As noted earlier in Peter’s blog, there are recent mathematical advances which required concentrated work for several years of silence for the authors.

There is no doubt in my mind the contemplative thinking asks that we recognize the essence of any equation, and a lot of times. The mind clicks a notch, when sitting by a stream(ask witten), and the mind had disassociated itself, from such efforts.

There is a always a incubative time for consideration, as you quote saids. I thought, all mathematicians had good focus?

For instance, perhaps string theory presents research problems that are more likely to reach fruition in one post-doc term than other areas?

As noted earlier in Peter’s blog, there are recent mathematical advances which required concentrated work for several years of silence for the authors. Are there sociological factors operating in physics that preclude the kind of work that might be needed for such breakthroughs?

Peter is of course completely capable of answering for himself, and has already done so. My perspective is somewhat different, in that I have a well-developed suggestion for the missing mathematical structure.

Let’s also assume absence of any new experimental guidance, then what alternative mathematical structures or approaches in our opinion (ie non string theory) would have enabled a viable leap (or even step) beyond the SM or GR? I assume you would approve of deeper investigation into the mathematical underpinnings of the SM like gauge fields/YM and Dirac operators, but people have looked (are looking) at this anyway surely?

I have looked one particular mathematical underpinning of the SM and GR since 1987, but despite rather remarkable progress the physics community has been completely uninterested. From this I have concluded that people who already know the correct Theory of Everything have simply no interest in learning about new mathematics, not in the 80s and not now. Mathematicians have in my experience always been much more open-minded, perhaps because everything that I have done has also been worked upon by some mathematicians because of its intrinsic mathematical interest.

More precisely, I’m talking about the quantum representation theory of the correct constraint algebras of GR and the SM. The constraint algebra (in covariant formulations) of GR is the group of 4-diffeomorphisms, and the constraint algebra of the SM is the group of gauge transformations based on SU(3)xSU(2)xU(1). Upon quantization these algebras acquire quantum correction, making them into higher-dimensional analogues of the Virasoro and affine Kac-Moody algebras. That such algebras exist, and that they have an interesting representation theory is by itself some kind of mathematical success.

This goes beyond field theory, because a 4D Virasoro algebra is a diffeomorphism anomaly in 4D, something which can not exist within field theory. Nevertheless, there are no assumptions about new physics here. 4-diffeomorphisms and SU(3)xSU(2)xU(1) gauge transformations are simply the correct constraints of GR+SM. So one reason why people have failed to go beyond GR+SM might be that there isn’t anything there; at least there are no conclusive experimental hints. There are some well-known mathematical problems, e.g. that GR and QM are inconsistent and that the SM is somewhat ugly (although by no means as ugly as string theory), but this may well be explained by the fact that people have missed the existence of the relevant anomalies.

In the absence of experimental guidance in 25 years now surely all possible alternatives are just wishful thinking too and can’t make any predictions either? Everything else that has ever tried to go beyond the SM and GR has run into their own technical brick walls too so you can’t really just single out string theory esp when it was the most promising.

I don’t think that loop quantum gravity is particularly promising neither. However, when evaluating the promise of an approach it is not fair only to judge the physical achievements (string theory: 0, LQG: 0, me: 0), without taking into account the amount of time and funding invested in it. Public spenders must expect public scrutiny, and big public spenders must expect more public scrutiny than small ones. If the funding to LQG were raised to string theory levels, e.g. by redistributing funding from string theory, and LQG didn’t make any spectacular progress after a decade neither, then it would be fair to criticize it too.

Another intrinsic aspect of string theory is the consistent overselling for the past 20 years. I always felt dubious about a theory without experimental support, but what convinced me that string theory is not only wrong but detrimental to science was a Physics Today article by Gordon Kane in 1997, entitled “String theory is not only testable, but super-testable”. The title vividly illustrates the complete discrepancy between the hype and the actual achievements. In this respect, string theory is totally unique in serious science, and can only be compared to pseudo-science.

A couple comments. You’re right that my own point of view is that, given the lack of experimental guidance, the most promising thing for theorists to do is to try and learn more about the mathematical structures used in the standard model and see if new and better ways of understanding them can be found. There seem to me to be quite a few things of this kind to investigate, but I can tell you from personal experience that if you try and talk to most theorists about these issues, they’re really not interested. The attitude has become very widespread that the only possible mathematically sophisticated approach to particle theory is string theory, and that anyone who thinks otherwise is just too stupid to be a string theorist. Throughout the late eighties and into the early nineties, besides doing string theory, Witten came up with a lot of new ideas about gauge theories, but for the last ten years or so he seems to have decided to devote his full energies to string theory.

I don’t think there’s only one thing people should be working on. In the absence of any particularly promising idea, which is where we are now, they should be trying out a wide range of different things. But there needs to be a much more honest process of recognizing when ideas don’t work and moving on to try something else. What’s completely dysfunctional about the field is the way it continues to be dominated by the idea of unifying the SM and gravity in an 11d M-theory of some kind, long after it should be clear this can’t work. It would have been unreasonable to demand predictions from string theory during the first few years that people were seriously looking into it, but twenty years later, the fact that it can’t produce a single prediction of any kind should count very heavily. String theorists should be honest about how bad the situation is, and stop heavily hyping and promoting the theory unless they can make some real progress with it.

The main question facing the field seems to me to be that of how to encourage more people to try different things, and not just stick to one failed idea because it is what every one else is doing.

I do not want to defer on recognizing your enthusiam either:)

The increasing complexity, of what one might reveal of the cosmo, with a microcosmic view, had me consider how either the string theorist or the LQGist might interpret, that same cosmos. Gamma detection is one view right.:)

There are obvious attempts to interpret quantum gravity. I was looking for how they might view the picture supplied in my previous post.

If it is becoming increasing complex , the basis of their determnations would have to have a foundation to begin with, right?

Mathematically, how could two views of picture supplied in previous post, be so different, and are they?

As I stand, under the arch of reason, I am asking about that one thing. City Slickers, was very interesting from my historical perspective:)

String theory, once it’s understood completely, cannot really be an approximation of anything deeper – it follows from its basic mathematical features.

Can you explain this in more detail for a layman?
(layman = math grad student, in this case)

I just want to say that I’ve seen your replies, and I find it inappropriate to answer this kind of feedback.

All the best
Luboš

I am going to go into suspended animation for a few decades. Could someone please revive me when Harvard physics professors start doing science again?

Stephen Weinberg was here in Stockholm in December 1984, attending the Rubbia-van Meer Nobel party. At a colloqium he predicted that some smart young string theorist would win the Nobel Prize in 1991. Well, that prediction was at least falsifyable.