# Prospects For a String Theory Phenomenology

Yesterday at the KITP Michael Dine gave a very good survey talk on Prospects for a String Theory Phenomenology. It’s pretty much hype free, has a much more realistic point of view than most talks on string phenomenology that I’ve seen, and gives a good idea of the current state of the subject.

Dine claims that almost all string theorists now accept the existence of flux vacua, although only some have adopted the anthropic landscape philosophy of Susskind et. al. He describes some string phenomenologists as closing their eyes to the problems represented by the large number of these vacua, and just working on some of the more tractable examples in the hope that something will turn up that will allow them to make some connection to the real world. He himself is convinced by the Denef-Douglas argument that even identifying a single vacuum state with sufficiently small cosmological constant is impossible, so that one has to make statistical arguments. He tries to have some optimism that perhaps this statistical study will allow one to make some kind of prediction, perhaps about whether the scale of supersymmetry breaking is low or high, although so far this has turned out to be impossible.

The discussion at the end of the talk is very interesting, with Dine acknowledging that there are lots of reasons he may be barking up the wrong tree and saying that he would be happier if this turned out to be the case. He quotes Witten as telling him that what he is doing can’t work, that there isn’t much point in trying to do the calculations he is trying to do because:

A.: “You are probably not going to succeed”, and

B: “If that is all you can do it would be a great disappointment. We have this beautiful theory and we are going to get everything out of it” [i.e. it would be unpredictive].

This entry was posted in Uncategorized. Bookmark the permalink.

### 44 Responses to Prospects For a String Theory Phenomenology

1. Peter Orland says:

Hi Peter,

As you and I have privately discussed, I don’t object to string theory as a laboratory to study gravity or unification per se. On the other hand I find myself very frustrated with the many scenarios devised to do phenomenology. The problem is not that these scenarios are complicated. It is that the complications cannot be forseen.

Imagine if early 19th century chemists, cooked up an atomic theory and tried to explain the bulk properties of matter (hardness, thermal conductivity, phase diagrams). They would certainly fail because they would lack statistical mechanics and the basic ideas of spontaneous symmetry breaking (crystallization). The only property they would have understood is the density of compounds and alloys (as Dalton did). The mathematical concepts needed to understand the rest would never been discovered without experiments. I am not a historian, and for all I know, some brilliant chemists in 1810 actually tried this. I admit am guilty of pseudo-historical speculation to justify my point, but I think it is obvious regardless of this speculation.

Often when experimentalists probed some higher orders of magnitude in energy scale, collective phenomena were discovered which were not forseen. This doesn’t only apply to particle physics, but from the first investigations of matter to the study of crystals and kinetic theory, to
atoms, etc.

If string theory (or something like it) is right, it seems far too ambitious to think that we can pick out the right scenario to describe nature. Nature is smarter than any of us.

2. Would I be right in saying that this is the first time Witten has been quoted as saying definitely that he thinks the landscape approach is probably wrong/not worth working on?

3. Benni says:

Suesskind also said in Munich to me in person that Witten hates the landscape because “we cannot get any predictions from it”. “Witten hates it” Suesskind said.

I’d definitely second Peter (Orland, not Woit). But it irks me whenever someone says that ST is far too advanced to be probed with current technologies.

This seems to me to be an example of petitio principii, or ‘begging the question’ in an argument. It’s a false analogy because it is proved by its own premise. If I chose to construct any theory that I said was the most advanced of all, but that could not be experimentally verified, I could easily state that it cannot be falsified or verified precisely because it is so advanced. There’s no way to argue against it because this is circular logic. This form of argument is used by Intelligent Design advocates fairly often. For example, I’ve actually heard someone say: “Looking at the complexity of the natural world and saying that there is no designer is like looking at Mount Rushmore and trying to find out what geological processes created such human-like rock formation”. You see how deceptive such logic games are, while essentially proving or saying nothing at all. I could make the same argument that you gave, for any form of quantum gravity that doesn’t make testable predictions. If one chose to play by those rules, one could say that the Flying Spaghetti Monster is so advanced so as to escape detection. The theory that music originated before language was brought up by Dennett as an example of theories that might sound great, but since there’s no way to verify that in the present, they are essentially of no use to us.

