i wont now either affirm or deny,

but indicate that h is hidden in alfa.

Siggest you replace alfa by its definition.

This equation E = e2/ 2ε₀αλ that allows calculating the energy of any localized photon from its wavelength without using Planck's constant, and which is derivable from numerous standard physics equations as explained above, also allows calculating the invariant rest mass of the electron if the wavelenth used is the electron Compton wavelength:

me=E/c2=e2/2ϵ0αλCc2=9.10938188E-31 kg

as explained in this paper published in 2013:

Article Unifying All Classical Force Equations

I wont argue with your formula,

Only with some of your historic tales.

They suddenly end in the past, or only with paul marmet.

But it probably would take too much historical research.

Dear Dr. André Michaud

Your proposal to derive the energy of a photon as:

E = (e²) / (2 ε₀ α λ)

is both interesting and methodologically coherent within the electrostatic framework you develop from Biot–Savart and Coulomb principles.

That said, I would like to offer a few observations from a quantum field standpoint.

While your formulation bypasses Planck’s constant explicitly, it remains implicitly embedded via the fine-structure constant,

α = e² / (4 π ε₀ ħ c).

So, when expanded, your expression still contains ħ (or h), albeit in composite form. In that sense, the quantization is redistributed algebraically, not fully eliminated.

Moreover, using static Coulomb-derived relations to define photon energy raises interpretational challenges. The photon is not a classical system of charges separated by distance d, but a massless, relativistic excitation of the quantized electromagnetic field. Associating its intrinsic energy with electrostatic-like charge interactions may require redefining our assumptions about photon localization or internal structure.

That said, the philosophical direction you take is meaningful. Suggesting that constants like h might emerge from deeper coupling relations — rather than being axiomatically fundamental — is an idea worth exploring. It resonates with developments in quantum geometry, emergent gravity, and alternative unification models.

If your formalism can be extended to demonstrate independence from ħ even after full decomposition of α, or if it yields testable deviations from conventional QED predictions, it would provide a compelling framework.

Thank you for initiating this stimulating discussion. I look forward to continuing the exchange.

Replacing alfa also gets rid of e^2, totally changing things.

You merely express a photon energy in coulomb energy terms, with lambda in place of d.

This does not necesarily have physical meaning.

Adam D. Nasser

Dear Adam,

Note that I do not have a doctor's degree,so I do not deserve this title.

Simply calling me André will be fine.

Thank you for your so constructive comments.

About your specific comment: "While your formulation bypasses Planck’s constant explicitly, it remains implicitly embedded via the fine-structure constant,"

Note that it is the entire equation E = (e²) / (2 ε₀ α λ) which is exactly equivalent to E=hf

Since not only α but each other constant of the equation can be isolated on the left side, don't you think that the same reasoning could be applied to any of them also?

That h is also part of e and of ε₀ ?

If you study closely the manner in which it was first derived in the 2007 paper, maybe you may come to a different conclusion:

Article Field Equations for Localized Photons and Relativistic Field...

Note also from the presentation of this discussion that it can also be derived from the standard Coulomb equation in which neither h nor the fine structure constant appear, and the same can be said of the Biot-Savart equation in the above referred paper.

You wrote: " Moreover, using static Coulomb-derived relations to define photon energy raises interpretational challenges. "

It does indeed. The standard Coulomb equation measures the force between charged particles that are physically separated and move separately in space as we well understand, and also allows calculating the energy induced in each of these charges as a function of the inverse of the distances separating them.

I invite you to study the de Broglie double-particle photon structure, to visualize more clearly how it may really describe truly localized photons involving 2 captive varying charges:

Article De Broglie’s Double-Particle Photon (Expanded republication PI)

In the classical Coulomb equation distance d is the physical distance separating 2 charged particles, for example.

What is new about this version of the Coulomb equation E = (e²) / (2 ε₀ α λ) is the introduction in replacement of spatial distance d by the electromagnetic transverse amplitude A= α λ/2π of oscillation of the 2 charges of the de Broglie double component E-field of the electromagnetic inner structure of the particle, that are symetrically captive of each other, related by the displacement current conceived by Maxwell on a plane perpendicular to the direction of motion of the particle in space.

His displacement current found no place in his wave theory eventually, but in localized quanta as conceived by de Broglie in the 1930's, it finally finds its proper usage.

α is a ratio. It is the ratio of the transverse electromagnetic amplitude of oscillation of the particle's energy on a plane perpendicular to the direction of motion of the particle over the classical longitudinal amplitude of the wavelength of the particle: A / (λ/2π)

You wrote: "That said, the philosophical direction you take is meaningful. Suggesting that constants like h might emerge from deeper coupling relations "

Yes. It can be shown that h emerges directly from electromagnetism and is not only a measured constant. See equations (2) and (3) in this paper:

Article The Last Challenge of Modern Physics: Perspective to concept...

You wrote: " If your formalism can be extended to demonstrate independence from ħ even after full decomposition of α, or if it yields testable deviations from conventional QED predictions, it would provide a compelling framework."

Note that there is likely to be some divergence with QED, since QED does not recognize a specific function to the local B-field, that plays an equally important function in electromagnetic mechanics to that of the local E-field, since the energy of a particle oscillates between these two modes at each cycle.

Dear André Michaud ,

Thanks again for such an insightful and generous reply. I really appreciate how open your framework is, and the clarity with which you lay out alternatives to the conventional dependency on Planck’s constant.

