Nanopoulos and co-authors have predictions from superstring theory that are “in strong agreement with NANOGrav data.” He has been at this now for almost 40 years. See for instance Experimental Predictions from the Superstring from 1985, where the superstring predicted a top mass of 55 GeV and 360 GeV squarks.

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How many free parameters does a study like this typically involve? I recall an anecdote, I think about Fermi rejecting a paper Freeman Dyson wanted to publish. Something about with so-many parameters, “I can model an elephant wiggling its trunk.” At what point did this wisdom fall out of favor?

LMMI,

The problems with “predictions of superstring theory” go way beyond the Fermi/Dyson sort, rather point to a deeper sociological problem that is not going away.

@Low Math, Meekly Interacting

As far as I am aware, this example was rather due to John von Neumann: Von Neumann’s elephant – Wikipedia

There is a paper on this topic (also linked in the Wikipedia article) where an elephant is fitted with four parameter and a fifth parameter is used for wiggling the elephant’s trunk: Jürgen Mayer, Khaled Khairy, Jonathon Howard. “Drawing an elephant with four complex parameters”

Link to a PDF of this paper: https://publications.mpi-cbg.de/Mayer_2010_4314.pdf

@LMMI

The plot in Figure 1 involves fixing 5 free parameters (see the text after Eq 10). However, note that the action used as a starting point (Eq 1) has 3 free *functions*, so even to get to those 4 parameters multiple assumptions and simplifications have been made. On top of that even to call Eq (1) “a prediction from superstring theory” is a stretch since it is really a specific 4D low energy field theory with N=1 supersymmetry, that would have to emerge from some compactification + supersymmetry breaking; it isn’t even the most general 4D N=1 supersymmetric effective field theory you could get, but rather “Wess-Zumino no-scale supergravity” which is chosen since you can use that to construct inflation models.

To unpack that, to get from “superstring theory” to what they do in this paper, you need to postulate that Naure has made use of a compactification + partial supersymmetry breaking that reduces to a specific class of 4D low energy supersymmetric theories that are motivated by the property that they are easy to work with in an inflationary scenario. This class of theories has three free functions. By making further simplifications (again motivated by computational convenience), one assumes that these free functions can be parameterized in terms of 5 parameters. Then, for a specific range of these 5 parameters, the power spectrum has a form that people guess (but no one has checked explicitly) will form primordial black holes. (In more detail, the usual argument for producing primordial black holes is that the power spectrum crosses a certain threshold in density — but at this threshold all that happens is perturbation theory breaks down, to actually show black holes form you would need to solve Einstein’s equations nonlinearly). If you tune the parameters right, you can arrange for the energy density of these PBHs to dominate over radiation at a specific time in the Universe’s past. Under this assumption, the time variation in the Newtonian scalar potential acts as a source term for gravitational waves. Given that you’ve tuned the parameters of the model to give you the transition to PBHs at the right time and with the right abundance, this source term will generate gravitational waves in the PTA band of the right amplitude. Incidentally, the paper does not give ranges for the parameters that are consistent with data, but rather one specific set of values, which one might call a set of measure zero.

I’ll leave it to you to decide for yourself how robust this prediction is.

@Wolfgang Keller

Dyson as well (it seems): https://www.youtube.com/watch?v=hV41QEKiMlM

I’d be be curious on Peter’s take on “either you should have a clear physical model in mind or rigorous mathematical basis.”

I think that Freeman Dyson tells that story about parameters in one of the videos in https://youtu.be/rs1jGsn61p8, although I am not sure which one out of 157 🙂

IIIRC it the phrase was “With 3 free parameters I can fit in an elephant, with 4 I can make it wiggle its trunk” (I am not sure about the exact numbers).

I don’t know how many wiggling elephants, tortoises, and unicorns one can fit into 10^500 variants of a theory, but if I understand to Peter and others correctly, the problem is that none of these variants can be written down and make any predictions anyway.

Maybe that’s enough about the Fermi/Dyson/von Neumann story.

Thanks to Andrew M for the explanation, which shows that number of parameters is the least of it (there actually is no real theory, and they are effectively choosing arbitrary functional forms, so, more like infinite number of parameters).

Naively comparing end of the abstract article: “such a signal can act as a clear signature of no-scale Supergravity and Superstring theory…” with its conclusion: “it may serve as a smoking gun of Superstring theory in GW observations…” one can hopefully conclude authors/reviewers have not made fools of themselves!

Thanks a lot to connoisseurs like Andrew M for helping enthusiasts, amateurs and possibly even critics or science whistleblowers in order to appreciate the phenomen(ologic)al masterpieces regularly produced by PhDs, post-docs & tenure track profs dreaming to become full professors in our contemporary big sciences-dependent, knowledge-driven & resources-limited society.

von Neumann via Fermi. Got it! And yes, thank you most kindly, Andrew M. Given my enthusiasm for the nanoGRAV story, I actually spent some time trying to comprehend the preprint. I did get the distinct sense a lot of, uh, choices were being made, but I clearly couldn’t discern even a fraction of it. “Overfitting” doesn’t really suffice. “Bullshit”, then?

This week’s hype in the British press was the muon g-2 results from Fermilab and focused on the possibility of new physics. I was asked by my wife (who has no physics background) what new physics was likely. My amateur response as a retired engineer was that the theoretical calculations based on the existing Standard Model of particle physics are exceedingly complex and there appear to be two distinct methods of calculation which differ at present, but I personally expect them to align in a year or so with the latest experimental results.

Very interested to hear your views.

Robert Cochran,

I’ve decided it’s best to just ignore the g-2 hype, the less attention it gets the better. The underlying story is as you say, and exactly the same as last announcement: the experimental result is consistent with one version of the SM calculation, which means no evidence for new physics here.