Frequently Asked Questions

Circularity problem:

Since you can’t observe anything about it directly, the multiverse must be justified in terms of another theory that can be tested and this is string theory. But if you talk to string theorists these days about how they’re going to test the unified theory that string theory is supposed to provide, their answer is that, alas, there is no way to do this, because of the multiverse. You see, the multiverse implies that all the things you would think that string theory might be able to predict turn out to be unpredictable local environmental accidents.

So, the multiverse can’t be tested, but we should believe in it since it’s an implication of string theory, but string theory can’t be tested because of the multiverse.

This has become probably the most common argument made by string theorists when string theory is criticized for being non-predictive. When I first heard it, my reaction was that this was a joke. How could anyone seriously try to claim that the predictivity situation of the SM quantum field theory (our most successful fundamental theory of physics, which makes a wealth of detailed, accurate, tested predictions) and string theory unification (a theory that predicts nothing) was the same? There’s obviously some sort of sophistry going on here, an attempt to claim that white and black are much the same, since they’re both shades of gray.

QFT is successful because it includes a specific class of theories that have a lot of symmetry, and a very tight mathematical structure. Making a few of the simplest possible choices for theories in this class, you get the SM, with a huge amount of very non-trivial, highly testable predictions, all of which have turned out to work perfectly. Yes, it’s true that you could instead look at extremely complicated examples of QFTs, making them so complicated that you would lose predictivity and start to get something more like string theory. This is true of just about any theoretical set-up, you can make it worthless by adding in complexity until it gets to the point that it will fit anything, while explaining nothing.

That’s the problem with string theory unification schemes: you have to put more into them than you get out, the hall-mark of a failed idea. Here’s an old comment that goes the problem in more detail:

http://www.math.columbia.edu/~woit/wordpress/?p=4065&cpage=1#comment-98564

If you can find out the answer to this question, please let me know. On rare occasions a trackback to one of my postings will appear there, but in general it seems to be arXiv policy to not allow such trackbacks. Way back when during the string wars Jacques Distler did publicly announce a policy designed to exclude links to bloggers that he decided were not “active researchers”, but for years now trackbacks to all sorts of news sources having nothing to do with “active researchers” have been appearing, while NEW is still banned for some reason no one will tell me.

Update (August 2017): Recently trackbacks to my postings have started to appear at the arXiv. I have no more idea why this change in policy occurred, any more than I know under what policy they were previously banned.

Update (November 2017): Looks like the ban is back on. I continue to have no idea why.

I don’t write a lot about quantum gravity, mainly because my interest in the subject is somewhat limited. The main reason for this is that the problem of just finding a quantum theory of gravity comes with the danger that even if you find one, you will have no way of knowing whether it has anything to do with reality. Quantum gravitational effects are unobservably small, so experiment likely will be of no help. Often the hope is that a unique and convincing way to quantize gravity will be found, but all evidence seems to be that popular ways of consistently quantizing gravity will lead to an arbitrarily large number of possibilities, with no way to tell between them. The string theory landscape is one example of this.

How to quantize gravitational degrees of freedom remains a deep and attractive problem, but my suspicion is that a successful solution to this problem will require understanding the relationship between gravitation and standard model degrees of freedom, unification if you will. Only with such unification is there likely to be enough connection between the rest of physics and a specific quantum gravity theory to get indirect evidence for it. String theory became very popular exactly because it promised to provide this sort of link, a promise which unfortunately did not turn out.

This blog reflects my own interests. If I’m not writing about X, it’s usually because I’m just not very interested in X. If you are interested in X and want to discuss it, the great thing about the internet is that there are probably places where you can find someone who is interested, and if not, start your own blog.

One of the worst things that has happened as a result of the failure of string theory unification is that many people have interpreted this as a failure of the whole idea of using mathematics in fundamental physics. The failure of string theory has nothing to do with the sophisticated mathematics involved, the problem is that string theory unification is just a bad physical idea that doesn’t work.

There are many possible places to look for inspiration for new progress in fundamental physics, with mathematics just one of them. Physics has traditionally made progress mainly through experiment, but we are at a time in history where we are hitting limits on our ability to explore experimentally new territory at high energy. Serious work on understanding the mathematical structures behind the incredibly successful Standard Model may be a much more difficult way to make progress, but it may be one of the few viable options we have still open.

