2. Electron interaction modes in RQT

After defining the internal resonance structure of the electron, RQT distinguishes how electrons participate in different coupling regimes. A free electron exposes residual open-channel behavior, described in standard physics by Coulomb-like field interaction. In orbital confinement, the electron occupies a closed resonance path around an inertial energy center, where orbital phase closure determines the stable radius. In static resonance distance-locking, no macroscopic orbital closure is required; instead, resonance structures maintain characteristic separations through direct phase-locking conditions.

2.1 Overview

After defining the internal resonance structure of the electron, RQT distinguishes how electrons participate in different coupling regimes.

RQT proposes three fundamental electron interaction modes:

These modes are not interpreted as fundamentally different particles, but as different coherent resonance configurations of the same underlying resonance structure.

2.2 Free Residual Coupling

A free electron exposes an open electromagnetic resonance channel. Standard physics describes the residual field-like interaction by Coulomb coupling:

$$ F(r)=\frac{K_E}{r^2} $$

with:

$$ K_E=k_e e^2 $$

where:

$$ k_e=\frac{1}{4\pi\varepsilon_0} $$

RQT interprets K_E as the intrinsic distance-independent coupling strength.

Phase coherence is achieved through relative movement of resonance structures, thereby matching the required phase conditions at the corresponding point in space.

For a circularly confined system:

$$ \frac{m_e v_r^2}{r}=\frac{K_E}{r^2} $$

leading to:

$$ v_r^2=\frac{K_E}{m_e r} $$

This relation already links coupling strength, inertia, and resonance radius without explicitly introducing forces or time.

2.3 Orbital Resonance Confinement

When two resonance structures couple directly rather than only residually, the interaction may transition from residual attraction into coherent phase-locking.

For a stable orbital resonance state:

$$ \Delta\phi = 2\pi n $$

Using resonance action:

$$ \phi=\frac{S}{\hbar} $$

and rotational resonance action:

$$ S\sim m_e v_r r $$

gives:

$$ m_e v_r r = n\hbar $$

Together with:

$$ \frac{m_e v_r^2}{r}=\frac{K_E}{r^2} $$

the orbital radius becomes:

$$ r_n = \frac{n^2\hbar^2}{m_e K_E} $$

leading to the Bohr radius:

$$ a_0=\frac{\hbar^2}{m_e K_E} $$

Numerically:

$$ a_0\approx5.29\times10^{-11},\mathrm{m} $$

or:

$$ a_0\approx52900,\mathrm{fm} $$

For positronium:

$$ e^- + e^+ $$

both structures possess identical inertia, leading to approximately doubled orbital radii:

$$ r_{\mathrm{Ps}}\approx2a_0 $$

In RQT, the proton functions as a comparatively stable inertial phase anchor fixing the resonance condition at its location, thereby allowing the electron to phase-couple at characteristic orbital radii.

In positronium, where both the electron and positron possess identical inertia, the phase relation extends symmetrically across the orbital system while continuously maintaining a coherent shared rotational phase center.

2.4 Static Resonance Distance-Locking

The characteristic resonance relation proposed by RQT is:

$$ d_R \sim \frac{K}{m c^2} $$

For electromagnetic resonance redistribution:

$$ K_E = k_e e^2 $$

leading to:

$$ \ell_e=\frac{2}{3}\frac{K_E}{m_e c^2} $$

Numerically:

$$ \ell_e\approx1.88\times10^{-15},\mathrm{m} $$

or:

$$ \ell_e\approx1.88,\mathrm{fm} $$

Typical experimentally observed femtometer-scale structures include:

2.5 Outlook: Multi-Electron Resonance Structures

RQT further considers the possibility that multiple electron like particles may form coherent resonance nodes within larger three-dimensional resonance structures.

Such nodes may form chains, lattices, shells, or extended resonance geometries.

Stationary resonance nodes may provide stable resonance channels enabling orbital resonance confinement of additional electrons.

Oscillating or rotational resonance nodes may generate further resonance channels capable of storing substantially larger resonance energy densities.

RQT proposes that such higher-energy resonance configurations may underlie the dominant energy content associated with nucleons and nuclear structures.