fronts appear in spatial sequence due to relative motion.

The Coherence Grid

The universal coherence field defines a fixed structural manifold. Any spatial interaction is a projection between the emitter’s coherence sequence and the observer’s registration vector.

The Fundamental Triangle of Coherence Interaction

This triangle models the relationship between emitter motion, coherence front projection and the observer’s registration.

Key variables include:
– v: Velocity of the source

– ℓ: Structural registration constant

– θ: Angle between the velocity vector and observer’s detection axis

– k₀: Spatial frequency in the source’s rest frame

– k: Spatial frequency as registered by the observer

Interaction Types by Angle

Cases:
– Longitudinal (Approaching, θ = 0°): k > k₀

– Longitudinal (Receding, θ = 180°): k < k₀

– Transverse (θ = 90°): k = k₀ with higher-order inefficiency

Conclusion

We now have the geometric model needed to interpret the Ives–Stilwell results structurally. The Triangle of Coherence Interaction defines how the spatial relationship between emitter and observer creates projection distortion of coherence density. This sets the stage for the full reconstruction of both first- and second-order Doppler effects without invoking time dilation.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams