It's remarkable, after almost 50 years of the Standard Model, the fine structure constant-the coupling of charged particles to the electromagnetic field at the scale of atomic physics-still leads to essays in numerology. (In comparison, the weak coupling constants or the strong coupling constant don't seem to provoke comparable mystical claims).

The fine structure constant isn't a constant and that's been understood for more than 50 years. That it has a ``small'' value, approximately 1/137, at atomic scales, that rises logarithmically with the energy scale, allows perturbation theory about free fields to be a very good approximation for describing natural phenomena at a very wide range of scales, relevant for applications.

The coupling between the electromagnetic field and point particles doesn't have anything to do with string theory-how to couple strings to the electromagnetic field is, however, known.

While the RG flow for the fine structure is known in perturbation theory, the value at any given scale doesn't matter, what matters is that it remain small for perturbation theory to be useful; it's the fixed point of the flow that really matters. That fixed point is't known, in fact, since its existence is inconsistent with perturbation theory (this was noticed first by Landau and called the ``Landau pole'').

How to use Feynman rules and Feynman diagram to perform calculations is known and doesn't have anything to do with point 3); it would be useful to actually study QFT before making statements that are, unfortunately, meaningless.

The Borwein integrals have meaning in mathematics; whether they have any meaning for QFT and, if then, any usefulness, for calculating the quantities that are of interest, must be shown, not proclaimed.

Dear Stam Nicolis Thanks about the input. The appearance of this constant in various aspects of particle physics is undeniable, from the energy differences between electrons in the same orbital to other fundamental interactions. It seems to be an inherent and fundamental relation governing particle behavior.

Consider, for instance, the interaction between two electrons in the same orbital, mediated by the exchange of photons—a concept elegantly depicted in Feynman's diagrams. These diagrams, rooted in quantum mechanics, derive from Lagrangian and Hamiltonian principles. In the progression from Newtonian mechanics to Einstein's general relativity, we observe a shift from the minimization/maximization of action with respect to time to a consideration of "proper time." Quantum mechanics takes this abstraction even further, introducing a complex interplay of time and space.

As we delve into the intricacies of particle physics, it becomes apparent that the deeper layers of understanding may reveal that time and space are not elemental but emergent phenomena. This notion aligns with the principles of string theory, a framework I find particularly appealing. Particles such as bosons emerge when their associated fields are excited at the right energy levels—a phenomenon recently exemplified by the discovery of the Higgs boson.

My line of reasoning prompts me to question the nearly mystical appearance of 1/137 in various quantum situations. While it's not precisely 1/137, could the Heisenberg Uncertainty Principle play a role in this deviation?

I invite you all to share your thoughts on this matter. Let's explore the profound connections between the fine structure constant and the underlying principles of particle physics. There may be no right or wrong answers, but our collective insights could lead to a deeper understanding of the fundamental nature of the universe.

Thank you for your time and consideration.

Best regards,

Of course its presence is ``undeniable'', it's the coupling constant of electrically charged particles to the electromagnetic field. But 1/137 isn't of any particular significance as such.

Hmmm, it's significance is a subjective matter to be honest. Feynman himself fancied about that number.

Its significance doesn't have anything to do with its numerical value at any particular scale. Its dependence on the scale is what matters. And that was only appreciated in the late 1970s. Whether Feynman or anyone ``fancied'' about its numerical value doesn't matter.

Dear Colleagues,

I hope this message finds you well. I would like to share some thoughts that originated from an engineering analysis perspective, akin to what is commonly known as Phi Analysis. When faced with a complex engineering problem, especially one where the underlying physics is not fully understood, engineers often resort to correlations. These correlations, derived through Phi analysis, may not precisely represent the actual physical equations but serve as valuable starting points.

My attention turned towards Borwein Integrals for the following reasons:

I acknowledge the speculative nature of these ideas, and I invite you to view this as a starting point for open discussions. Your insights and suggestions are invaluable as we explore unconventional paths that may lead to innovative perspectives in understanding unknown physics.

Thank you for your time, and I look forward to our collaborative exploration.

Best regards,

Borweins' article is found here for free: https://carmamaths.org/resources/db90/pdfs/db90-119.00.pdf

Fine Structure Constant at higher energies:

Accounting for the value of the fine structure constant at high energies which could be around 1/127, I would say that at higher energies, waves of higher frequencies/energies can emerge and be a dominant factor thus changing the value of the fine structure constant known to be around 1/137. This is perfectly fine with string theory, where strings can vibrate at higher energies. String theory predicts supersymmetry, that is particles do have their partners, and it is believed that these supersymmetric particles are found at higher energy levels that are not reachable by CERN. These is aligned with that change in the fine structure constant, when higher energies are reached then other particles emerge and their probability is no longer negligible affecting the value of the fine structure constant, this is related to the Feynman Diagrams, when these new particles affect the interactions. In addition, I have found a software that is called Mathematica by Wolfram ( https://www.wolfram.com/resources/physics/), for scientists fond of these topics but not the mathematical strength to develop these ideas into mathematical models, I recommend employing Mathematica, propose different hypothesis until you get 1/127 and 1/137 range.