So essentially, we could choose to ‘take it on faith’ that ST is so advanced that all we can do is sit and wait for a few hundred years and that it will eventually proved correct, once the rest of science catches up to the level of brilliance that ST theorists are already working at. But this is something that has never been asked in the history of science. Theories, like definitions, sometimes aren’t so much right or wrong as useful and useless. ST can provide a useful context and has helped people in understanding gauge theories and so forth (or so we are told), but overall has it been very useful to theoretical physics as a whole? I think this is a more important question than if it is right or not, is asking the old ‘What has it done for us lately?’

5. anonymous says:

I find it very amusing that while you accuse string theorists of being a cult of Witten followers, they rationally look at the equations of the theory, while you guys fixate on what he “likes” or “hates”. This is physics: who cares what someone likes? Truth matters!

6. milkshake says:

P. Orland: Your analogy about chemists is misleading. Using atomic theory, they could make all kinds of qualitative and quantitative predicticon: exact composition of yet-undiscoverd salts. Behaviour of gases. Connectivity rules/molecular shape of carbon-based chemicals. Periodic table.

First you guess. Then you figure consequences of the quess and compare them with experiment. If it’s wrong…

7. woit says:

gunpowder,

As far as I know, Witten’s only public comment about the landscape so far has been something like “I wish it weren’t true, but I have no good arguments against it”.

anonymous,

I’ve repeatedly, in great detail here, made the scientific case that the kind of computations Dine is talking about can’t possibly lead to a legitimate scientific prediction. In response I’ve been denounced as a crackpot and repeatedly informed by string theorists that I don’t know what I’m talking about. I’m not going to apologize for reporting that Dine says Witten agrees with me on this point. As you might have noticed, I have an extremely high opinion of Witten, while at the same time being quite capable of disagreeing with him when I think the truth of the matter is not on his side.

8. anonymous says:

Peter:

A legitimate scientific prediction, in model building, consists of writing down your model, giving a convincing argument that it isnt yet ruled out, and making at least *one* prediction that can be verified by future experiment. Tye’s
inflationary models and Tye/Polchinski’s cosmic superstring ideas certainly fall within this rubric. So do many ideas for particle physics models motivated by the string constructions. None of them are a “prediction of string theory,” they are models which came out of string theory and which are predictive at the normal level of particle physics or cosmological model building. I find it very disingenuous to try and claim string theorists need to derive the whole world from top down to be doing legitimate model building. No one else ever does that, in science. Dine was, unfortunately, apparently focused on that unlikely goal

9. woit says:

anonymous,

If Tye/Polchinski would stop talking about “predictions of string theory”, and be careful to explain that they are talking about specific models, not string theory itself, there would not be a problem. That’s not what they’re doing.

People are welcome to work on specific models, they just shouldn’t sell the implications of these specific models as “predictions of string theory” or “tests of string theory”.

10. anonymous says:

Hi Peter:

If one of their models were verified, and the resulting string network had
the low $P$ or multiple species of (p,q) strings characteristic of the
warped throat models, I would consider this evidence for string theory.
That is the sense in which such people call searches for such things tests of string theory; verification would provide evidence for a natural string based model, while falsification means that kind of string model is wrong. I completely agree (as would they I am sure!) that none of these models are inevitable consequences of string theory. Most string theorists I have heard go out of their way to stress this when presenting any model building type results. But verification of some prediction of this kind of model would be a big clue for string theorists, maybe telling them which limit of the theory is relevant to nature (if any). This is how all of science works; this process also led to the correct quantum field theory description of particle physics (it was not some instantaneous top down epiphany, but rather winnowing of a large structure to limits that seemed consistent with data). Anyway this view seems to be in partial agreement with yours. But I do think that because of this kind of model building, combined with future experiments, string theorists may well eventually learn which kind of vacuum is relevant, and make some predictions.

11. a says:

anonymous: can you give concrete examples about which possible developments could lead to which predictions?

12. George Giles says:

When Einstein was working on the General Theory of Relativity he had some experimental facts, and a load of intuition. He had the physics but not the math. Marcel Grossman and he then went looking for it and found it in Riemannian Geometry. It seems that String Theory is taking the opposite approach, a whole load of math (formally undecidable theories at that) and are searching for the physics.

Now even a blind pig finds an acorn every now and then, but it seems that the current approach is from a historical prospective, unlikely to be successful. My gut feel is Newton followed an approach like Einstein, not one like Witten et al.

I have to wonder if String Theory has gone from diminishing returns to vanishing returns to paraphrase Milton Friedman.