Actually, professionally I’m happy as a clam. I live in one of my favorite places in the world, and am well-paid to work at a great university with wonderful colleagues who I continually learn from. I also learn a lot from teaching here. Anyone who thinks I’m embittered about anything is someone who doesn’t know me. All in all, life has been extremely kind to me in many ways, far more than I deserve, starting with an excellent choice of parents.

My background includes a Ph.D. in particle theory from Princeton, and many years working in mathematics departments. String theory is a highly technical subject, but my mathematics background makes that aspect of the subject not so impenetrable. It is true that some aspects of string theory are highly complex, with the state of research quite a murky business where only a few true experts can tell you exactly what is going on. Over the past more than ten years of internet discussions one way I have learned things is by arguing about them with those much more expert than me. I’ve found that if I get something wrong, I quickly am informed about this and set straight. On the other hand, if I point out a problem with string theory and get in return a heap of personal abuse rather than an explanation of my mistake, that has also been highly informative.

String theory is not a new, promising idea that needs time to develop. It has been around for about forty years, has been intensively pursued by thousands of physicists for about thirty years now. The end-result of all this work has just been a better understanding that the huge problems with the idea of string theory unification seem to be fatal. If you make the most optimistic assumptions about string theory unification schemes doing what they are supposed to, you end up with the “landscape”, a theory which can’t predict anything at all.

The basic problem with string theory unification research is not that progress has been slow over the past 30 years, but that it has been negative, with everything learned showing more clearly why the idea doesn’t work. The problem with progress in string theory as a function of time is not the size of the derivative, but its sign.

I delete a lot of the comments submitted here. For some postings, the majority of submitted comments get deleted. I don’t delete comments because the commenter disagrees with me, actually comments agreeing with me are deleted far more often than ones that disagree with me. The overall goal is to try and maintain a comment section worth reading, so comments should ideally be well-informed and tell us something true that we didn’t already know.

The most common reason for deleting a comment is that it’s off-topic. Often people are inspired by something in a posting to start discussing something else that interests them and that they feel is likely to interest others here. Unfortunately I have neither the time nor inclination to take on the thankless job of running a general discussion forum here.

No plans to do so right now, and if I ever do, it would be a very different kind of book than the first. In that book I put pretty much all I have to say to a general audience, and not much has changed over the past decade since it was written.

A book that doesn’t seem to exist that I’d like to work on would be something along the lines an advanced undergraduate to graduate level textbook on topics in mathematics and quantum theory. Maybe someday I’ll find time and opportunity to start that project, but not this semester…

Update, summer 2013: I have been writing a book on quantum mechanics from the point of view of representation theory, the latest version is here.

Update: The new book will be published by Springer, publication date is December 2017.

Update: The book has been published, see here.

From this comment.

The issue is not whether there’s more than the observable universe out there. That may very well be, and maybe someday we’ll even understand inflation well enough to have a good model of what that might be. The point though is that there is zero evidence that whatever else there is has different physical laws than ours, and that is what is needed to make the whole anthropic business work. In simple models of inflation, whatever else is out there will have the same laws as ours, so yes, you can get a multiverse, but a pretty boring one. You can use string theory or something else to come up with much more complicated models that give you pretty much any physics you want in different parts of the multiverse, but there’s no evidence for these, they are untestable and explain nothing.

On December 2, 2011 I wrote here about early indications that ATLAS and CMS were both seeing something that looked very much like a Higgs at 125-6 GeV. The discovery-level results were first discussed here, on June 17, 2012. The public announcement from CERN was on July 4, 2012.

In recent years I’ve seen very well-known physicists try and make this argument: string theory is falsifiable, because if an experiment shows quantum mechanics fails, then string theory would be falsified.

It’s hard to know where to start with this, since it seems to me on its face absurd, and makes me worry about the people making it. One comment would be that even if an experiment were done falsifying QM (very unclear what that even means) then it is likely that some idea associated with string theory would get invoked as a possible explanation. Other than that, of course when one is talking about falsifying an idea, one means falsifying the distinctive aspects of the idea.

