Wave Coherence Demystified

A Plain-Language Guide to the Parametric Acoustic Resonance Theory (PART)

Stephen Horton | Independent Researcher | February 2026

The Wave Coherence Blog Series Part 1: The Strange History of Zero Resistance

The Big Idea in One Sentence

Superconductivity — the phenomenon where electricity flows with zero resistance — might not be about electrons pairing up. It might be about sound. Specifically, about building a tiny acoustic echo chamber inside a crystal that’s so perfectly tuned it sustains itself on nothing but the heat around it.

Wait, Sound? In a Crystal?

When physicists talk about “phonons,” they’re talking about vibrations moving through a crystal lattice — atoms jiggling and passing that jiggle to their neighbors. That’s literally what sound is: organized vibration moving through a medium. We just don’t call it sound because it’s happening at 50 trillion cycles per second inside a piece of metal instead of at 440 cycles per second coming out of a guitar.

But the physics is the same. And that’s the starting point for everything that follows.

The Swing Set Analogy

Imagine a kid on a swing. There are two ways to keep them swinging:

The normal way (direct pushing): You stand behind the swing and push at just the right moment every time it comes back. This is how conventional physics thinks about superconductivity — phonons directly “push” electrons into paired states (Cooper pairs), and if the thermal noise (wind, friction) gets too strong, the pushing can’t keep up, and the swing stops. That stopping point is the critical temperature, Tc.

The parametric way (changing the rope length): Instead of pushing the swing, imagine you could rhythmically shorten and lengthen the chains — pulling them shorter as the swing reaches the top, letting them out at the bottom. You’re not pushing the swing at all. You’re changing a parameter of the system (the rope length) at twice the swing’s natural frequency, and that modulation pumps energy into the swing.

This is called parametric amplification, and it’s a real, well-understood phenomenon used in everything from radio receivers to quantum computers.

The PART framework says superconductivity works like the second method, not the first. The critical temperature Tc isn’t where pairs break — it’s where parametric gain (gp) equals loss. The central identity of the theory: Tc = gp.

So What’s Actually Happening Inside the Crystal?

Picture a hydrogen-rich crystal — like H3S, the material that superconducts at -70°C under extreme pressure. Inside this crystal:

The heavy atoms (lanthanum, sulfur, etc.) are the walls of a room. They’re massive and relatively stationary, like the concrete walls of a concert hall. They define the boundaries.

The hydrogen atoms are the air inside the room. They’re light (hydrogen is the lightest element), so they vibrate at incredibly high frequencies. They are the acoustic medium.

Pressure is the room’s tuning knob. Squeezing the crystal changes the spacing between atoms, which changes the resonant frequency — exactly like tightening a guitar string raises its pitch.

When everything is tuned right, the hydrogen atoms set up a standing wave — a stable, self-reinforcing vibration pattern, like the resonance you hear when you sing the right note in a tiled bathroom. Electrons get caught in this standing wave pattern like surfers riding a wave. They move together, in lockstep, with zero resistance. That’s superconductivity.

The Laser Connection

Here’s where it gets interesting. A laser works like this:

You pump energy into a gain medium (like a ruby crystal or a gas tube)
That energy causes atoms to emit photons (light particles)
Mirrors on each end of the tube bounce the photons back and forth
Each pass through the medium stimulates more atoms to emit photons at the same frequency, in the same direction
The result: a coherent beam of light

The lasing threshold is the pump power where the light produced on each pass just barely exceeds the light lost through the mirrors and absorption. Below threshold: just a dim glow. Above threshold: a laser beam.

PART says superconductivity works the same way:

Laser	Superconductor (PART)
Gain medium (ruby, gas)	Hydrogen sublattice
Cavity mirrors	Heavy atoms at the boundaries
Pump energy	Ambient heat (!!)
Lasing threshold	Tc (critical temperature)
Coherent light beam	Coherent acoustic standing wave
Laser output	Zero-resistance current

The critical temperature Tc is reinterpreted as a threshold, not a wall. It’s the temperature where acoustic gain (energy pumped into the standing wave) exactly equals acoustic loss (energy leaking out as heat). Below that temperature, gain wins — the standing wave builds up, electrons ride it, and you get superconductivity.

The Ammonia Octave: Nature’s Built-In Amplifier

Here’s the part that gets wild.

In a parametric oscillator, you need the pump frequency to be exactly twice the signal frequency. That 2:1 ratio is called an octave — the same relationship between a low C and a high C on a piano.

The ammonia molecule (NH3) and ammonium ion (NH4+) just… have this built in:

N-H bending vibration: ~50 THz (this is the “signal” — the frequency that matters for superconductivity)
N-H stretching vibration: ~100 THz (this is the “pump” — exactly double)

The stretch mode naturally feeds energy into the bend mode through the molecule’s own anharmonicity (the fact that real molecular bonds don’t vibrate perfectly symmetrically). It’s like having a swing set where the chains automatically shorten and lengthen at the right rhythm — no external pusher needed.

