Spring Break

Posted on March 11, 2015 by woit

I’m heading off soon on spring break, planning on traveling to Scandinavia and hoping to see a solar eclipse. There hasn’t been much news recently from the math and physics worlds, and it’s unlikely I’ll be blogging until I get back (around the 24th), so will turn off comments while away.

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GR100

Posted on March 7, 2015 by woit

I hadn’t thought until recently about the fact that this year is the 100th anniversary of Einstein’s discovery of the field equations of general relativity, so there will be quite a few events taking place commemorating this (for a list of some, see here). This week’s Science magazine has a special issue on the topic. It includes news stories about LIGO and gravitational waves, new tests of the equivalence principle, and possible tests of GR from observations of the black hole at the center of our galaxy.

There’s also a review of a book from a few years ago about Einstein’s search for a unified theory, Einstein’s Unification by Jeroen van Dongen. The review addresses something I mentioned in my recent essay about mathematics and physics, that the development of GR provides a good example of a successful theory coming out of not just experiment and “physical intuition”, but motivated also by the serious use of deep mathematical ideas. According to the review:

Einstein employed two strategies in this search [for the GR field equations]: either starting from a mathematically attractive candidate and then checking the physics or starting from a physically sensible candidate and then checking the mathematics. Although Einstein scholars disagree about which of these two strategies brought the decisive breakthrough of November 1915, they all acknowledge that both played an essential role in the work leading up to it. In hindsight, however, Einstein maintained that his success with general relativity had been due solely to the mathematical strategy. It is no coincidence that this is the approach he adopted in his search for a unified field theory.

Besides the fact that Einstein said so, other evidence for the primacy of the mathematical strategy in this case is the simultaneously successful work by mathematician David Hilbert, who was definitely pursuing the mathematical strategy.

While I think there’s an excellent argument that a mathematical approach was crucial in Einstein’s discovery of the field equations, the later history this book deals with also shows the dangers this can lead to. Einstein spent much of the rest of his life on a fruitless attempt to get a unified theory by pursuing the same mathematics he had so much success with in the case of GR. It’s a good idea to keep in mind both examples. On the one hand, trying out some new deep mathematical ideas can lead to success, on a time scale of a few years. On the other, if you’ve spent 30 years pursuing a mathematical framework that has gone nowhere, maybe you should do something else. A lesson that Einstein’s successors at the IAS might want to keep in mind…

The story about new tests of the equivalence principle contains the usual nonsense about testing “string theory predictions”:

Using beryllium and titanium, they found gravitational and inertial mass equal to one part in 10 trillion, as they reported in Physical Review Letters in 2008. That’s not quite precise enough to test string theory predictions.

That “string theory predicts violations of the equivalence principle” is what used to be called a “factoid”, something not true repeated so often that it becomes a fact. It seems though that usage has changed, with “factoid” now often being used to refer to something true. A new word is needed.

Update: See here for an article by Michel Janssen and Jurgen Renn discussing in detail the question of the “mathematical” versus “physical” strategies in Einstein’s discovery of the GR field equations.

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Quick Links

Posted on February 25, 2015 by woit
  • The LHC is getting close to the point where it can be restarted with a 6.5 TeV beam energy. Latest news here, schedule here. Plan is for a sector test late next week (beam in part of the machine), beam in the whole machine March 23. First physics run May 18th.
  • Next week there will be a conference in Venice devoted to neutrinos, blogging going on here.
  • There may be some progress on the Mochizuki/abc front. Ivan Fesenko has written up some notes that try and put Mochizuki’s ideas in context with some other more conventional parts of mathematics. The week after next will see a workshop in Kyoto, with lectures from Go Yamashita on the abc proof. Another recent survey talk by Mochizuki is here.
  • The latest AMS Notices has a series of articles about the life and work of Arthur Wightman, one of the main figures in the effort to make rigorous sense of quantum field theory.
  • In my essay about math and physics, I mentioned the Atiyah-Bott work on the moduli space of solutions to the Yang-Mills equation in the case of Riemann surfaces. This has an intriguing analog to the function field case, which was discussed already by Atiyah and Bott. Dennis Gaitsgory has a new paper out that touches on this in the context of his proof (with Jacob Lurie) of the Weil Tamagawa number 1 conjecture for function fields (see here). The new paper has the footnote: “The contents of this paper are joint work with J. Lurie, who chose not to sign it as author.”
  • Returning to physics, Princeton University Press announced that Frank Wilczek will edit a Princeton Companion to Physics, modeled on the wonderful Princeton Companion to Mathematics, which was edited by Tim Gowers. Publication is planned for 2018.
  • Caltech hosted a workshop the past couple days, inaugurating the Walter Burke Institute for Theoretical Physics. Hopefully they’re well-funded enough to put videos or slides online. John Preskill’s remarks at a celebration of the event are available here. He gives some principles for doing science that I very much agree with. In recent years I’ve become especially aware of the importance of his first principle: “We learn by teaching”, since I’ve been learning a lot that way. As the trend grows towards institutes modeled on the IAS and prestigious positions that involve no teaching, I think this needs to be kept in mind.

