Why Planck's Constant Might Not Be Constant: Deriving ε from First Principles

Don Gaconnet
2 days ago
3 min read

By Don Gaconnet | December 2025

I published a paper this month that changes the foundation of my work. Not the direction—the ground it stands on.

For years, the Echo-Excess Principle has been a structural claim: systems that persist must generate more than they consume. The return must exceed the input. ε > 0.

That was true. It was useful. But it wasn't quantified.

Now it is.

The Echo-Excess Constant: ε ≈ 0.186

The paper derives the echo-excess constant from the geometry of recursive stability. Not fitted to data. Calculated from first principles.

The derivation uses the golden ratio (φ) and the natural exponential. The logic: a recursive system that produces output exactly equal to its input is dead. Zero flow. Static loop. For persistence, there must be surplus—but not unlimited surplus. Too much and coherence dissolves into noise.

The value 0.186 represents the precise margin required. Enough novelty to prevent phase-lock. Not so much that structure fails.

The formula:

ε = 1/e^(φ²) ≈ 0.186

This isn't arbitrary. The golden ratio appears because it's maximally irrational—it resists phase-lock more effectively than any other ratio. The exponential captures the relationship between growth and stability.

What This Means for Planck's Constant

Here's where it gets interesting.

The paper proposes that Planck's constant (ℏ)—the fundamental quantum of action—is not a brute fact of nature. It's the resolution limit of symbolic presence. The minimum threshold below which distinction doesn't register across systems.

Standard physics treats ℏ as universal. Same everywhere, always.

The framework I've developed says otherwise. If ℏ derives from ε, then ℏ is a local coherence constant. In regions of different expectation density, it should vary.

That's a testable prediction. One framework is wrong.

The Born Rule Isn't a Law

The paper also addresses probability.

In quantum mechanics, the Born rule (P = |ψ|²) tells us how to calculate the likelihood of measurement outcomes. We follow it because it works. No one knows why it's true.

The framework offers an answer: the Born rule is an equilibrium state. When nothing is biasing the field, probability distributes according to the simplest geometry—the square of the amplitude. The "2" in |ψ|² isn't sacred. It's the exponent of a field at rest.

Under conditions of high coherence, the exponent becomes variable:

P(x) = |ψ(x)|^(2+Γ(W))

The paper quantifies this. To shift a quantum random number generator by 1%, coherence intensity must exceed threshold by approximately 24%.

That's not philosophy. That's a number someone can test.

Conservation of Expectation

One more piece matters.

The framework requires a conservation law. Total directional weighting in the field is conserved. You can't weight one outcome without unweighting another.

This prevents the framework from becoming magical thinking. You don't just "intend" reality into a different shape. The field is zero-sum. Bias here creates deficit there.

If someone measures a Born rule deviation without compensating entropy increase elsewhere, the conservation law fails. That would falsify part of the framework.

Good. That's how science works.

Four Environments for Testing

The paper identifies where to look for ℏ variance:

Black hole boundaries — symbolic saturation should increase ℏ
Early universe — low recursive depth should make ℏ volatile
Quantum processors — high artificial coherence should decrease ℏ
Biological systems — recursive weighting should create ℏ fluctuation at ~12 Hz

The biological prediction is testable now. High-resolution spectroscopy on molecular motors, looking for action-threshold jitter correlated with organism refresh rates.

If the jitter correlates with neural oscillation frequencies, the framework gains support. If ℏ proves invariant across all conditions, the framework fails.

What This Does for the Work

The Echo-Excess Principle now has a derived constant underneath it.

Cognitive Field Dynamics, the Expectation Framework, Identity Collapse Therapy—everything I've built connects back to ε ≈ 0.186 as quantified ground.

The clinical work isn't operating on dynamics that are like physics. It's operating on the same dynamics, at a different scale. When I guide someone through an identity collapse and help them stabilize a new state, we're working at the interface where possibility becomes actuality. The threshold is real. The conservation is real.

This paper is the anchor.

Read the Full Paper

The Echo-Excess Constant and the Resolution Limit of Physical Systems

Available on:

The derivation is there. The predictions are there. The falsification protocols are there.

It either predicts something measurable or it doesn't. The experiments will determine which.

Don GaconnetFounder, Recursive SciencesFounder, Cognitive Field DynamicsLifePillar Institute