13. anonymous says:

a:

Well, I already mentioned, discovery of cosmic strings with certain network properties would give evidence for a class of models of inflation discussed in many papers over the past few years, and some of these properties were first suggested by string constructions (not field theory ones). There are other kinds of inflationary experiments (measuring nonstandard features of the density/temperature fluctuation spectrum) that will be launched in the next five years and could test another class of string inflation models.

In particle physics, obviously large extra and warped extra dimensions drew much attention because they have spectacular signatures at LHC (though I think they are quite unlikely). Verification of either would again be a big hint about which kinds of string models matter; both warped and large extra dimension models have recently been found in detailed studies of string compactification with flux.

5th force experiments may eventually find moduli with small mass. In supersymmetric string models, one class of gauge mediated models would predict moduli in the sub eV range. If both the moduli and the spectrum of gauge mediation were seen, this would be a hint.

Other people have found mediation scenarios where distinct spectra of sparticle masses result from specific extra dimensional structures (anomaly mediation, gaugino mediation, mirage mediation,…) which you can read about in review articles.

Altogether, the discoveries of LHC, future CMB experiments, and 5th force type experiments (together with gravity wave detectors) have all kinds of ways of giving us hints about high energy physics. A confluence of several hints could select the right kind of string model. Of course luck would also be required (how lucky would we be if there are extra dimensions at LHC??). But thats always been the way experiment helps theory; a lot of hard work developing the theory, and eventually, a decisive stroke of good luck in what is discovered. Arguing that one cannot be sure that experiment will give big hints about the right string model in the next decade is silly; that is obviously true, and has been equally obviously true for all really interesting theoretical developments in the past century. We will need to get lucky, but there are many ways to do so, some of which we haven’t thought of yet. Thats why I am excited about this field.

14. steve says:

The following statement from our host clarifies what I asked about models vs. theories on the previous thread:

“If Tye/Polchinski would stop talking about “predictions of string theory”, and be careful to explain that they are talking about specific models, not string theory itself, there would not be a problem. That’s not what they’re doing.
People are welcome to work on specific models, they just shouldn’t sell the implications of these specific models as “predictions of string theory” or “tests of string theory”.”

If string “theory” is just a framework for generating specific models, and it is specific models rather than the framework as a whole that are to be tested empirically, then the dispute collapses to a much smaller and more manageable level. The only residual problem would be if, regardless of their merits, models developed out of the string framework received more favorable evaluations than models constructed some other way. Absent evidence of that, I’d be inclined to think that the hype about strings is silly but not too damaging.

15. anonymous says:

All of the models of TeV scale physics I mentioned (large extra dim, warped
extra dim, gaugino mediation, anomaly mediation,…) were actually developed by people who received PhDs that are NOT in string theory. They all classified themselves as particle phenomenologists or model builders. Those works are all famous and well cited, and their authors received faculty positions (those who did not already have them). String theorists were very happy to build on their ideas, or try to find them in string theory. So there has been interplay, but I think it would be grossly unfair to say that only models that are constructed by string theorists, or first derived from string considerations, have been “hyped”. It would be hard to imagine more hype than that surrounding the extra dimensional models that were NOT conceived of (first) by string theorists. More generally, however, the interaction between strings, cosmology, and particle phenomenology has been very healthy in the past decade. It is now hard to even classify some people who work in two or three of the fields. This is a good thing.

16. Dick Thompson says:

Just on the topic of a nineteenth century calculational atomic theory, Daniel Bernoulli in the eighteenth century used basic “corpuscles” acting elastically under conservation of momentum to derive PV = const. He or someone else might have taken the next step, identified “heat” with the summed vis viva of the corpuscles and the temprature with their mean vis viva and derived the virial theorem. I don’t think a limited “kinetical chemistry” theory was impossible at that time, and historical analogies are always questionable because of the great influence of individual personalities on both past and present.

17. Peter Orland says:

Milkshake,

I think you missed the point of my analogy.

As you say, you make a guess. Calculate. Check against experiment. Make another guess. And so on. The point is that none of us is smart enough to start from a very high (low) energy scale and guess how nature should be at a very low (high) energy scale without a LOT of guesses and calculations and experiments
in between. Well, I think it can’t be done.