    I also agree with his last principle: “Nature is subtle”, and found very interesting his comments on the holographic principle:

    Perhaps there is no greater illustration of Nature’s subtlety than what we call the holographic principle. This principle says that, in a sense, all the information that is stored in this room, or any room, is really encoded entirely and with perfect accuracy on the boundary of the room, on its walls, ceiling and floor. Things just don’t seem that way, and if we underestimate the subtlety of Nature we’ll conclude that it can’t possibly be true. But unless our current ideas about the quantum theory of gravity are on the wrong track, it really is true. It’s just that the holographic encoding of information on the boundary of the room is extremely complex and we don’t really understand in detail how to decode it. At least not yet.

    This holographic principle, arguably the deepest idea about physics to emerge in my lifetime, is still mysterious. How can we make progress toward understanding it well enough to explain it to freshmen?

    From what I can tell, the problem is not that it can’t be explained to freshmen, but that it can’t be explained precisely to anyone, since it is very poorly understood. The AdS/CFT conjecture is now older than some of my current students, with a literature of more than 10,000 papers, but taking a look recently (see here) at what should be a toy model case (AdS3/CFT2) reminded me just how little seems to be truly understood. This is a quite odd and I think historically unprecedented situation.

  • Somewhat related to the holography question, for anyone interested in condensed matter physics, I recommend taking a look at Ross McKenzie’s blog Condensed Concepts. He discusses some of the issues related to attempts to use holography in condensed matter. He also has a recent paper (with Nandan Pakhira) showing a violation of a bound suggested by holographic arguments.

Update: On the multiverse mania front, tomorrow Science Friday is hosting Sean Carroll to continue his war against falsifiability and the conventional understanding of science, joined by Seth Lloyd to help promote the multiverse. Perhaps it should be “Pseudo-science Friday”?

Update: Michael Harris’s book now has a blog, which promises to discuss topics that didn’t make it into the book.

Update (March 7): Beam is back in the LHC (well, at least in a part of it). There was a successful test today, sending beam into one sector in one direction, two in the other, see here.

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This Week’s Hype

Posted on February 20, 2015 by woit

A quarter-century or so ago, one of common arguments for string theory research was that it was “the only game in town”, in the sense that it was the only possible way to get a unified theory. For instance, back in 1987 David Gross had this to say:

So I think the real reason why people have got attracted to it is because there is no other game in town. All other approaches of constructing grand unified theories, which were more conservative to begin with, and only gradually became more and more radical, have failed, and this game hasn’t failed yet.

As years went on and string theory unification went nowhere, this often was replaced by a new “only game in town” argument, that string theory was the only possible quantum theory of gravity. This argument got strong disagreement from people pursuing Loop Quantum Gravity or any number of other ideas.

This week, Quanta magazine has a new version of the argument, reporting that “Researchers are demonstrating that, in certain contexts, string theory is the only consistent theory of quantum gravity. Might this make it true?” The new argument (based on this and this) seems to be that string theory is the only possible theory of quantum gravity because if you look at a certain class of CFTs (based on orbifolds by permutation groups) and invoke the AdS/CFT conjecture for AdS3/CFT2, the 3d gravity theory in the large N limit would have a density of states more characteristic of string theory than a conventional particle theory.

