The Chronic Incompleteness of String Theory

Ex-string theorist turned philosopher Richard Dawid has become known over the years for his arguments that string theory is a theory to be evaluated not by the conventional scientific method, in which experiment plays a role, but by “post-empirical theory assessment” methods. He has a book about this, and I’ve written about his arguments here, here and here.

Today he has a new paper out, entitled Chronic Incompleteness, Final Theory Claims, and the Lack of Free Parameters in String theory, which tries to address the “chronic incompleteness” problem of string theory’s claim to be a complete unified theory. This problem is starting to look very serious:

Rather than bringing the time horizon for the completion of fundamental physics from virtual infinity to somewhere within our lifetime, string theory’s final theory claim seems to be associated with an extension of the time horizon for the completion of this particular theory that may, once again, virtually reach towards infinity.

In other words, there’s a chronic problem of string theorists not being able to tell us what the theory actually is, and now it’s looking like they’ll never be able to do so. Dawid is right that this is the root of the problem, not usual excuses like “it predicts stuff, but you’d need an accelerator as big as the galaxy to test these predictions” or “the equations are just too hard to solve”.

One question here is that of defining what “string theory” even means anymore. Dawid does the best he can with this in a footnote:

Here as throughout the entire paper, the term ‘string theory’, if not specified otherwise, denotes the overall theory that aims at describing the observed world and is identified by the present knowledge on perturbative superstring theory, duality relations, etc.

This isn’t exactly a precise definition, it’s basically just “string theory is a conjectural theory with a certain list of properties which I’m not going to even try and describe, since that would get really complicated and different people likely have different lists”.

In the main text, Dawid explains that “string theory has no fundamental dimensionless free parameters”, a claim often made that I’ve always found kind of baffling. If you don’t know what the theory is, how do you know that it doesn’t have free parameters??? He makes a great deal of this assumption, adding in the argument that this lack of parameters means no classical limit, and I guess thus no formulation of the theory as “quantization” of something describable in classical terms.

I don’t really see what the big deal is about having a quantum system that is not defined as the quantization of some classical system. A simple example of such a system is the qubit that we often start teaching quantum mechanics with. Somehow Dawid wants to get from “not quantization of a classical system” to “we can’t ever hope to write down the theory”, but I don’t see how this follows.

He examines various possibilities for how the problem of no fundamental theory can be resolved. His alternative C is the obvious one: we just haven’t found it yet. He would like to argue that this might not be right, that string theory is a new and different kind of science:

…string theory and the conceptual context within which it is developed is in a number of ways substantially different from anything physicists have
witnessed up to this point. Therefore, it is far from clear whether prevalent physical intuitions as to which kinds of questions can be expected to have a fully calculable theoretical answer are applicable in this case. It seems
difficult to rule out that what seems to be a question that finds a fully calculable theoretical answer in fact rather resembles the case of the leaf carried by autumn winds and just defies calculation.

Dawid seems to argue that string theory may be an example of what he calls alternative A:

Even in principle, there exists no mathematical scheme that is empirically equivalent to string theory and generates quantitative results that specify the fundamental dynamics of the theory. In that case, the fundamental theory is conceptually incomplete by its very nature. It has no fundamental dynamics and no set of solutions that can be deduced from its first principles. The fundamental theory merely serves as a conceptual shell that embeds low energy descriptions (ground states of the theory) consistent with the principles encoded in the fundamental theory. Those low energy descriptions contain specified parameter values and do generate quantitative results. But there is no way to establish from first principles how probable specific ground states of the system are.

His summary of his vision of string theory is as follows:

Full access to a theory without free parameters thus might be expected to require representations that don’t have their own classical limit. The fact that they cannot be developed by generalizing away from a classical limit seems to impede the full formulation of a final theory even once one has found it. The resulting idea of a fundamental theory whose full formulation is hidden from the physicists’ grasp because its most adequate representation lacks intuitive roots has even more radical rivals, which amount to questioning the possibility of calculating the dynamics of the fundamental theory either within the bounds of human calculational power or as a matter of principle.

At one point Dawid acknowledges that some people have drawn the obvious conclusion about the current situation, the one consistent with our usual understanding of science:

It has been suggested by various exponents and observers of contemporary fundamental physics (see e.g. Smolin 2003, Woit 2003, Hossenfelder 2018) that the chronic incompleteness of string theory represents a substantial failure of the research program that is indicative of a strategical problem that has afflicted fundamental physics in recent decades.

He doesn’t like this conclusion, so argues that this time it’s different:

Considering the range and character of the very substantial differences that set the current state of fundamental physics apart from any previous stage in the history of physics, there is little reason to expect that theory building at the present stage can be judged according to criteria that seemed adequate in the past.

While he doesn’t say so, this argument takes him back to the problem of how one is to judge “string theory”, but taking a position even more radical than his earlier one. The argument now seems to be that we’re supposed to consider accepting as the final, fundamental theory of physics, a “theory” that is not just untestable, but is a “chronically incomplete” framework based on something we can never hope to define or understand. I’m having trouble understanding why this is supposed to be science rather than another human endeavor that it looks a lot more like, theology.

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12 Responses to The Chronic Incompleteness of String Theory

  1. Lee Smolin says:

    Dear Peter,

    Does Dawid not consider the context, which is that “string theory”-defined as you like, is one of several different theories, hypotheses or research programs to complete the standard model and quantize gravity and that in the end it will be evaluated by contrasting it with alternative or rival theories? This is a basic theme of philosophy of science back to Kuhn, Lakatos, and Feyerabend.

