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  Why is the fine structure constant roughly 1/137? Conjectures?

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At low energy, the fine structure constant is 1/137.03...  Dirac called the search for an explanation a big problem and so far nobody knows where the value comes from.

But surely, there must be some conjectures on what determines the number? Is the number due to some hidden structure of electric charges? Is it due to some hidden structure of photons? Is it due to some hidden process details during photon emission or absorption?

Are there any ideas that are serious (non-numerological!) on its origin? Google scholar does not yield much. Are there any ideas that circulate only from mouth to mouth?

asked Dec 13, 2022 in Open problems by Otto [ revision history ]
edited Dec 14, 2022

Thank you - I did not know those. Probably all three are wrong, but at least they tried. Chapeau!

3 Answers

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The only plausible conjection is a fluke.

answered Dec 16, 2022 by Vladimir Kalitvianski (102 points) [ no revision ]

There is no experimental hint for this conjecture, and no argument why this should be "plausible".

All history of theoretical physics is an attempt to describe numerically this or that experiment. One can construct plenty of dimensionless constants in physics, but they may have a physical meaning only if they are encountered in meaningful calculations.

$1/\alpha$ is not an integer, so there is no a real mistery here. $c/v_0$ is not obliged to be an integer.

$\alpha$ never comes alone in calculations, but always it is accompanied with other physical variables (as a product). Only together they have some meaning.

Take another atom - with another nucleus charge Z, and the ground state *characteristic* velocity $v_0 (Z)$ will be different. Take an excited Hydrogen state $|n,0,0\rangle$, and the corresponding *characteristic* velocity $v_n$ will be different, so you can obtain many dimensionless ratios, as a matter of fact.

No part of this bizarre text has any relation to the question, or even to the proposed answer. 

@Otto: If you mean "hidden structures" mentioned in your question, then no, my text has no relation to them. I reason in terms of the Sommerfeld clear interpretation who first obtained this famous number. Your "Why" question is simelar to "Why $\pi$ is roughly 3?".

But we know why pi is roughly 3 - and we do not why alpha is roughly 1/137. The question is: why could it have this value?

Yes, we know exactly why - in the both cases they are experimental data.

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Well, I don't think that "fluke" is the right word for it, more as "arbitrary".

Anyway, even if you'll get an answer it will just raise more questions.

My QFT 1 and 2 teacher said that 137 is in gimmetria the word for "Kabbala" (in Hebrew: "קבלה").

But he looked to me  to be a little MAD... :-D

answered Dec 18, 2022 by MathematicalPhysicist (200 points) [ no revision ]

1/137 is arbitrary? Hm, what is the evidence for this statement?

Of course, it is not arbitrary - it is calculated from some measured data within some theoretical models.

By arbitrary I mean that we extract it from experiment.

We might as well ask about other physical constants why they have the values they have, it's just the way it is.

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My answer is "probably", if your question is what I think it is: Does the fine structure constant have a pure numerical origin? But if so it has not been found, and if you find it you'll be very famous, as such pure math origin would shed light into how the physical constants the fine structure constant was measured and calculated from relate to each other.

answered Jan 7, 2023 by dan watkins [ no revision ]

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