The most obvious problem here is that it is in 3 space-time dimensions, where there are no physical gravitational degrees of freedom. The S-matrix of quantum gravity is exactly calculable in flat 3d space: it’s zero. There’s a very long history of studying 3d quantum gravity, as a toy model without gravitons, but with just topological degrees of freedom. For more about this, see for instance Steve Carlip’s 1998 book on 3d quantum gravity, which works out a large number of different ways of quantizing 3d gravity (not including string theory). One problem with the argument that string theory is the only way to quantize gravity because it is the only way that works in 3d is that, as Carlip shows, there’s a long list of other completely different ways to do this (all arguably not that relevant to the problem since none have gravitons). This is also quite different than the usual argument that string theory is needed to quantize gravity, which is based on the occurrence of a spin 2 graviton in the spectrum of the string theory.

Ignoring the obvious problem of no gravitons and being in the wrong dimension, there are other problems with the argument, for instance the claim that looking at permutation orbifolds tells you about all CFTs, or the claim that a large density of states at high energy means you have to have a string theory. The article quotes Matt Strassler about this:

But these aren’t really proofs; these are arguments. They are calculations, but there are weasel words in certain places… And just finding a stringy density of states — I don’t know if there’s a proof in that … This is just one property.

Carlo Rovelli sums up the issue with using this to hype string theory and excuse its failures:

They should try to solve the problems of their theory, which are many, instead of trying to score points by preaching around that they are ‘the only game in town.’

I haven’t followed closely work on AdS3/CFT2, but it is a quite interesting topic, although not because it promises a proof of the “universality” of string theory. Chern-Simons theory is based on a very similar relation between a topological 3d qft and 2d CFTs, and there we have some idea what is going on, although many fascinating questions remain. One might hope that AdS3/CFT2 provides a context where one could understand things using some ideas from the Chern-Simons context. This is what Witten did back in 2007 in his paper Three-Dimensional Gravity Revisited (I wrote about this before the paper here). My understanding is that problems with Witten’s proposal later surfaced, I’d be curious to hear from an expert on the latest state of that (perhaps Witten can write a “Three-Dimensional Gravity Revisited Revisited” paper).

There are a lot of wonderful questions still not understood about this story, but I don’t see that using it to argue that string theory is the “only game in town” does anything other than throw one more thing on the pile of outrageous hype generated by string theory partisans over the last 30 years.

Update: There’s been a change to the Quanta article, adding to the quote from Lee Smolin, who is making much the same point I was making in this posting:

“And even in that case [2+1 d], there have existed for a long time counterexamples to the string universality conjecture, in the form of completely worked out formulations of quantum gravity which have nothing to do with string theory.” (String theorists argue that these particular 2+1 gravity theories differ from quantum gravity in the real world in an important way.)

This whole thing really is very strange: on the one hand string theorists are arguing that only string theory can give you quantum gravity, based on an argument in 2+1 d. When you point out to them that there are well-known counterexamples to their argument in 2+1 d, they say “well, things are different in 2+1d than in other dimensions”. Just bizarre…

Posted in This Week's Hype | 18 Comments

Towards a Grand Unified Theory of Mathematics and Physics

Posted on February 14, 2015 by woit

A draft of an essay I’ve written, with plans to submit it to the FQXI essay contest, is available here. Constructive comments welcome…

People who have a take on the subject that has nothing to do with what I’m writing about are encouraged to submit their own essays to FQXI, but not to post them here.

Update: Thanks to all commenters for often helpful comments. I’ve revised the essay a bit, mostly by adding some material at the end, material that to some extent addresses important issues raised by some commenters.

Update: The essay has been submitted and is posted here.

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The Singular Universe and the Reality of Time

Posted on February 14, 2015 by woit

Lee Smolin has a new book out last month, co-written with philosopher Roberto Unger, entitled The Singular Universe and the Reality of Time. To get some idea of what he’s up to, there’s a review by Bryan Appleyard at The Sunday Times (non paywalled version here), another Bryan Appleyard piece here, and interviews with John Horgan and at Scientia Salon. In other news about Smolin, he’s one of the winners of this year’s first Buchalter Prize in cosmology.