For an alternate version of this answer, see
http://www.math.columbia.edu/~woit/wordpress/?p=5358&cpage=1#comment-136521

Not really. The standard claim that if you go to high enough energies string theory predicts that you will see string excitations with linearly rising energy and characteristic string theory scattering amplitude behavior are based on perturbative string theory. Non-perturbatively, it is very unclear if this behavior will survive: what if you start producing black-hole states, for instance? The standard conjecture about perturbative string theory is that it is just one special corner of a theory called “M-theory”, which generically does not necessarily contain string-like states at all. Yes, if you were to see characteristic string-like behavior at the Planck scale, you would have good evidence for string theory, but string theory unification does not require this at all, with many models not having this behavior.

If you don’t believe me, maybe you’ll believe Arkani-Hamed, see this posting, which includes:

In the question session, he made the same point I often end up arguing with string theory proponents about, saying (1:14) that if “you can do experiments at the string scale, wouldn’t help you at all”. The idea that you would see string excitations on a compactified space he characterizes as a misguided old idea from the 1990s. If there’s a landscape, the possibilities are so complex for Planck scale behavior that you can’t predict what experiments at that scale would see.

For more, see here

http://mathoverflow.net/questions/133203/explanations-for-mathematicians-about-the-falsifiability-or-not-of-string-the

Update (11/2018): For a related argument that string perturbation theory doesn’t sensibly predict anything at the Planck scale, see this preprint from Banks and Fischler:

String theorists have avoided thinking about this problem because the perturbative S matrix has finite matrix elements in Fock space, once one goes to sufficiently high dimension. However, as the four dimensional case shows, the real issue has to do with infinite numbers of arbitrarily soft gravitons. This is related then to the behavior of the perturbation series for very high orders, and we know that it diverges badly[17]. Indeed, when one thinks about the physics this S-matrix is supposed to describe, it becomes obvious that no perturbative treatment of this question is adequate. For example, it is widely believed[18] that scattering of two gravitons, at an impact parameter smaller than the Schwarzschild radius of the center of mass energy, will produce a black hole. The gravitational S-matrix in any number of dimensions, thus describes processes in which scattering of a finite number of particles produces a collection of large black holes, which can orbit around each other emitting gravitational bremstrahlung, coalesce, and ultimately decay. Can anyone seriously claim that the finiteness of the perturbative S-matrix elements of a badly divergent perturbation series settles the question of whether the soft graviton state produced in this process is a normalizable state in Fock space? The only non-perturbative model of gravitational scattering in Minkowski space, of which we are aware is the large N limit of Matrix Theory[20]. In this model, soft gravitons correspond to very small matrix blocks, which carry very small transverse momentum. As N goes to infinity, it’s clear that we must examine the question of whether the unitary scattering matrix of the finite N theory decouples from the states with infinite numbers of such small blocks. There is absolutely no indication that it will do so.

Update (4/2019): From the introduction to a recent textbook on string theory:

A big “hole” in string theory has been its perturbative (only) definition. With the advent of nonperturbative dualities, it was hoped that this shortcoming can be bypassed.Although the nonperturbative dualities have shed light in many obscure corners of string theory (obscured by strong-coupling physics), they never managed to bypass the Planck barrier. The Planck scale is always duality invariant, and any dual description is well defined for energies well below that Planck scale. We have no clue from string theory what happens near or above the Planck scale, as the relevant physics looks nonperturbative from any point of view.

Update: The text below out of date. Recently I have a proposal (quite incomplete) for an approach to unification using twistor geometry. This proposal is described in this blog posting, and in detail here.

Older text:

I don’t have such a theory, and agree that the lack of good ideas is the strongest argument in favor of the continued pursuit of not very good ones like string theory unification.

In general terms though, I think the lesson of the last forty years is that the Standard Model has turned out to be far better than people have thought. Given this, it seems like a good idea to take it seriously as a truly fundamental theory, not just a low energy approximation to something different and better. There is much that we still don’t understand about the Standard Model, especially outside of perturbation theory. Much of the physics of QCD remains a mystery. Outside of perturbation theory, the behavior of the electroweak interactions is not understood, with, as far as I can tell, no completely consistent non-perturbative formulation of the theory. Working on these problems is not popular because they are very hard.

