Counting String Theory Standard Models

I saw a paper on the arXiv and couldn’t resist a (snarky) comment. Here is the abstract:

We derive an approximate analytic relation between the number of consistent heterotic Calabi-Yau compactifications of string theory with the exact charged matter content of the standard model of particle physics and the topological data of the internal manifold: the former scaling exponentially with the number of Kahler parameters. This is done by an estimate of the number of solutions to a set of Diophantine equations representing constraints satisfied by any consistent heterotic string vacuum with three chiral massless families, and has been computationally checked to hold for complete intersection Calabi-Yau threefolds (CICYs) with up to seven Kahler parameters. When extrapolated to the entire CICY list, the relation gives about 1023 string theory standard models; for the class of Calabi-Yau hypersurfaces in toric varieties, it gives about 10723 standard models.

Isn’t  10723 also the number of angels that can dance on the head of a pin? That number of models for the price of one theory looks like a bargain to me!

But, seriously, people often complain that string theory isn’t really scientific because it isn’t predictive. That clearly isn’t true. String theory is the most predictive theory ever: it can predict anything you want!



10 Responses to “Counting String Theory Standard Models”

  1. Anton Garrett Says:

    “Faith is the substance of things hoped for, the evidence of things not seen.”

  2. Anton Garrett Says:

    “String theory is the most predictive theory ever: it can predict anything you want!”

    It has some way to go to match economics, though…

  3. Admittedly I don”t know that much about it, butI think that it is true that string theory has a diifult stand because of lack of testable predictions. However, that is distinct from the case mentioned above, which involves the string-theory “landscape”. One might as well say that Newtonian theory is useless because Earth is not unique, but rather there is an astronomically large number of possible planets. 😎

    Indeed, it might be that the theory-of-everything approach which would explain the values of all constants of nature and so on (though of course not “everything” in a practical sense) is doomed and that the multiverse, in some cases (not all) in combination with the anthropic principle, might be a better explanation (in the non-anthropic cases perhaps there is a probability argument for some parameters, but some might be just chance). Kepler’s mathematical theory of the relative distances of the planets was wrong; the correct answer is much more akin to the application of the anthropic principle to the multiverse.

    This doesn’t mean that there can be no ultimate explanation, but the burden of proof is on those who believe that there is to come up with such a theory. 🤓

    One can of course have the multiverse as a hypothesis, just as people could (and did) imagine a plurality of worlds before others were discovered, but it would be more convincing if the multiverse were the outcome of some theory, which could be the case if string theory does hold up, with the landscape essentially being the multiverse.

    • Anton Garrett Says:

      Nobody should be satisfied with a situation in which we cannot predict which of two recorders attached to a Stern-Gerlach apparatus will be triggered by the next electron. Perhaps if that question is addressed, the horrendous complexities of string theory will become superfluous.

      • Perhaps, but, again, where is the burden of proof?

      • Anton Garrett Says:

        Proof of what proposition/claim/hypothesis? I don’t understand your comment. The aim of science is to improve testable prediction.

      • I mean that it is one thing to complain that one doesn’t like what one observes in the Stern-Gerlach experiment, and quite another to come up with some better theory, which of course must fit all observations. Similarly, it does seem that the anthropic principle and/or the multiverse is the best explanation for some observations. “I just don’t like it” is not a valid objection; one needs to present a better explanation.

      • Anton Garrett Says:

        That it is not easy to come up with a hidden variable theory is no demonstration that one doesn’t exist. It took a few centuries from Aristotle to Galileo as I recall.

        The multiverse would fall in that case as it is based on quantum theory. The anthropic principle, done correctly, is fine (too often it isn’t done correctly), but it is not physics; rather it is an ontological explanation in an area other than physics.

    • telescoper Says:

      A Theory of Anything is not the same as a Theory of Everything.

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