The book is written in a rather unusual style, with the first two thirds or so by Unger, the rest a shorter contribution from Smolin, together with a section discussing where they disagree. It’s neither a popular science book, nor a technical work of philosophy, but something somewhere in between, best perhaps compared to something one rarely now sees, a work of “Natural Philosophy”. I found the long section by Unger rather hard going and not very rewarding, and realized that I have a fundamental problem with this sort of writing. Arguments about physics and mathematics made in natural language leave me often unable to figure out exactly what is being claimed. Sometimes this is because I’m not familiar enough with a philosphical tradition being invoked and its associated use of terms, sometimes I suspect it’s because natural language is just too imprecise and ambiguous.

The Smolin section is shorter and written with more precision, making it easier to get an idea of what he’s trying to claim. To seriously address all his arguments would be a large project I’m not able to undertake, but here is a list of “hypotheses” or “principles” that he arrives at:

  • The uniqueness of the universe.
  • The reality of time.
  • Mathematics as the study of evoked relationships, inspired by observations of nature.

For the first of these I don’t really disagree. Smolin takes this as an hypothesis of no “multiverse”, an hypothesis that science may be able to confirm or disconfirm. Our current best understanding of science shows no evidence for a multiverse, so anyone who wants to posit one needs to come up with some significant evidence for one, experimental or theoretical, and I haven’t seen that happening. It’s entirely possible that a compelling theory may emerge that naturally implies a multiverse, but that’s not currently the case. Unlike Smolin, I wouldn’t take this as an hypothesis, more just would say that the question of multiple universes is well worth ignoring until someone comes up with a good reason to pay attention.

For the second, one problem is that I’m not exactly sure what it means. I guess that when I hear the word “real” I’m always rather suspicious that a meaningless distinction is being invoked (i.e. is the wave-function “real”?), and start trying to remember what it was I once understood about ontological commitments from reading Quine long ago. Part of what Smolin is referring to I think I’m sympathetic with: the nature of time remains mysterious in a way that space isn’t. While relativity treats them on an equal footing, in quantum theory this is not so clear. My suspicions about this mystery though tend to focus on the analytic continuation between Minkowski and Euclidean signature, which I’d guess is quite different than Smolin’s concerns (see hypothesis three…)

What Smolin seems to have in mind here is the hypothesis that physical laws are not “timeless”, but can evolve in time, with an example the ideas about “Cosmological Natural Selection” he has worked on. One problem with this is that the question then becomes “what law describes the evolution of physical laws?”, with an answer re-introducing “timeless” laws. Smolin refer to this as the “meta-law dilemma” and devotes a chapter to it, but I don’t think he has a convincing solution.

On the third hypothesis, about the nature of mathematics and its relationship to physics, I just fundamentally and radically disagree. For a shorter version of Smolin’s argument, see this essay, which he has recently submitted to the FQXI essay contest. I’ve been writing something about how I see the topic, will blog about it here very soon. What I’m writing isn’t a response to Smolin’s arguments, but a positive argument for the unity of math and physics at the deepest level.

My problems with Smolin’s point of view aren’t especially about his arguments concerning Platonism and whether mathematical objects are “real” (see earlier comments about what’s “real”), they’re about arguments like this one, where he argues that the explanation for the “unreasonable effectiveness of mathematics” in physics is not some deep unity, but just

mathematics is a powerful tool for modelling data and discovering approximate and ultimately temporary regularities which emerge from large amalgamations of elementary unique events.

The argument essentially is that mathematics is nothing more than a calculational tool that just happens to be useful sometimes in physics. This is a common opinion among physicists, and a big problem for me is that here Smolin is not taking a provocative minority point of view, but just reinforcing the strong recent intellectual trend amongst the majority of physicists that the “trouble with physics” is too much mathematics. As I’ve often pointed out, the failures of recent theoretical physics are failures of a wrong physical idea, rather than due to too much mathematics, with the multiverse just an endpoint of where you end up if you throw away all non-trivial mathematical structure in pursuit of a bad idea.