The reason it can’t be done is that every time you go to smaller scales, there is the possibility of new statistical/collective/nonperturbative phenomena happening. In
my foolishly naive analogy, I was trying to say that this is like
starting from the notions of atoms and calculate properties
of matter. It’s impossible without investigating the molecular
level (kinetic theory), van der Waals forces (electricity
and magnetism), electrons and nuclei (quantum mechanics), and
the mean field theory of crystals (spontaneous symmetry breaking).

Continuing this analogy (since I don’t have a better one), string theory would be like the quantum theory of electrons and nuclei. Imagine trying to extract bulk properties of matter from a many-body theory of electrons an nuclei! It can only be done in hindsight. Too many sophisticated phenomena happen between an Aangstroem unit and a centimeter.

I’m not saying that it isn’t worthwhile to study the theory we guess is fundamental. I just have no confidence that one can stretch that theory from the Planck mass to 10 TeV and make sensible predictions. That doesn’t mean the theory is wrong, but that we aren’t smart enough to guess what happens at intermediate energy scales.

18. a says:

anonymous, you answered mentioning many possible natural solutions to the Higgs mass hierarchy problem. Do you still hope that dark energy will turn out to be something natural, rather than an unnaturally small cosmological constant?

If not, it seems better to see nothing new at LHC and get a second stroke on naturalness: a defeat naturalists vs anthropists = 0 : 2 would carry a strong message, while an impact 1 : 1 would not clarify this big issue.

19. anonymous says:

Hi a:

There are as yet (as far as I know), no good “natural” solutions to the
cc problem. But logically speaking, all the evidence for the string landscape just means that there are many vacua, some of which plausibly have small enough lambda. It could be that they are “populated” by cosmology in such a way that some dynamics enters in explaining the observed value. Needless to say, despite very many attempts in this direction (with various modifications of the Hartle/Hawking wavefunction, or more…questionable…approaches by Turok and Steinhardt), nothing less tuned or more convincing than just a small cosmological term explained by Weinbergs argument has emerged. But again, the evidence for the landscape just means small lambda can be accomodated in string theory, it does not necessarily mean anthropics has to be the explanation.

Arkani-Hamed and Dimopoulos and various others have tried to think of ways that LHC could give evidence for un-naturalness. The attempts are kind of forced, since there are good explanations for the higgs mass that come pretty easily out of string theory (at least as easily as their more contrived, though very testable, proposed “anthropic” models). But I agree if one of those models, or “higgs only,” came out at LHC, it would be another big pointer to a new notion of naturalness, very possibly indicating the landscape again.

20. relativist says:

Hi anonymous

“the evidence for the landscape just means small lambda can be accomodated in string theory” – the word evidence’ here has taken on a rather unusual meaning. You presumably mean something like theoretical support’ rather than evidence in the usual sense of the word. Indeed Vilenkin tries to run it the other way and say that the small value of Lambda (which is evidence in the usual sense – it is an observed piece of data!) is evidence for the landscape – and for the multiverse, which is not observable in any ordinary sense of that word. This seems to be stretching ideas of scientific proof to a great degree – compare with what is taken as adequate proof in say solid state physics or quantum optics.

OT: I suppose everyone has noticed that physics/0610168 references our host.

22. anonymous says:

Relativist:

Yes, I just meant evidence for many vacua in string theory, using standard physical techniques to abnalyze the vacuum structure. I did not mean there is experimental evidence. But it is true that the many vacua may well turn out to offer the best hope of accomodating (explaining??) The small cc in a quantum gravity theory. Of course we would need other more traditional tests of string theory to make this at all convincing, as all reasonable string theorists would acknowledge.

23. Who says:

OT: I suppose everyone has noticed that physics/0610168 references our host.

I noticed that. It is Hedrich’s paper reporting on a study he did for the German equivalent of NSF, about the state of theoretical physics. I think our host had a blog sometime back that was partly about Hedrich and some coverage in the German press.

24. LDM says:

Referring to footnote 12 of the physics/0610168 about string theory and GR…

If you actually check what Feynman said in the “Feynman Lectures on Gravitation”, page 30…you will see that the (so far undetected) graviton, does not, a priori, have to be spin 2, and in fact, spin 2 may not work, as Feynman points out.

This elevation of a mere possibility to a truth, and then the use of this truth to convince oneself one has the correct theory, is a rather large extrapolation.

