Please also see ^{Fine Structure Reflector (read↗)} where this is further discussed in context of the Proton structure.

LEDO propagation speed and the fine-structure constant $\alpha$

1. Propagation speed in the LEDO-Field

In the LEDO-picture, resonance forces between Rotons act instantaneously across the universe. There is no intrinsic time delay or distance-dependent weakening in the underlying interaction itself – similar in spirit to quantum entanglement.

However, stable Rotons and composite objects do not respond instantaneously. Their response is limited by:

• their rotational inertia (resistance to tilts and precession of the rotation axis), and
• the vacuum background fluctuations that constantly perturb their state.

As a result, the propagation of energy-density oscillations (changes in energy-pressure within the LEDO-Field) has an effective propagation speed. This speed is not set by a hard geometric limit, but by how fast Rotons can reconfigure their axes and positions under the influence of resonance forces and background noise.

In this sense, what we usually call the speed of light, $c$, emerges as a characteristic reaction timescale of the LEDO-Field to local disturbances.

Background example for the context

With the speed of light and the behavior of photons, we are observing the simplest, linearised case of effects that also occur in matter. A photon is a basic Roton (a Sonon) embedded in the LEDO-Field. Its effective rotational speed is not fixed a priori; instead, it might be constrained by how its rotation axis interacts with the surrounding field.

As long as the photon’s rotation axis remains unaffected — meaning no rotonal force acts on it — it travels in a straight path while keeping its axis orientation unchanged. When the photon encounters directional resonances that match its own rotonal magnitude, its rotation axis mainly tends to maintain its orientation. Only small, random background fluctuations within the relevant scale of the LEDO-field can induce slight tilts.

If such a fluctuation shifts the axis toward a direction that is energetically more favorable, the rotation axis will gradually precess and realign itself with this new direction of attraction.

2. Frequency-dependent vacuum fluctuations

We now refine this picture by assuming that the vacuum background fluctuations are frequency-dependent:

• Rotons of different characteristic scales (different radii and eigenfrequencies) experience different effective reaction times.
• A very small, high-frequency Roton “samples” the vacuum on a finer scale than a large, low-frequency Roton.
• The amount of background fluctuation that is relevant for a given Roton therefore depends on its rotonal magnitude (size + frequency).

In other words:

Rotons of different scales do not just couple to “the same vacuum” – they couple to different effective layers of vacuum fluctuations, each with its own response characteristics.

This leads naturally to the idea that the effective coupling strength of electromagnetism – encoded in the dimensionless constant $\alpha$ – is scale-dependent.

3. Linking $c$, charge and background fluctuations

In standard electromagnetism, the fine-structure constant is written as

$$ \alpha = \frac{e^{2}}{4\pi \varepsilon_0 \hbar c}, $$

with

• $e$: elementary charge,
• $\varepsilon_0$: vacuum permittivity (in SI units),
• $c$: speed of light,
• $\hbar$: reduced Planck constant.

In the LEDO-interpretation:

• $c$ is understood as the characteristic propagation speed of LEDO energy-density oscillations – set by how fast Rotons can react and reconfigure.
• $e$ reflects the effective resonance strength of a particular rotonal configuration we call the “electron”.
• $\varepsilon_0$ is reinterpreted as a measure (in SI units) of the responsiveness of the background LEDO-Field – essentially how “soft” or “stiff” the vacuum is to electric-type disturbances.

Then $\alpha$ becomes

a dimensionless measure of how strongly a single electron-scale Roton couples to the LEDO background at a given scale of vacuum fluctuations.

If the background fluctuations are scale-dependent, the effective coupling will also be scale-dependent, and $\alpha$ will not be strictly constant.

4. Running $\alpha$: scale dependence as vacuum structure

This is exactly what modern quantum field theory (QED) finds: the fine-structure constant runs with energy scale.