In his essay, Smolin gives a discussion of mathematics itself which I think few mathematicians would recognize, defining it as “the study of systems of evoked relationships inspired by observations of nature”, and consisting in bulk just of elaborations of the concepts of number, geometry, algebra and logic. I started my career in physics departments, and I’m well aware of how mathematics looks from that perspective (even if you have a lot of interest in math, like I did). My experience of moving to work in math departments made clear to me that the typical ideas of physicists about what mathematics is and what mathematicians do are highly naive, with Smolin’s a good example.

I’ll end with just one example of what I see is wrong about the conventional physics view that Smolin represents. A big application of mathematics to physics is the use of the rotation group SO(3). In that case it’s true that many of the applications can be thought of as concerning approximate aspects of complicated physical systems, and derived from working out precisely the implications of our experience dealing with the 3d physical world. But, besides the chapter on angular momentum operators (and thus SO(3) representation theory) in every quantum mechanics textbook, there’s an earlier chapter where the Heisenberg commutation relations are given as fundamental postulates of the theory. A concise way of stating this postulate is that quantization is based on a specific unitary representation of a Lie algebra (the Heisenberg Lie algebra). This is not approximate, but the fundamental definition of what we mean by quantum theory. The structure here is very deep mathematics (appearing for instance in number theory, the theory of theta functions and of Abelian varieties), and is far removed from the kinds of mathematics that one runs into as typical approximate calculational tools when studying physical problems. This is just an example, but there are many others. I don’t think that if you look at them you can sustain the argument that deep mathematics and deep physics are not close cousins with a unity we only partially understand.

Anyway, more detail to come about this…

Posted in Book Reviews | 14 Comments

Short Items, and a Quick Book Review

Posted on February 13, 2015 by woit
  • Peter Orland has a new blog, Ensnared in Vacuum, where he’s writing about some non-perturbative QFT questions.
  • Physics Today this month has book reviews of two books about theology and the multiverse (one of which I wrote about here). There was a time when I would have thought that discussions of theology wouldn’t be what Physics Today covers, but evidently that’s no longer the case.
  • On a related topic, Kate Becker at The Nature of Reality has an article entitled Does Science Need Falsifiability? It’s about the campaign by physicists like Sean Carroll and Lenny Susskind against the Popperazi who keep pointing out that giving up on falsifiability puts physics in danger of becoming, well, theology. Frank Wilczek has a very sensible take on the subject:

    “I think falsifiability is not a perfect criterion, but it’s much less pernicious than what’s being served up by the ‘post-empirical’ faction,” says Frank Wilczek, a physicist at MIT. “Falsifiability is too impatient, in some sense,” putting immediate demands on theories that are not yet mature enough to meet them. “It’s an important discipline, but if it is applied too rigorously and too early, it can be stifling.”

    On Twitter, the usually mild-mannered Wilczek makes clear his feeling about this

    Not often I refer to a “pernicious” “faction”, but appropriate here.

    Mysteriously, he has a new website, for a company “Wolfcub Vision, Inc”.

  • Frank Close has a new book out, Half-Life, which is essentially a biography of the physicist Bruno Pontecorvo. It’s also a gripping spy story, investigating the question of exactly why Pontecorvo fled with his family to the Soviet Union in 1950. There’s no smoking gun found, but all the evidence Close lays out makes the case that it is quite likely that Pontecorvo had been spying for the Soviets, fleeing when warned that he was in danger of being exposed.

    Freeman Dyson has a much better review of the book in the New York Review of Books than I could ever write. He argues that Pontecorvo made a mistake by fleeing to enforced isolation in Russia, that in the worst case if caught he would have spent a few years in jail, then could have resumed his career. That things would go this way would not however have been clear to Pontecorvo: the Rosenbergs were arrested just before he fled, and things didn’t work out so well for them.

    Besides the fascinating spy story, there’s also a lot of history of nuclear physics during the 30s, 40s and 50s, much of which I wasn’t aware of, as well as quite a bit about Pontecorvo’s later work on neutrinos. If you’re interested in the history of 20th century physics, this is something you’ll find well worth reading.


