MDA-P01 | The Formal Paper

The Formal Paper — Page 1 of 5

The Physics of Coherence

Order Parameters and Phase Transitions

David Lowe — POF 2828 — 2026

FACTS Framework

FSocial systems possess a measurable order parameter (χ) that undergoes phase transitions identical in mathematical form to physical systems. If χ does not correlate across domains, this claim is falsified.
APhase transition mathematics is substrate-independent. Coherence is measurable through behavioral proxies. The ordered phase has a definable baseline.
Cχ is the Master Equation's coherence variable. This page establishes the physics foundation that Pages 2–5 build upon.
TAny system with an order parameter, a control parameter, and measurable coherence will exhibit phase transition dynamics at the critical threshold.
SLandau theory of phase transitions. BCS theory of superconductivity. Ising model. Empirical data presented in Page 4.

What Coherence Means in Physics

In physics, coherence refers to the degree of correlation or alignment within a system. A coherent system is one where the components act in concert rather than independently.

This is not metaphor. It is measurable.

In a laser, photons are coherent when they share the same phase and frequency. In a superconductor, electrons are coherent when they form Cooper pairs. In a ferromagnet, atomic spins are coherent when they align.


The Order Parameter (χ)

Physicists quantify coherence using an order parameter—a measurable quantity that equals zero in the disordered (high-entropy) phase, is non-zero in the ordered (low-entropy) phase, and changes discontinuously at the phase transition.

Order Parameters Across Systems

Ferromagnet

χ = net magnetization

Superconductor

χ = Cooper pair density

Crystal

χ = lattice order


The Phase Transition

When a system crosses its critical threshold (Tc), coherence collapses:

Phase Transition Equation

χ ∝ |T − Tc|β    for T < Tc  (ordered phase)

χ → 0             for T > Tc  (disordered phase)

T = temperature  |  Tc = critical temperature  |  β = critical exponent (typically 0.3–0.5)

This transition is sudden, not gradual. It is universal across systems—same math, different substrates. And it is predictable once Tc is known.


A Concrete Example: The Superconductor

Below Tc — Ordered

Electrons form Cooper pairs. Electrical resistance equals zero. The system exhibits quantum coherence at macroscopic scale.

Above Tc — Disordered

Cooper pairs break apart. Resistance returns. Coherence is lost.

"The mathematics does not care what the substrate is. It only tracks the order parameter."


The Key Insight

Phase transition mathematics describes any system where components can be ordered or disordered, a control parameter governs the transition, and coherence is measurable.

The question becomes:

What if social systems have an order parameter?

Page 2: The Variable Substitution