Now, coming back to the core equation you’re exploring:

E = e² / (2 ε₀ α λ)

Your point about h not being explicitly needed because it’s embedded in α is definitely fair. And when we unpack α from its standard definition:

α = e² / (4 π ε₀ ħ c)

—we can see that ħ (and h) is still technically there, even if indirectly. But what makes your take interesting is that you seem to be asking a deeper question: do we need to treat h as fundamental? Or is it just a derived result of deeper relations between constants?

That opens a big door. Because it pushes us to rethink whether h is really a foundational block of nature—or if it might emerge from more fundamental ratios or couplings in electromagnetism or field structure. This resonates with ideas from emergent gravity and some topological quantum theories, where constants aren’t inserted but arise from constraints.

I also see the beauty in replacing d with something like α λ / 2π, from the transverse oscillation in de Broglie’s photon model. It’s a bold move that links localization and energy geometry in a tight way. Still, I do wonder if such substitution fully captures photon behavior under relativistic conditions. Because even if the energy math works, the physical meaning might still need some care—especially since photons are not just charged bits but field excitations with quantum behavior.

But again, what you’ve done here isn’t just numerical consistency—it’s a conceptual challenge. If the results match experiments without relying on h explicitly, that says something big. Maybe we’ve taken h as a primitive too quickly, when it could be a result of a deeper configuration.

And if your equations do succeed in pulling h straight from electromagnetic mechanics—rather than assuming it—that’s a huge conceptual win. It means constants might not be fundamental “givens,” but consequences of how fields interact.

I don’t see any of this as contradiction, honestly. More like parallel roads trying to lead to the same mountain peak. Yours just takes a less traveled and very creative path.

personal note to André Michaud ,

When you mentioned that you don’t consider yourself deserving of the “Dr.” title, that honestly struck me. In a field where names and degrees often speak louder than ideas, your response was a rare reminder that true scientific value comes from clarity, consistency, and humility—not from what letters follow our names. That kind of integrity is what gives science meaning. It’s an honor to learn from someone who puts the work above the title.

Adam D. Nasser

Dear Adam,

You wrote: " Your point about h not being explicitly needed because it’s embedded in α is definitely fair. And when we unpack α from its standard definition:"

OK with me if you draw this conclusion. I just remind you that h is explicitely taken out of the left side of the relation by moving it to the right side during the establishment of the right side term: E=hf = e2/ 2ε₀αλ, so hf becomes the equivalent of e2/ 2ε₀αλ.

You wrote: " That opens a big door. Because it pushes us to rethink whether h is really a foundational block of nature "

Note that h is definitely still needed, because photons emitted by de-exciting electrons in atoms are always quantized as multiples of h by structure, due to the resonance relation that de Broglie discovered and published in his 1924 thesis, as he established that the Lyman series obeys a clear integer series, with integer 1 corresponding to the Bohr radius orbital, and 2, 3... corresponding to the diminished multiples of the frequencies related to the further away matastable orbits of the Bohr atom.

It turns out that all photons frequencies emitted by all atoms also are quantized resonance multiple of h.

Put in clear perspective in these two papers:

Article Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Article Electromagnetic and Kinematic Mechanics Synchronized in thei...

The potential use of the new equation that doesn't need h is that after any quantized photon emission, each photon is subject to "infinitesimally progressively" increase its energy by nearing a large mass (blue shift), or just as progressively diminish its energy by moving away from a large mass (red shift). In such cases, the wavelength will just as progressively vary, with no notion whatsoever of having to diminish or increase by h increments or multiples.

But this new equation turns out to be only a minor feature of electromagnetic mechanics. What is major and that it allowed to develop are the general equations of the oscillating local E and B fields that animate half of the energy of any photon.

If you dig eventually deeper into the model, you will progressively become familiar with all the other benefit of this integration.

If this can help your study, since you seem to have developed an interest for the model, all papers published since year 2000 are directly linked from this index:

Article INDEX -Electromagnetic Mechanics (The 3-Spaces Model)

You wrote: "When you mentioned that you don’t consider yourself deserving of the “Dr.” title, that honestly struck me. In a field where names and degrees often speak louder than ideas, your response was a rare reminder that true scientific value comes from clarity, consistency, and humility—not from what letters follow our names. That kind of integrity is what gives science meaning. It’s an honor to learn from someone who puts the work above the title."

I mean that I don't deserve the Dr. title simply because I never graduated as such. I am a pure blood outsider. Whenever people assume that I have this degree, I always inform them that I don’t, so that no embarrassing misunderstanding eventually develops.

Editors in particular who invited me to publish all of my papers, except the first about the first wave of derivations from Marmet's discovery, systematically assumed that I had this title. I always immediately informed them of the contrary to avoid any misunderstanding about this.

Thank you for your appreciation. Note that I did not write this series of papers to impress the formal community. Only so that electromagnetic mechanics becomes referred to again after 120 years of neglect, since it was left on the way side as SR was adopted in 1907.

Prof. Halim Butayeb will talk electromagnetism on youtube today

Dear all,

I’ll be live on YouTube this Saturday, May 24 at 10:00 AM (Ottawa time) to discuss computational electromagnetism with moving matter.

I will explain why I now consider the theory of relativity a blessing: it has led scientists to waste time on metaphysics; in doing so, it has left a vast, largely untouched branch of science where meaningful contributions can now be made

📺 Link to join: https://www.youtube.com/live/32ATuRxa-5o?si=eTDiezmtOF0HTKyx

Feel free to join and bring your questions!

Best regards,

Halim