Update: For another new book, Steven Weinberg’s To Explain the World, I fear that I don’t have the time to read it and write a review. However, here are two interesting reviews, pro and con.

Update: For two hints about “Wolfcub Vision”, a commenter points out that Wolf cub=Wilczek in Polish, and a correspondent points me here.

Update: David Mumford has a posting Is it Art? at his blog, motivated by my friend Dan Rockmore’s equations project. An article about the recent panel discussion of this at Yale is here.

Posted in Book Reviews, Multiverse Mania | 16 Comments

IPMU Conversation with Edward Witten

Posted on February 6, 2015 by woit

I recently heard from Hirosi Ooguri that a transcript of a long conversation with Witten held at the time of his Kyoto Prize award has just appeared in the Kavli IPMU Newsletter. It’s a truly fascinating document, giving some great insights into Witten’s work at the boundary of math and physics and how he sees the state of ideas in this area. It’s wonderful that he was induced to give such a thoughtful and extensive explanation of both the history and significance of these various topics.

Just to pick out a couple examples, the discussion of geometric Langlands describes a lot of detailed history that I was unaware of. I had noticed that in their first massive (still unpublished) paper that started the subject, Beilinson and Drinfeld credit Witten with “the main idea” (I wrote about this in detail here). But there was nothing in what Witten has written that corresponds to what they did, and experts I talked to didn’t see how this came from Witten. Witten tells the true story this way:

Actually, the very little bit of what Beilinson and Drinfeld were saying that I could understand made me wonder if the work of Nigel Hitchin would be relevant to them, so I pointed out to them Hitchin’s paper in which he had constructed commuting differential operators on the moduli space of bundles on a curve. Differently put, Hitchin had in a certain sense quantized the classical integrable system that he had constructed a few years before. Although I understood scarcely anything of what Beilinson and Drinfeld were saying, I did put them in touch with Hitchin’s work, and actually, in their very long, unpublished foundational paper on geometric Langlands that you can find on the web, Beilinson and Drinfeld acknowledged me very generously, far overestimating how much I had understood. All that had really happened was that based on a guess, I told them about Hitchin’s work, and then I think that made all kinds of things obvious to them. Maybe they felt I knew some of those things, but I didn’t. But anyway, there were ample reasons in those years to think that geometric Langlands had something to do with physics, but as you can see I still couldn t make any sense out of it.

He also describes how he came to the idea of interpreting geometric Langlands as a form of mirror symmetry, inspired by things he learned from David Ben-Zvi at lectures about the Langlands program bringing together mathematicians and physicists at the IAS.

He contrasts his work in recent years relating Khovanov homology and gauge theory with the geometric Langlands work, saying that he thinks the Khovanov homology ideas are in a form such that mathematicians are more likely to be able to appreciate their roots in gauge theory:

I think it s actually very difficult to see what advance in the near term could make the gauge theory interpretation of geometric Langlands accessible for mathematicians. That’s actually one reason why I m excited about Khovanov homology. My approaches to Khovanov homology and to geometric Langlands use many of the same ingredients, but in the case of Khovanov homology, I think it is quite feasible that mathematicians could understand this approach in the near future if they get excited about it. I believe it will be more accessible. If I had to bet, I think I have a decent chance to live to see gauge theory and Khovanov homology recognized and appreciated by mathematicians, and I think I’d have to be lucky to see that in the case of gauge theory and the geometric Langlands correspondence – just a personal guess

About the geometric Langlands story, he thinks there is still much to be understood, including its connection to conformal field theory:

In fact, part of the original work of Beilinson and Drinfeld on geometric Langlands has still not been understood to my satisfaction. Here I have in mind the use of conformal field theory at what they call the critical level (level -h, where h is the dual Coxeter number) to construct the A-model dual of certain B-branes (the ones that are associated to opers, in the language of Beilinson and Drinfeld). Davide Gaiotto and I obtained a few years ago a reasonable understanding of what electric-magnetic duality does to the variety of opers, but I still do not really feel I understand its relation to conformal field theory. However, in the last few years physicists working on supersymmetric gauge theories in four dimensions and their cousins in six dimensions have made several discoveries involving the role of conformal field theory at the critical level, so the time may well be right to resolve this point.