    What if an experiment confirms the hypothesis of Diosi, Penrose and others, that quantum dynamics becomes non-linear in order to disallow superpositions of macroscopically distinguishable gravitational fields? This begins to appear to be possible within a decade. To my knowledge no version of string theory predicts this, hence string theory might be simply disconfirmed, via the standard methodology of science.

  2. anon says:

    “I don’t really see what the big deal is about having a quantum system that is not defined as the quantization of some classical system. A simple example of such a system is the qubit that we often start teaching quantum mechanics with.”

    A bit of a tangent, but according to Kirillov’s orbit method, can I not regard a qubit as the quantization of the first nontrivial integral (co)adjoint orbit of SU(2)?

  3. “…string theory and the conceptual context within which it is developed is in a number of ways substantially different from anything physicists have witnessed up to this point.”

    Last time we heard from Dawid he argued that it counts in favor of string theory that the theory is *not* all that different from the physics we know up to this point. It’s what he called the “Meta-Inductive Argument.” This didn’t work, of course, because if anything that argument would count in favor of asymptotically safe gravity. Must have been inconvenient.

  4. Roger says:

    I am puzzled by Dawid’s frequent usage of “chronic incompleteness” without defining it. I see two possible definitions:

    chronic incompleteness – physicists keep trying to develop it into a meaningful theory, and keep failing.

    chronic incompleteness – it fails to make any predictions, even with complete initial data.

    The first is like “chronic pain”, and the second is just a fancy way of using time as an adjective.

  5. Even in principle, there exists no mathematical scheme that is empirically equivalent to string theory and generates quantitative results that specify the fundamental dynamics of the theory.

    Giving up on Hilbert’s 6th problem?

  6. Peter Woit says:

    Roger,
    Maybe it’s because it’s end of semester here, but to me “chronic incompleteness” brings to mind some of my students. In their case though, they almost always end up handing in something for evaluation….

  7. Peter Woit says:

    anon,
    Yes, but that kind of “quantization” isn’t what Dawid is referring to, he’s talking about systems with a “classical limit”. In the case of spin, you could try and interpret spin s as corresponding to a sphere with area proportional to s, then take as “classical limit” s goes to infinity. Then you could try and understand the qubit as the opposite spin half limit of the “classical” system at infinite spin. Dawid is quite right that this is not going to work. The point though is that we have other ways of understanding quantum systems that don’t start with a conventional classical system and our intuitions about it.

  8. Roger says:

    My dictionary defines chronic as having long duration, or recurring. Seeing “chronic incompleteness” in a semi-technical paper makes me think it means something technical, like “the initial value problem is ill-posed”, or that string theory cannot make long duration predictions. Or maybe he is just hiding string theory’s shortcomings in an opaque phrase.

  9. Amos says:

    Regarding this quote: “It has been suggested by various exponents and observers of contemporary fundamental physics (see e.g. Smolin 2003, Woit 2003, Hossenfelder 2018) that the chronic incompleteness of string theory represents a substantial failure of the research program…”

    Are those publication dates correct? I thought the Smolin and Woit books are copyright 2006. But even in the References section of Dawid’s paper, where he lists author, title and publisher, both books are listed as 2003.

    As an aside, it always seems strange to me that the Woit and Smolin books are so routinely cited as if they were the “big bang” of published skepticism toward string theory, considering that (for example) Penrose 2004 contains a highly critical/skeptical survey of the string theory program, and even discusses the sociological aspects (prestige of Witten, etc). Not to mention the critiques of Feynman and Glashow already in 1988. I suppose if the Woit and Smolin books really are 2003 they would take precedence over Penrose, but not if they were published in 2006 (as Wikipedia says).

  10. Peter Woit says:

    Amos,
    I don’t know why Dawid has those dates. The actual publication date was 2006. However it is true that my book was basically finished in 2003, when it was under consideration for publication by Cambridge University Press. For the full story, see here
    http://www.math.columbia.edu/~woit/wordpress/?p=245

    Of course it’s true that from the beginning many physicists were aware of and complaining about the problems with string theory. Most of the public such complaints I was aware of when writing in 2002 were mentioned with citations in the book.

  11. Lee Smolin says:

    Dear Amos,

    My book “The trouble with Physics” was published in 2006. No version was available before that. It was preceded by a few papers which compared different approaches to quantum gravity on purely scientific criteria,(ie no sociology), such as

    Lee Smolin, How far are we from the quantum theory of gravity?, hepth/0303185.

    but I don’t know if Dawid referred to these.

    Putting Peter and my books in 2003 rather than 2006 is a serious historical mistake, as 2003-2006 was a period of intense debate about the applicability of the athropic principle and the multiverse. My book and its reception would have been very different had it come out in 2003.

    Regarding Sabine’s comment, I argued in my review of Dawid’s book, that his three non-empirical criteria for assessing a theory were satisfied very well by loop quantum gravity, and I’d agree they are also met by asymptotic safety. This is not to make an argument for either of those theories, but to demonstrate that Dawid’s criteria are ambiguous and are of no help when one is faced with several competing theories or research programs. That is of course the present situation.

    ”String Theory and the Scientific Method. Review of a book by Richard Dawid.”, in the American Journal of Physics, 2014.

    Thanks,

    Lee

  12. Peter Woit says:

    Re Lee’s correct comment about the history, in more detail the story of my book is that the 2003 version had nothing about the multiverse/anthropics, which was a topic that only got going in 2004. The version published in 2006 did have a chapter about this, but that chapter was written in 2004-5, after I had given up on Cambridge and found another publisher. I think Lee is quite right that the nature of the 2006 debate that both of our books triggered had a lot to do with the fact that it was taking place in the context of many string theorists signing on to the idea that string theory implied a multiverse/anthropic explanation for fundamental physics.

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