LEDO–Wave Reflection and the Fine-Structure Constant

Proton as a Reflector of LEDO Waves With a Forward Angle of $2\alpha$

The following interpretation and insight might come very striking for the more quantum physics engaged reader. All starting with this question: “What if a Proton was only a reflector of the directed rotonal LEDO-Wave of an Electron?”

This would immediately answer the following questions:

• Why does a proton have the exact same (opposite) “charge” as an electron?
• How might the hyper-fine-constant relate to geometrical aspects

1. Summary

If a proton acts as a LEDO-wave mirror for a single electron, and LEDO waves propagate at the medium-speed $c$, then a clear geometric condition appears:

The proton must reflect LEDO waves forward by the angle
$$ \psi = 2\alpha \approx 0.0146\ \text{rad} \approx 0.84^\circ $$
so that the returning LEDO wave re-intersects the electron exactly when it arrives.

Here,

$$ \alpha = \frac{1}{137.035999\ldots} $$

is the fine-structure constant, the universal strength of electromagnetism.

For higher shells $n$ the forward reflection angle is:

$$ \psi_n = \frac{2\alpha}{n} $$

This produces a clean resonance hierarchy consistent with the known spectral level spacing of hydrogen.

2. Conceptual Interpretation

2.1 LEDO Motivation

In the Roton–LEDO interpretation:

• The electron emits an inward LEDO-wave toward the proton.
• The proton reflects the wave outward.
• The reflected wave must meet the electron at its future position, not its past one.

Because the electron moves with

$$ v = \alpha c $$

and LEDO waves move at $c$, the electron only shifts a small angle during the round trip.
The proton must therefore reflect the wave slightly forward, by exactly $2\alpha$.

2.2 Does This Reinterpret $\alpha$?

In standard physics, $\alpha$ appears as:

• the electromagnetic coupling constant,
• the source of fine structure,
• the basis for spin–orbit corrections,
• the key of the Rydberg constant,
• central to Compton/Thomson scattering,
• and most precisely extracted via the electron’s $g-2$ anomaly.

However, nothing in standard theory explains why $\alpha$ has this particular value.

In the LEDO framework:

$\alpha$ arises naturally as the geometric ratio between
electron orbital speed and LEDO propagation speed,
enforcing a closed-loop resonance between emitted and reflected waves.

Thus, $\alpha$ becomes not just a coupling strength but a geometric self-consistency condition.

2.3 Implications

• $\alpha$ functions as a phase-locking ratio in the LEDO model.
• Orbital stability becomes a resonant wave-return effect instead of pure probabilistic stationarity.
• Shell scaling ($\psi_n = 2\alpha/n$) mirrors decreasing fine-structure splitting with larger $n$.
• The proton serves as a directional reflector, ensuring resonance continuity.

3. In-Depth Derivation

3.1 LEDO Round-Trip Time

Electron orbit radius: $r$
Electron speed: $v = \alpha c$
LEDO-wave speed: $c$

Round-trip LEDO time:

$$ t_{\text{LED}} = \frac{2r}{c} $$

3.2 Electron Angular Motion During This Time

Angular velocity:

$$ \omega = \frac{v}{r} = \frac{\alpha c}{r} $$

Angle moved during LEDO round trip:

$$ \Delta\varphi = \omega, t_{\text{LED}} = \frac{\alpha c}{r} \cdot \frac{2r}{c} = 2\alpha. $$

3.3 Required Mirror Angle

To ensure re-intersection of wave and electron:

$$ \psi = 2\alpha $$

Numerical value:

$$ 2\alpha \approx 0.0146\ \text{rad} \approx 0.84^\circ $$

3.4 Higher Bohr-Like Shells

For shell $n$:

• $r_n = n^2 a_0$
• $v_n = \frac{\alpha c}{n}$

Then the forward reflection angle becomes:

$$ \psi_n = \frac{2\alpha}{n}. $$

This scaling aligns well with decreasing energy level spacing in known hydrogen spectra.

4. Intermediate Remarks

The Alpha in our equations arrives simply because this is the ratio between the electrons speed and radius.

Our Model does NOT describe yet, why 1/137 shall be a more optimal angular velocity, and why electrons “fall” into that funnel.

This LEDO–reflection geometry unites:

• electron orbital motion,
• LEDO propagation,
• proton reflection,
• and the fine-structure constant $\alpha$,

into one coherent resonance condition:

The electron is continuously re-attracted by its own returning LEDO-wave
only if the proton provides precisely the forward reflection angle $2\alpha$.

Whether this represents:

• a geometric reformulation of quantum structure,
• a deeper meaning of $\alpha$,
• or the foundation of a resonance-based atomic model,

remains open and promising for further exploration.