Among the many other highly interesting comments, one was Witten’s take on the possible connection of quantum field theory to number theory. He has a long history with this, going back to conversations with Atiyah in 1977 in which Atiyah suggested some connection between Langlands and Montonen-Olive. Witten writes

I was skeptical about Montonen-Olive duality, I didn’t seriously try to relate it to Langlands duality and I didn’t try to learn what Langlands duality was. I did not learn anything more about these matters until the late 1980s. Then I learned just superficially about the Langlands correspondence. If one knows even a little bit about the Langlands correspondence and a little bit about conformal field theory on a Riemann surface, one can see an analogy between them. I wrote a paper that was motivated by that but then I realized that my understanding was too superficial to lead to anything deep, so I abandoned the matter for a number of years.

Later of course, he followed work on geometric Langlands and ultimately found the connection to gauge theory he worked out with Kapustin. As far as current prospects for connections to number theory, he has quite a few comments, but thinks the subject is still a dream that is not ripe:

For me personally−it’s a dream that eventually number theory would make contact with physics some time, but I doubt it will be soon. There are all kinds of areas where specific number theory formulas appear in physics, and these may be clues that the dream will come true one day. But to really get me excited, somehow the number theory would have to enter the physics in a more structural way. I m not that interested in a specific formula that comes out of a physics calculation in a more or less ad hoc fashion. Number theory would have to be more integrated with the physics to get me excited, and I don t see that happening soon. In my work, I concentrated on the geometric form of the Langlands correspondence because I could see that there was hope to really understand it in the context of the physics-based tools that were at hand. There might be something like that one day for the Langlands correspondence of number theory, but probably a lot is missing and we do not know what has to happen first.

This just gives a taste of the conversation, there is lots, lots more there, on a wide range of topics. Highly recommended reading for anyone with an interest in this area, I’ve never seen anything like it.

Posted in Langlands | 23 Comments

Planck Data Out

Posted on February 5, 2015 by woit

Long awaited data from the Planck satellite was released today, papers available here. The accompanying press release leads with results about the timing of the first stars, 500 million years or so after the big bang, with little mention of the very early universe. This is also the main topic of BBC News coverage.

This paper reports a bound on r of .08-.09, exactly what Shaun Hotchkiss was predicting earlier this week here. This appears to be pretty much the end of the line for hopes that Planck would see primordial gravitational waves, with the paper seemingly pointing to other experiments being necessary to get below r=.05 (see page 35).

The BBC News story also characterizes these bounds as ruling out the simplest inflationary models, requiring they be supplemented by “exotic physics”.

What is clear from the Planck investigation is that the simplest models for how that super-rapid expansion worked are probably no longer tenable, suggesting some exotic physics will eventually be needed to explain it.

“We’re now being pushed into a parameter space we didn’t expect to be in,” said collaboration scientist Dr Andrew Jaffe from Imperial College, UK. “That’s OK. We like interesting physics; that’s why we’re physicists, so there’s no problem with that. It’s just we had this naïve expectation that the simplest answer would be right, and sometimes it just isn’t.”

For about as long as I can remember, string theorists and multiverse fans have been pointing to Planck data as the test of their ideas. For cosmic strings, the last Planck data release had a paper ruling them out. I don’t see a paper on this topic out or projected for the new data, it seems that this is now something not even worth looking for.

We’ve also been hearing for years that Planck will test supposed evidence of bubble collisions indicating other universes, see for instance this article about this paper, where the article states that

Data from the Planck telescope should resolve the question once and for all.

I don’t see anything in the new data even looking for this. Has it already been ruled out, without any publicity, or did the Planck people think it was something not worth even looking for?

Posted in Uncategorized | 18 Comments

A Letter to the AMS

Posted on February 3, 2015 by woit

Leonid Reyzin at Boston University has drafted a letter in response to the recent article published in the Notices by Michael Wertheimer of the NSA (discussed here). He’s collecting signatures, and if you’re a member of the AMS I urge you to consider contacting him and adding yours. If you know others who might be interested in signing, please forward the link to them.

Posted in Uncategorized | 10 Comments