The molecule is its own parametric amplifier.

Other molecules have this too, to varying degrees:

Molecule	Bend	Stretch	Ratio	Verdict
NH3/NH4+	~50 THz	~100 THz	~2.0	Perfect octave
PH3/PH4+	~33 THz	~70 THz	~2.1	Strong candidate
BH4-	~35 THz	~73 THz	~2.1	Strong candidate
CH4	~42 THz	~90 THz	~2.2	Slightly off

This gives materials scientists a new screening tool: instead of just calculating electron-phonon coupling strength, look for molecular building blocks with octave vibrational relationships.

The Mind-Bending Part: Heat Isn’t the Enemy

In the conventional picture, heat destroys superconductivity. Raise the temperature, and thermal vibrations shake the Cooper pairs apart. Tc is the temperature where destruction wins.

PART flips this on its head: heat is the fuel.

Think about it through the laser analogy. A laser needs a pump source to maintain population inversion. Where does the PART superconductor get its pump energy? From the thermal bath — the ambient heat in the environment. At any temperature above absolute zero, the thermal environment is constantly exciting the N-H stretch mode at ~100 THz. That stretch mode parametrically feeds the bend mode at ~50 THz. The bend mode sustains the coherent standing wave. The standing wave carries the supercurrent.

The thermal environment is not fighting the superconductor. It’s powering it.

This is not perpetual motion. The energy comes from somewhere — the environment cools down (infinitesimally) as the superconductor harvests thermal energy and converts it from random noise (high entropy) into an organized standing wave (low entropy). It’s the same thermodynamics as a refrigerator or a thermoelectric generator, just happening at the quantum scale inside a crystal lattice.

The system only needs one thing to get started: a seed — an initial kick to get the standing wave going past the gain-loss threshold. After that, the thermal bath takes over. Think of it like push-starting a car with a dead battery: you push it to get the engine turning, the engine catches, and then it runs on its own fuel. You don’t keep pushing.

Real-World Evidence

This isn’t just armchair theorizing. Several experimental observations that are puzzling under conventional theory make sense in this framework:

Anomalously strong flux pinning in hydrides. When you try to push a magnetic field through a superconductor, it resists. In hydride superconductors, this resistance is way stronger than defect-based models predict. Under PART, you’re not just pushing past a crystal defect — you’re trying to punch a hole in a coherent standing wave. That’s like trying to create a dead spot in a laser cavity. It takes enormous energy.

Anharmonicity keeps showing up as essential. Multiple research groups have found that anharmonic corrections increase predicted Tc in hydride superconductors. Conventional theory treats this as a correction. PART says it’s the whole point — the anharmonicity is the parametric gain mechanism.

Non-equilibrium superconductivity. Researchers have used ultrafast laser pulses to transiently enhance superconducting states. Under PART, that laser pulse is an acoustic seed — it’s push-starting the standing wave.

What This Means for the Future

If PART is right, it changes the engineering problem completely. You’re no longer trying to find materials where electrons pair up at high temperatures. You’re trying to build acoustic resonant cavities at the atomic scale. That means:

Screen materials for octave relationships — not just electron-phonon coupling strength
Engineer crystal quality like optical engineers engineer mirror coatings — reduce losses, improve boundary conditions
Use acoustic seeding — external sound pulses (at THz frequencies) could push Tc higher
Maintain hydrogen atmospheres — keeping the acoustic medium intact and impedance-matched
Stop fighting heat and start using it — design the parametric coupling to harvest thermal energy more efficiently

The paper proposes eight testable predictions, each of which could validate or falsify the framework. The most dramatic: an external acoustic seed pulse should measurably raise the effective Tc above its equilibrium value. If that experiment works, it changes everything.

The Bottom Line

Phonons are sound. We’ve known this for a century. What we haven’t done is take it seriously as an engineering principle for superconductor design. The PART framework does exactly that — treating the crystal lattice as an acoustic instrument to be tuned, amplified, and sustained, rather than an electronic structure to be optimized.

The question of superconductor design becomes: how do you build, tune, seed, and sustain a resonant cavity at the atomic scale?

The answer might be encoded in the vibrational modes of the simplest molecules in the universe. We just need to listen.

This article is a plain-language summary of “Wave Coherence Model of Superconductivity: Parametric Acoustic Resonance Theory (PART)” — Working Paper v2.0, February 2026, by Stephen Horton.

Published: Horton, S. (2026). The Wave Coherence Model (1.0). Zenodo. https://doi.org/10.5281/zenodo.18500774

The Wave Coherence Blog Series Part 1: The Strange History of Zero Resistance Part 2: Wave Coherence Demystified — The PART Framework Stephen Horton — Independent Researcher — February 2026