25. Anonymous 17 says:

Has anybody noticed hep-th/0610241, which seems to be the start of non-commutative geometry phenomonology. Connes and co-authors predict the mass of the Higgs boson. String theory appears to be starting to fall behind.

26. Bert Schroer says:

I find this point which Hedrich revives quite interesting. The massless finite helicity Wigner representation (say integer spin for simplicity) have all one property in common, their inner products cannot be written in terms of integrals over local densities. In order to do this (and also to implement interactions) you have to introduce “potentials”(the vectorpotential for h=1, the metric potential for h=2 where the field strength would be the linearized Lorentzian Riemann tensor etc.). This creates a dilemma in the quantum theoretical setting (none if one stays classical) since there is a No-Go theorem: there are simply no covariant pointlike fields in the Wigner-Fock Hilbert space. There are two ways out. Either you give up the Hilbert space in intermediate calculation and admit ghosts (which of cause can only be used as “catalyzers” because you have to get rid of them at the end of the calculation); this is the BRST cohomological setting. The alternative is to use covariant potentials which however describe string-localized fields (which fluctuate simultaneously in Minkowski- and the string-directional de Sitter space). In both cases you end with potential fields whose short distance behaviour is not worse than that of a scalar free field (in contradistiction to the field strength whose scale dimension increases with the helicity). The renormalizable interactions are precisely of the “gauge” kind (although that language is not very appropriate in the second setting since you never leave the physical Hilbert space) but for the sake of this discussion it would be justified to call them all “gauge theories” (not only the case h=1).
In some sense the Einstein-Hilbert gravity interaction should be in this family of interacting h=2 theories. But there is a profound conceptual problem: the diffeomorphism invariance (according to Einstein an active transformation which also changes the points) is not the same as gauge invariance (phase transformation) which only effects the fibers over points.
I think it would be very interesting to re-investigate the issue of ref. 12 of Hedrich using the gain in conceptual understanding.
By mere coincidence some of this points were discussed yesterday in the samizdat blog.

27. D R Lunsford says:

Bert said

In some sense the Einstein-Hilbert gravity interaction should be in this family of interacting h=2 theories. But there is a profound conceptual problem: the diffeomorphism invariance (according to Einstein an active transformation which also changes the points) is not the same as gauge invariance (phase transformation) which only effects the fibers over points.

Yes, this is exactly the key point and why all attempts to make the gauge potentials part of the metric via KK ansatz are doomed. Pauli already knew that.

-drl

28. D R Lunsford says:

The paper by Hedrich is outstanding and long overdue.

-drl

29. Bert Schroer says:

The word “phase transformation” may be misleading (I was already thinking about coupling these higher helicity potentials as external fields to quantum matter). I would expect these transformation to be linear (generalization of h=1 gauge transformations). I would be surprized if this issue has not been already adressed in the literature. What is however important here is to start from the Wigner representation theory in order to avoid playing formal games with ad hoc higher tensor fields.

30. Bert Schroer says:

D R Lunsford
I did not know about Pauli’s criticism, very interesting! Where did you see this?
There is an independent much more profound argument against KK coming from algebraic QFT. This is based on the observation that inner symmetries result (the DHR analysis) from the representation theory of local observables. It is the representation theory (modulo isomorphisms) of these local nets which leads to the statistics of particles as well as to the existence of charge-carrying fields which intertwine the charge sectors and encode the statistics into inner symmetry properties of these charge carrying fields such that the original observables are reproduced as the fixed point algebra of the field algebra. In 4 spacetime dimensions the emerging symmetry concept is that of compact groups. If you would not have locality the possibilities of representations would be too big and not be classifiable. The conceptual situation of observables—charge carrying field algebra (i.e. its construction from the observables) is precisely following Marc Kac’s dictum: “how to hear the shape of a drum”. It is totally absurd to think that such a situation can emerge from little rolled up spatial dimensions (KK is however possible in the classical setting, but is does not solve any physical problem). But there is nothing which one can do against collective madness; one just has to let it play out.

31. egbert says:

DRL said:

Bert said

In some sense the Einstein-Hilbert gravity interaction should be in this family of interacting h=2 theories. But there is a profound conceptual problem: the diffeomorphism invariance (according to Einstein an active transformation which also changes the points) is not the same as gauge invariance (phase transformation) which only effects the fibers over points.

Yes, this is exactly the key point and why all attempts to make the gauge potentials part of the metric via KK ansatz are doomed. Pauli already knew that.

