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Paul Dirac gave his viewpoints on the dimensionless constant (click to see the youtube video). For example, he mentioned the fine structure constant $$ \alpha\sim\frac{1}{137}. $$

It is not clear that whether Dirac gave this presentation before or after the invention of renormalization group. But Dirac said that

"physicists think that there must be a reason for the the dimensionless fine structure constant to be this value instead of others: $ \alpha\sim\frac{1}{137}$. At present, there is no satisfactory answer for this. But with the future development, people believe that the reason will be found."

Is Dirac viewpoint still correct under the current modern physics view (in the 2021, in the 21 century)?

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  • $\begingroup$ Well, if it were very different the universe might not support carbon-based life forms, or even carbon. $\endgroup$
    – Jon Custer
    Commented Mar 5, 2021 at 0:48
  • $\begingroup$ @JonCuster - That is a reason we wouldn't see such a universe. But I think the question is what we know about reasons why it has the value ~$1/137$ instead of another value. Have we made progress? $\endgroup$
    – mmesser314
    Commented Mar 5, 2021 at 1:32
  • $\begingroup$ But 𝛼∼1/137 is a value we observe in the length scale of our measurable range. If we go to a shorter distance or the larger energy, the 𝛼 will run to a larger coupling because the QED quantum electrodynamics tells us that the 𝛼 will run. So by taking this into account, do you think Dirac comment still is valuable and valid? $\endgroup$ Commented Mar 5, 2021 at 2:05
  • $\begingroup$ According to the answers at physics.stackexchange.com/q/440211/123208 we still don't know. $\endgroup$
    – PM 2Ring
    Commented Mar 5, 2021 at 2:10
  • $\begingroup$ This is known as Dirac's large numbers hypotheses. From his youthful appearance it is clear that this photo was taken prior to RG, but I heard him him give a similar talk in the 1970s. $\endgroup$ Commented Mar 5, 2021 at 14:00

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Paul Dirac is obviously referring in this quote to the actual physical origin of the FSC and namely regarding the electron and why this value of $\sim 1/137$ and not to any effective theories as mentioned in a previous answer.

In that sense he stands correct even for today's knowledge.

Unless, someone gives analytically or algorithmically a solution to the physical origin of the FSC, meaning the most fundamental explanation of what this ratio actually physically represents in the electron, the source of the electromagnetic phenomena, which mathematically is a proportionality constant and usually refers fundamentally to geometry, the FSC physical origin is still undiscovered.

Many have tried but all have failed. The FSC $α$ seems tightly embedded to whatever intrinsic mechanics and charge flux manifold the electron particle may have. However, since the SM view of the electron is a dimensionless point massive particle there is no such thing according to the SM therefore no room left for exploration and thus a dead end. The SM simply prohibits any intrinsic mechanics for the electron. Therefore, there is nothing more to say about its origin except of deriving it from its measured intrinsic values like charge $-e$ and angular momentum but these are really not a fundamental explanation of its origin:

$$ \alpha=\frac{1}{4 \pi \varepsilon_{0}} \frac{e^{2}}{\hbar c} \approx \frac{1}{137} $$

Also, notice that at the time Dirac was referring to the FSC "mystery" the SM was not yet established although he was later on declared as one of the creators of the SM today. He was searching all his life to explain the physical origin of this Universal constant but it is ironic that his theories shaped a model that makes it impossible to explain further.

Of course there is always the Beyond the SM branch of research but this also seems to obey until now the basic axioms of the known SM and dares not to deviate theoretically unless something is proved experimentally and any other theoretical research is characterized as heretic.

However, let remind here that one of the biggest discoveries in quantum mechanics by Goudsmit and Uhlenbeck who first theorized that the electron has physical spin angular momentum which lead after to the experimental discovery of the intrinsic quantum spin (i.e. attributed as not classical in the SM) magnetic dipole moment of the electron, their theory was also initially characterized by many as a heretic view of the known at that time quantum theory but they proceeded anyway to publish their theory.

Maybe some bold researcher(s) will indeed come forward in the future as predicted by Dirac to find the origin of this very important for our Universe constant that will unlock as many argue our deeper understanding in physics.

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Is Dirac viewpoint still correct under the current modern physics view (in the 2021, in the 21 century)?

No, it's old-fashioned. A significant percentage of physicists (I can't give you a number) have a new paradigm based on the string theory landscape and eternal inflation.

In string theory there are a vast number of possible vacuum states: $10^{272,000}$, according to the Wikipedia article. They are believed to have a vast number of different values for the fine structure constant, and for all other dimensionless physical constants.

In inflationary cosmology the multiverse has a vast number of pocket universes, each in a random vacuum state.

We happen to live in a pocket universe where the fine-structure constant is approximately 1/137, the muon-electron mass ratio approximately 207, etc.

In this paradigm, pocket universes with radically different values of the fine-structure constant (and/or other dimensionless physical constants) exist, but are not capable of having physicists in them.

This viewpoint is common at the Stanford lectures and physics colloquia that I attend. The physicists who accept it would consider trying to "derive the fine-structure constant" to be laughable numerology, like trying to derive how many teeth humans have.

Leonard Susskind's 2005 book The Cosmic Landscape is a popular account of this paradigm. Susskind has been awarded the 1998 J. J. Sakurai Prize and the 2018 Oskar Klein Medal and is one of the most eminent physicists in the world. His 2003 paper “The Anthropic Landscape of String Theory” has more than 900 citations. Others associated with this viewpoint are the equally renowned cosmologists Alan Guth, Andre Linde, and Alexander Vilenkin. Peter Woit has written that

The string theory anthropic landscape point of view has now become so widely accepted and entrenched in the particle theory community that various people are making their claims about having had the idea first.

The new paradigm is highly-speculative, but entirely mainstream, physics.

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  • $\begingroup$ If there is a still-newer paradigm that I don’t know about, I hope someone will add another answer. I’m not sure whether downvotes are because what I have described is outdated, or because I have poorly described this paradigm, or because the downvoters prefer Dirac’s viewpoint that we will eventually be able to explain the values of all the dimensionless constants. $\endgroup$
    – G. Smith
    Commented Mar 5, 2021 at 5:20
  • $\begingroup$ I hear that on the east coast they still hope to find the right string theory vacuum and explain the constants that way. $\endgroup$ Commented Mar 5, 2021 at 5:51
  • $\begingroup$ @MitchellPorter Are the vacua still based on how the extra dimensions compactify? If so, can one take, say, a specific Calabi-Yau or $G_2$ space (or whatever spaces people are currently using) and actually calculate the low-energy effective theory and its constants? Or is this still something for the future? $\endgroup$
    – G. Smith
    Commented Mar 5, 2021 at 5:58
  • $\begingroup$ Something for the future, mostly. Most such calculations still rely on supersymmetry... It occurs to me that if there's an even newer paradigm, it's using "swampland conjectures" to obtain new, non-anthropic bounds on the constants. $\endgroup$ Commented Mar 5, 2021 at 6:03

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