Personally I’m fascinated by the amazing deep relationships between fundamental mathematical issues in representation theory and the formalism of gauge fields, spinors and the Dirac operator that make up the SM. A better understanding of these relationships may very well teach us either something new about mathematics, or something new about physics.

No, this is completely untrue. Here’s the actual story behind that, you can judge for yourself.

• In one of my early blog posts, (August, 2004, this one), I linked to a piece in Scientific American by Bousso and Polchinski promoting the multiverse and the string theory landscape. I stand by the substance of what I wrote there (what they are promoting is pseudo-science that Einstein would disapprove of). It seems though that Polchinski was quite upset by what I wrote.
• In March 2006 he complained about the 2004 posting here, as part of a discussion about why the arXiv was banning trackbacks to my blog (they still are, for reasons no one will reveal, see here). In his complaint he quoted the posting without naming me. When I read it my first reaction was “that’s kind of over-the-top, I wonder who wrote it?” After Googling revealed it was me, I thought it a good idea to apologize to him, which I did here.
• I learned later that Polchinski was privately telling people “I won’t read Woit’s blog because he wrote that Weinberg was senile” in an attempt to try and personally discredit me (and, it appears, to convince the arxiv to ban trackbacks to my blog, see his acknowledgement here that this was part of the arxiv trackback issue, something not known to me at the time).
• The story of the supposed Weinberg reference has to do with this November 2005 blog entry, which I’ve just reread and seems to me perfectly accurate. It’s a serious discussion of an article by Weinberg about the multiverse. Back in those days I basically allowed all comments, rarely deleted any (this changed later). In an early comment on this posting, a commenter implied that Weinberg had become a “pathetic old man”. I tried to defend Weinberg in this response:
  

  One of my colleagues this morning, after being shown the Weinberg article, commented that Weinberg must just be senile. Unfortunately I don’t think that’s what’s going on. Weinberg wants to be part of whatever the hot topic in particle theory is, and the landscape is the hot topic these days. It’s being driven mainly by younger people, not by seventy-year-olds, and you can’t put their behavior down to senility.

  A problem with making quick comments on blogs is that they’re often not as well thought out as they should be. I remember thinking after this was posted that its characterization of Weinberg as motivated by “hot topics” was kind of dumb, but I thought the point I was making should have been clear. Weinberg was certainly not senile, and the problem was not him or any “pathetic old men”, but “younger people” who were driving this. One person I specifically had in mind here was Polchinski and his Scientific American article, which was the sort of thing Weinberg would never have written (compare the Scientific American article to the Weinberg article discussed in the posting). It seems though that Polchinski recognized himself here, despite my avoiding naming him.

  I didn’t think this needed saying at the time, but of course I had then and have now the greatest respect for Weinberg, who is one of the great figures of the field. I took my first course on gauge theories from him at Harvard, and learned a lot from his papers and from his books on quantum field theory.

  The story of the episode in my office was meant not to in any way slur Weinberg, but to point out that many scientists find anthropic multiverse claims to be obvious pseudo-science. The colleague in my office earlier that day was not a physicist, but someone generally well-informed about physics, aware that Weinberg was a distinguished physicist, who happened to choose that particular way to express distaste for the multiverse business as pseudo-science. I had explained to him that Weinberg certainly wasn’t senile, that this had somehow become the hot topic among some theorists like Polchinski, and that it was the popularity of pseudo-science among people like him that was the real problem, with the older generation usually more sensible (see for instance his elder colleague David Gross).

In January 2016, Polchinski posted a paper on the arxiv with a section devoted to a personal attack on me based on one sentence in the 2005 blog comment discussed above. This section was removed in a later version of the paper on the arXiv, he says because he recognized that since he had trackbacks to my blog banned, it was unfair that one would not appear to this paper (true enough…). The version attacking me does appear on his website, with added material about what is wrong with me.

No, string theory hasn’t actually predicted anything, you’ve been misled. Innumerable bogus “string theorists finally find a way to test string theory” claims have been made over the years, a relatively early one was this one. For some postings with more details about such claims see here.

For a relatively sensible explanation of some of the technical problems with trying to construct a “string theory vacuum” state and use it to recover known physics, see here.