The string wars seem to still be going on, with the latest salvos coming from Ashtekar and Witten. In a very interesting recent interview, at the end Ashtekar has some comments about string theory and how it is being pursued. About claims that string theory is the only possible way to get quantum gravity he says:
I don’t know why science needs such statements; indeed, scientists should not make such statements. Let the evidence prove that it’s the only theory. Let the evidence prove that it is better than other theories or let its predictions be reproduced more than those of others. Science should not become theology. And, somehow such statements have a strong smell of theology, which I don’t like.
About AdS/CFT and the current state of its relation to quantum gravity:
We seem to be using these gravity ideas in other domains of physics rather than solving quantum gravity problems. I don’t think that the quantum gravity problems have been solved. And I have said this explicitly in conferences with panels – in which Joe Polchinski, Juan Maldacena and I were panellists – that, in my view, this is very powerful and these are good things. However, the AdS/CFT conjecture is the only definition of non-perturbative string theory one has – and it’s a definition, it’s not a proof of anything. It talks about duality, but there’s no proof of duality. To have a duality, A should be well defined, B should be well defined and then you say that A is dual to B. Since we don’t have another definition of string theory, we cannot hope to prove that string theory is dual to its conformal field theory. You can define string theory to be the conformal field theory. You have to construct a dictionary relating string theory in the bulk and conformal field theory on the boundary. That dictionary has not been constructed in complete detail.
Again, nobody is taking anything away from the successes that the AdS/CFT duality has had; but there is a big gap between the successes and the rhetoric. The rhetoric is at a much higher level than the successes. So, for example, in this conjecture, first of all the space-time is 10 dimensional. The physical space-time is supposed to be asymptotically anti-de Sitter, which has a negative cosmological constant. But we look around us, and we find a positive cosmological constant. Secondly, the internal dimensions in the conjecture, or this definition, are macroscopic. The Kaluza-Klein idea is that there are higher dimensions but because they are all wrapped up and microscopic, say, at Planck scale, we don’t see them. That’s plausible. But here, in AdS/CFT duality, they need the radius of the internal dimensions to be the same as the cosmological radius. If so, if I try to look up I should see these ten dimensions; I don’t. So, it can’t have much to do with the real world that we actually live in. These are elephants in the room which are not being addressed.
… there are these obvious issues and practitioners just pretend that they don’t exist. And that to me is unconscionable; I feel that that’s not good science. I don’t mean to say string theory is not good science, but publicizing it the way it’s done is not good science. I think one should say what it has done, rather than this hyperbole.
A good example of the problems Ashtekar is concerned about is provided by an article in the latest Physics Today by Witten with the title What Every Physicist Should Know about String theory. It’s devoted to a simple argument that string theory doesn’t have the UV problems of quantum field theory, one that I’ve seen made by Witten and others in talks and expository articles many times over the last 30 years. This latest version takes ignoring the elephants in the room to an extreme, saying absolutely nothing about the problems with the idea of getting physics this way, even going so far as to not mention the first and most obvious problem, that of the necessity of ten dimensions.
The title of the article is the most disturbing thing about it. Why should every physicist know a heuristic argument for a very speculative idea about unification and quantum gravity, without at the same time knowing what the problems with it are and why it hasn’t worked out? This seems to me to carry the “strong smell of theology” that Ashtekar notices in the way the subject is being pursued.
Witten is a great physicist and a very lucid expositor, and the technical story he explains in the article is a very interesting one, with the idea that most physicists might want to hear about it a reasonable one. But the problems with the story also need to be acknowledged and explained, otherwise the whole thing is highly misleading.
Besides the obvious problems of the ten dimensions, supersymmetry, compactifications, the string landscape, etc. that afflict attempts to connect this story to actual physics, there are a couple basic problems with the story itself. The first is that what Witten is explaining as a problematic framework to be generalized by string theory is not quantum field theory, but a first-quantized particle theory, with interactions put in by hand. This can be used to produce the perturbation series of a scalar field theory, but this is something very different than the SM quantum field theory, which has as fundamental objects fields, not particles, with interactions largely fixed by gauge symmetry, not put in by hand. For such QFTs, there is no necessary problem in the UV: QCD provides an example of such a theory with no ultraviolet problem at all, due to its property of asymptotic freedom.
Another huge elephant in the room ignored by Witten’s story motivating string theory as a natural two-dimensional generalization of one-dimensional theories is that the one-dimensional theories he discusses are known to be a bad starting point, for reasons that go far beyond UV problems. A much better starting point is provided by quantized gauge fields and spinor fields coupled to them, which have a very different fundamental structure than that of the terms of a perturbation series of a scalar field theory. A virtue of Witten’s story is that it makes very clear (while not mentioning it) what the problem is with this motivation for string theory. All one gets out of it is an analog of something that is the wrong thing in the simpler one-dimensional case. The fundamental issue since the earliest days of string theory has always been “what is non-perturbative string theory?”, meaning “what is the theory that has the same relation to strings that QFT has to Witten’s one-dimensional story?” After 30 years of intense effort, there is still no known answer to this question. Given the thirty years of heavily oversold publicity for string theory, it is this and the other elephants in the room that every physicist should know about.
Update: For another take on string theory that I meant to point out, there’s an article quoting Michael Turner:
Turner described string theory as an “empty vessel,” and added: “the great thing about an empty vessel is that we can put our hopes and dreams in it.”
The problem is that the empty vessel is of a rather specific shape, so only certain people’s hopes and dreams will fit…
Update: Many commenters have written in to point out this article, but I don’t think it has anything at all to do with the topic of this posting. There are lots of highly speculative ideas about quantum gravity out there, most of which I don’t have the time or interest to learn more about and discuss sensibly here.
Update: It is interesting to contrast the current Witten Physics Today article with a very similar one that appeared by him in the same publication nearly 20 years ago, entitled Reflections on the Fate of Spacetime. This makes almost the same argument as the new one, but does also explain one of the elephants in the room (lack of a non-perturbative string theory). It also includes an explanation of the T-duality idea that there is a “minimal length” in string, an explanation I was referring to in the comment section when describing what I don’t understand about his current argument.
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