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)?

  • $\begingroup$ Well, if it were very different the universe might not support carbon-based life forms, or even carbon. $\endgroup$ – Jon Custer Mar 5 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 Mar 5 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? $\endgroup$ – annie marie heart Mar 5 at 2:05
  • $\begingroup$ According to the answers at physics.stackexchange.com/q/440211/123208 we still don't know. $\endgroup$ – PM 2Ring Mar 5 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. $\endgroup$ – Lewis Miller Mar 5 at 14:00

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.

  • $\begingroup$ 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 Mar 5 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. $\endgroup$ – Mitchell Porter Mar 5 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 Mar 5 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. $\endgroup$ – Mitchell Porter Mar 5 at 6:03

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