Is there a simple and obvious way to get from the first observation (diff inv is not gauge inv) to the second (KK is doomed)? I’m probably missing something that’s obvious to both of you, but it sounds like Witten is missing that same thing as well, among others, so perhaps I can be forgiven for not seeing it right away.

32. D R Lunsford says:

egbert – Witten is a mathematical genius but Pauli was connected at the belly button to the Universe, and his arguments win in my book. Having great skill at math does not confer physical insight.

-r

33. woit says:

Please, this is not sci.physics. Stop trying to turn it into a discusssion forum for your favorite ideas about GR. This is completely off-topic.

34. Bert Schroer says:

I agree with Peter that this does not fit the headline of this blog, sometimes an interesting issue throws a weblog of topic.
It is however a subject which I addressed in my Samizdat article. So may be Egbert I could answer your question over there. Another possibility is that you use my email address. But then an interesting subject will be lost to the typical reader of Peter’s weblog which is not fitting the purpose of a scientific weblog. Since Peter is very interested in the use of representation theory for particle physics he may actually also be interested to know arguments which show that in the quantum setting there is a deep clash with the KK idea (independent of Witten’s opinion).

35. egbert says:

Let’s continue at my new blog.

In fact, I propose that, whenever a conversation wanders into realms that aren’t appropriate for the host blog, a new blog post should be instantiated somewhere and a link posted to the original blog, so that those who wish to follow the conversation can do so.

36. Bert Schroer says:

Egbert
when I tried to follow your suggestion to move my 2 last contributions under Samizdat over to your new blog (as a kind of branched-off sub-blog to Peter’s) and to start a more extensive discussion from there I realized that there must have been a malfunction with Peter’s weblog because the list of names on the right margin does not correspond to the content after opening. What worries me even more is that only the continuation of my yesterday’s contribution appears fully, the blog I wrote immediately before is incomplete (it lost 2/3 of its content) and unforyunately I did not make a copy. So before moving over, let us wait and see if Peter can check what happened.

37. Peter Woit says:

Bert,

I have no idea what the problem might be. What you see in the comment section of the blog is all that there is.

38. Bert Schroer says:

O.K., maybe there was a malfunction in the uploading. Of course I can reconstruct what I wrote and place it as a comment into Egbert’s comment section, but I need some time (I will be able to do this today). So I invite all reader’s who are interested in that particular issue to move later in the day to Egbert’s weblog
http://kaluza-klein.blogspot.com/
(which I do not want to see as a competition to Peter’s but rather as a means to continue with interesting points which are slightly off-topic).

39. C says:

Hi anonymous

“both warped and large extra dimension models have recently been found in detailed studies of string compactification with flux.”

Could you provide a link to this work, or a hint such as the names of the authors, to help me find the papers?

Thanks very much.

C

40. anonymous says:

Hello C:

There are by now lots of papers on these things, but I think it is reasonable to point to:

For scenarios involving exponential warping like Randall/Sundrum, a standard reference is now arXiv:hep-th/0105097 by Giddings et al. The references in that paper and the citations to it provide a much larger guide to the relevant literature. Those models are important in hep-th/0301240, the original “KKLT” paper on flux compactification.

String derived models of large extra dimensions are described in
hep-th/0505076 by Conlon et al which focuses on phenomenology, and the citations/references of that paper.

41. C says:

Hi anonymous

Thanks very much.

C

42. Thomas Love says:

Peter, Thanks for the link to Michael Dine’s talk. I listened to it and it was just like being there. I fell asleep 15 minutes into his presentation and was awakened by the applause at the end of his talk. I did go back the next day and listen to the whole thing. His comments at the end seem to reflect the reality of the problems with string theory, he was discussing the many states of string theory:

At 1:08:12 into the recording(slightly edited):

“You line up your graduate students. You give them each a barcode for one of these states. They start calculating. They come back 6 months later and they’ve calculated the second order correction. It looks pretty good. They come back two years later they’ve calculated the third order. It looks pretty good. Twenty years later they come back with the eighteenth order—it didn’t work. Ok, throw this out.”

I only listened because Dine is at UC Santa Cruz, where I received my PhD. I’m glad I got out in time. I wouldn’t want to spend twenty years getting a PhD! His comments reminded me of why I left physics after one year of grad school and switched to math: the whole paradigm of perturbation theory makes no sense whatsoever!