Over the last twenty years there has been an endless stream of hype about “tests of string theory”, pretty much all of it complete nonsense. For some examples just from the first few months of this year, see here, here, and here. Most of these examples seem to have been generated by confused PR people who misunderstood carefully worded comments by various physicists about the relation of their work to string theory. The average person just finds it hard to believe that it really could be true that there is no way to test a theory that has gotten so much attention for so long from so many prominent people.
Today there’s new nonsensical hype about testing string theory, but this time it’s due not to a clueless press relations person, but to several physicists, including the one who decides what gets into the hep-th arXiv and what doesn’t. The hype isn’t buried in the article somewhere, it’s in the title: Falsifying String Theory Through WW Scattering. In their abstract, the authors claim to derive a bound on coefficients of operators in the effective electroweak Lagrangian such that “a measured violation of the bound would falsify string theory.”
The first striking thing about this paper that purports to show that string theory is falsifiable is that there’s actually nothing about string theory in it. It’s only four pages long, and the first three pages consist of an introduction followed by some calculations in the non-linear sigma model one might want to use as an effective low-energy theory of pions. This is just a warm-up exercise for the real calculation that the authors want to make some claims about, which involves the low energy effective action for a non-linear sigma-model coupled to gauge fields. This is the model that one expects to describe the low-energy behavior of the Higgs field coupled to electroweak gauge fields, if one takes the Higgs mass to be very large.
The authors go on to just copy the terms in the relevant Lagrangian down from a 1993 paper by Appelquist and Wu, then stop and promise to actually calculate the relevant bounds in a forthcoming paper. Unless one wants to try and sit down and do oneself the calculation the authors haven’t done yet, it’s hard to know what these bounds will actually say and whether they will really be non-trivial. It’s also unclear to me exactly how all of this depends on the Higgs mass, which I guess is being assumed to very high, thus violating the known indirect experimental bounds from precision electroweak measurements (which assume the standard model). Very hard to tell about any of this, since it’s dealt with in a paragraph with no equations.
It turns out that the author’s proposal isn’t a proposal to falsify string theory at all, but a proposal to falsify the idea that physics satisfies Lorentz invariance, analyticity and unitarity at high energies. This would falsify our standard ideas about QFT, but it wouldn’t falsify current ideas about string theory. The authors don’t define what they mean by “string theory”, but presumably they mean some version of perturbative string theory. This involves a divergent series (even granting the conjecture that one can make sense of these amplitudes at more than two loops), so it’s unclear how one is going to “falsify” that. Standard ideology about non-perturbative string theory (“M-theory”) is that it will involve some new ideas about space and time, so I don’t see how one can assume that it won’t violate the analyticity and Lorentz invariance properties characteristic of QFT in flat space-time. I’m not convinced that the author’s proposal will falsify anything, but if it does, it will be QFT that is falsified, not string theory. After all, this paper is a QFT calculation (or, more accurately, a promise to do a QFT calculation), not a string theory calculation.
The authors note the problems of non-predictivity generated by the Landscape, and in the first version of the paper write:
Moreover, even if it is found to be difficult to generate the proper model from string theory, one would sooner accept the notion that it is the theorist’s imaginations which are insufficient than conclude that string theory has been falsified.
In the second version of the paper, they seem to realize that this attitude of “one” is kind of unscientific, and they change it to
Moreover, even if it is found to be difficult to generate the proper model from string theory, some would sooner accept the notion that it is the theorist’s imaginations which are insufficient than conclude that string theory has been falsified.
This new version leaves it unclear who this unscientific “some” is. In both versions they note correctly that:
This line of reasoning has resulted in sharp criticism of the theory.
This paper is motivated by the “swampland” program of trying to find effective field theories that can’t be the low energy limits of a string theory. I’ve written about the problems with this elsewhere, and blog postings by Distler have amply embodied what some of them are. In his first posting on the Swampland he gave as an example of a low energy effective theory that couldn’t come from string theory one with only one or two generations, only to be told by a commenter how to construct such things from string theory. He has a more recent blog posting called Avatars of Nonlocality? about the swampland work of Arkani-Hamed and collaborators that motivated this new paper. In a comment there, Arkani-Hamed takes him to task:
This post is a great illustration of what I dislike about blogs and more specifically trackbacks. As I explained to you when you were visiting Harvard last week, your first point about the RG running is standard effective field theory (with an abbreviated discussion in our paper because it is fairly common knowledge–read Georgi’s book). I of course don’t object to your writing a paper to clarify these points to yourself or others. But this is minor. More importantly, as I also explained to you both in email and in person, what you write about the DGP model is totally wrong…
Now, in general I don’t care about what is said on blogs, as I believe they largely fulfill the primate desire to look and see what the other monkeys are doing, and I think they are a big waste of time. But I do object to having a trackback, linked from my paper, to a post about it that claims that one of the central claims is wrong, when a 45 second computation, even done for the reader’s convenience in the paper itself, refutes the argument.
This whole subject really is a swamp, if you ask me, and has nothing at all to do with physics, including nothing to do with the supposed “falsifiability of string theory”. It will be interesting to see if a referee thinks otherwise.
Update: It has been pointed out to me that I’m being a bit unfair to the authors in characterizing the calculation in this paper as a “warm-up exercise”, since they claim that it is a correct first approximation to the actual calculation that they intend to do.
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