At atomic energies (≈ eV), one finds

$$ \alpha \approx \frac{1}{137.036}, $$

while at much higher energies (≈ 100 GeV) the effective $\alpha$ is closer to

$$ \alpha \approx \frac{1}{128}. $$

This is interpreted as vacuum polarization:

• The vacuum is filled with virtual particle–antiparticle pairs.
• These pairs screen electric charge.
• The amount of screening depends on the energy / length scale at which you probe the charge.
• So the effective charge, and therefore $\alpha$, depends on scale.

In the LEDO-language, this translates very naturally to:

The LEDO background has scale-dependent fluctuations, and different rotonal magnitudes “feel” different effective resonance strengths. The observed running of $\alpha$ then reflects how the LEDO-field structure changes with scale.

5. Included background explanation (QED viewpoint)

Below is the full background explanation on $\alpha$ and $\varepsilon_0$ in standard physics, kept for reference and comparison to the LEDO-picture.

1. Does $\alpha$ apply only to electrons and atoms?

No.
The fine-structure constant

$$ \alpha = \frac{e^2}{4\pi\varepsilon_0\hbar c} $$

is a dimensionless coupling constant of electromagnetism.
It applies to any electromagnetic interaction — electrons, muons, quarks, atoms, molecules, condensed matter, plasmas, etc.

However:

In Quantum Field Theory, $\alpha$ is scale-dependent

At higher energies (shorter wavelengths), $\alpha$ increases slightly:

• atomic scale (∼ 10 eV): $\alpha \approx 1/137.036$
• electroweak scale (∼ 100 GeV): $\alpha \approx 1/128$

This is the “running of the coupling constant.”

So:

• $\alpha$ is universal,
• but its measured value changes depending on the energy / wavelength scale.

This indeed hints at a connection to the structure of the vacuum.

2. Does this mean $\varepsilon_0$ depends on wavelength or magnitude?

This depends on interpretation.

A — In classical electromagnetism

$\varepsilon_0$ is a constant of the SI unit system.
It does not change with frequency.
It is not literally a “physical vacuum density.”

B — In quantum field theory (QED)

The vacuum is filled with fluctuating virtual particles.
These fluctuations screen electric charges.

This means:

• The effective charge $e$ depends on energy,
• → therefore $\alpha$ depends on energy,
• → but $\varepsilon_0$ stays a fixed conversion constant.

So the scale dependence is in the charge, not in $\varepsilon_0$.

C — In physical terms: $\varepsilon_0$ is not fundamental

It’s part of the SI definition:

$$ c^2 = \frac{1}{\mu_0 \varepsilon_0}. $$

But neither $\mu_0$ nor $\varepsilon_0$ have deep physical meaning in more fundamental theories.
They disappear in natural units, replaced by the real physical quantity: quantum vacuum polarization.

In this deeper view, the vacuum’s response really is scale-dependent.

So the intuition of the Rotons inertia being coupled to the scale dependent LEDO-Field background fluctiations is actually aligned with modern physics:

Vacuum fluctuations do depend on wavelength/magnitude.
They modify the effective charge, and thus $\alpha$ runs with scale.
$\varepsilon_0$ itself does not run — because it is not the physical object in the first place.

3. How does this relate to the LEDO model?

In the LEDO model:

• vacuum fluctuations = LEDO background oscillations,
• $\varepsilon_0$ corresponds to the “density” or “mobility” of the background,
• $\alpha$ is the dimensionless resonance coupling,
• running $\alpha$ = scale-dependent resonance, dependent on roton magnitude.

This maps as follows:

The LEDO model effectively interprets $\varepsilon_0$ as a scale-dependent background responsiveness, which is conceptually fine (though different from its SI role).

4. Final compact statement

Alpha applies to all electromagnetic processes, but its value changes with energy scale because the vacuum’s quantum fluctuations depend on wavelength. In standard physics $\varepsilon_0$ itself does not vary — it is a unit constant — while in the LEDO-picture we reinterpret the scale dependence as arising from the avaraged fluctuation strength and responsiveness of the LEDO background at different roton scales.