Unifying ℏ and α

ℏ and α in a Charge-Admittance Framework

Abstract

We propose a physically intuitive reinterpretation of Planck’s constant ℏ and the fine structure constant α as geometric and energetic constraints arising from the structured response of a coherent charge-admittance field. Rather than treating ℏ and α as fundamental but unrelated constants, we explore a unifying view: ℏ defines the minimum stable loop diameter of coherent charge motion, while α defines the minimum separation between such loops, as governed by Coulombic strain. These constants, viewed in relation to the vacuum impedance Z₀ = √(μ₀/ε₀) describe not particles in space, but stable phase relationships in an evolving, impedance-graded field.

Introduction

In conventional physics, Planck’s constant (ℏ) and the fine structure constant (α) appear as disconnected entities. ℏ quantifies the scale of quantum action, while α emerges empirically in electromagnetic interactions, governing the coupling strength of charges. Their roles are deeply embedded in quantum theory, but their origins remain obscure.

In the Charge Admittance (CA) framework, energy flow through a structured μ₀/ε₀ field creates localized coherences — discrete, spinning loops of charge that stabilize as “particles.” This view naturally reframes ℏ and α as emergent constraints of the medium, not imposed constants.

Field Background: Revisiting the Vacuum

Rather than a passive void, the CA vacuum is a lattice of response — a medium that permits or resists energy propagation according to its local admittance to charge. This dynamic is governed by:

• Permittivity (ε₀): response to electric field propagation.
• Permeability (μ₀): response to magnetic field propagation.
• Vacuum impedance: Z₀ = √(μ₀/ε₀)

We revisit the expression for α:

   

This identity reveals vacuum impedance (Z₀) as an active participant in setting α, yet it is often hidden in canonical expressions. Its reappearance points to a unified substrate — one whose structural behavior defines constants rather than requiring them.

ℏ as Minimum Loop Diameter

We interpret ℏ as the minimum internal diameter of a self-coherent energy loop — the smallest stable configuration in which a disturbance (charge) can cycle without radiating away:

• ℏ defines not only quantization of action (E·t) but also structural coherence.
• Any energy circulation below this scale decoheres — it cannot sustain structure against the field’s impedance.

This reinterprets the Planck scale as a threshold of stability, not a limit of measurement.

α as Loop Separation Constraint

In this context, α serves a complementary role:

• It sets the minimum spatial spacing between coherent charge loops.
• This arises not from symmetry breaking, but from Coulombic repulsion between phase-bound charges in a field that cannot accommodate tighter packing.

We propose that α reflects a geometric packing density — a tension limit in the lattice’s ability to sustain phase-coherent loops side-by-side.

Coherence Field and the Birth of Particles

Combining the above:

• The vacuum becomes tiled with charge loops (fuzzballs),
• Each with minimum loop diameter ℏ,
• And minimum spacing set by α.

Together they define a modular structure of stable energy — the origin of particles, not as “things,” but as topological constraints in a phase-aligned medium.

Phase Failure and Mass Emergence

We further suggest that when a charge loop spins faster than its field can support — approaching coherence limits — its ability to sustain directional difference collapses. The result is:

• A “blur” of charge and trailing field (hole),
• Loss of external radiative energy,
• Emergence of localized inertia — mass.

This phase-decoherence threshold may be what defines mass-energy equivalence, and suggests a relationship between ℏ, α, and mass stabilization.

Implications for Field Structure

These insights imply a vacuum composed not of two interacting fields (electric and magnetic), but of trillions of micro-coherent field events — each producing an E and B field at right angles, diminishing via Poynting vectors, and interacting collectively to form gradients:

• Lattice density = impedance profile.
• Impedance gradient = gravity.
• Coherence spacing = charge interaction constraint.

Toward a Unified Expression

We close by proposing an avenue for formal unification:

   

Future work will explore whether both ℏ and α can be derived directly from geometry of phase loops in a structured ε₀/μ₀ medium — potentially explaining not just their values, but their universality.

Conclusion

ℏ and α are not arbitrary or extrinsic. In a Charge Admittance universe, they define the spatial and energetic tiling rules of coherent motion — not constants imposed on reality, but the outcome of how reality holds itself together.