P-adic Numbers and Cosmology

Posted on October 4, 2011 by woit

The next math department colloquium at Stanford will feature Lenny Susskind lecturing on p-adic numbers and cosmology, here’s the abstract:

The biggest conceptual problem of cosmology is called the measure problem. It has to do with the assignment of probabilities in an exponentially inflating universe, which falls apart into separate causally-disconnected regions. Neither I nor my friends had ever intended to learn about p-adic numbers until we realized how similar such a universe is to an endlessly growing tree-graph. The result has been some new insights from p-adic number theory into the measure problem and other puzzles of eternal inflation. Within the constraints of a one-hour lecture, I will explain as much of this as I can.

I’ve no idea what this is about, but I’m guessing that Susskind is somehow drawing inspiration from two facts:

  • p-adic integers can be represented using a “tree” diagram vaguely remniscent of the logo for the Stanford theoretical physics group on their web-site.
  • The p-adic integers, unlike the usual integers, are compact, so you can put a finite measure on them.

    • It’s hard to believe that any of the special features of these mathematical structures will make the problems of eternal inflation go away, but who knows…

    Coincidentally, I’ve spent a lot of time recently learning about the p-adics, with a very different motivation. The way these things come up in mathematics is that you can think of number theory as being about a space, the space of prime numbers. The p-adics appear naturally when you decide to ask what happens locally near one point (i.e. at one prime). P-adic integers correspond to power series expansions, p-adic numbers to Laurent series. Various people have thought about analogies between conformal field theories on a Riemann surface, where one also wants to focus on what happens at a point and use representation theory methods, and the Langlands program which does something similar in number theory. This is part of the geometric Langlands story, and has roots in a remarkable paper of Witten’s from 1988 entitled Quantum field theory, Grassmannians, and algebraic curves.

    As I’ve mentioned before, this semester here at Columbia we have Harvard’s Dick Gross as Eilenberg lecturer, and he’s giving a wonderful series of lectures starting with local Langlands. I’m hoping at some point to put together what I’ve been learning about this and possible connections to QFT in some readable form, but at the moment things are still too speculative and hazy. In any case, no sign that these ideas are going to solve the problems of cosmology…

    Update: The Susskind et al. paper on this topic is now out at the arXiv. A p-adic model is studied, but no reason is given to believe that it has anything to do with eternal inflation and cosmology.

    Posted in Multiverse Mania | 18 Comments

    Two for Two

    Posted on October 4, 2011 by woit

    Back in 2004 I made my first venture into Nobel Prize predictions, then decided to retire from that business. This year I came out of retirement with another prediction. After the posting, I consulted with experts who assured me that the right names were Perlmutter, Riess and Schmidt, something I thought I mentioned in a comment, but it appears that I didn’t, instead leaving this to Shantanu.

    Congratulations to Perlmutter, Riess and Schmidt. The theoretical significance of their tour de force observational work remains still controversial, but it richly deserves the Nobel prize.

    Posted in Uncategorized | 6 Comments

    New Pursuit of Schrodinger’s Cat

    Posted on October 3, 2011 by woit

    Prospect magazine has an excellent new article by Philip Ball on recent developments in the fundamental problem of the interpretation of quantum mechanics: why don’t we see superpositions? Most popular discussions of this seem to me to be stuck back in debates from the 1930s, and ignore the main question. QM is a simple, beautiful mathematical structure that works perfectly experimentally, the confusing question is that of how classical behavior emerges during a measurement process (typically involving huge numbers of degrees of freedom, making analysis difficult).

    At the end of the article, Ball mentions one particularly intriguing set of ideas, due to Wojciech Zurek, about “quantum Darwinism”. For more about this, see Zurek’s survey here.

    There’s a new preprint out by Steven Weinberg on Collapse of the State Vector. Weinberg claims that “There is now no entirely satisfactory interpretation of quantum mechanics”, and refers for more detail about this claim to Section 3.7 of his Lectures on Quantum Mechanics, a manuscript that is “to be published”. I’m definitely looking forward to this book when it comes out. The sort of thing that Weinberg examines in the preprint though, modifying QM to take into account wave-function collapse, is the kind of idea I’ve never found promising. Why modify QM, it works perfectly and is mathematically extremely aesthetically compelling? Better to keep QM as is, and closely examine one’s understanding of what the problem really is.

    Posted in Uncategorized | 16 Comments

    This Week’s Hype

    Posted on September 28, 2011 by woit

    It had to happen. New Scientist managed to find a physicist willing to describe the OPERA result as “evidence for string theory”:

    So if OPERA’s results hold up, they could provide support for the existence of sterile neutrinos, extra dimensions and perhaps string theory. Such theories could also explain why gravity is so weak compared with the other fundamental forces. The theoretical particles that mediate gravity, known as gravitons, may also be closed loops of string that leak off into the bulk. “If, in the end, nobody sees anything wrong and other people reproduce OPERA’s results, then I think it’s evidence for string theory, in that string theory is what makes extra dimensions credible in the first place,” Weiler says.

    Update: hep-ph is chock-a-block with papers purporting to explain the OPERA results, using theoretical models of varying degrees of absurdity. There is however one much more sensible paper this evening, from Cohen and Glashow, which points out that superluminal neutrinos would produce electron-positron pairs via bremsstrahlung, and lose energy, which is not observed. This is also incompatible with Super-Kamionkande and IceCube data. No matter what sort of extra dimensions you introduce for the neutrinos to travel in, the OPERA claim seems to be in violent disagreement with other observations.

    Posted in This Week's Hype | 69 Comments

    This and That

    Posted on September 27, 2011 by woit
  • Since everyone wants to hear about the faster-than-light neutrinos, here’s some additional information about why I don’t believe it. Jon Butterworth explains here the problem with timing the neutrinos at the CERN end. In a postscript, a senior member of OPERA points out that he and four other senior members of the collaboration kept their names off the paper. Their reasoning seems to have been that this is a very preliminary, likely wrong, result, being sold as more robust than it is. Tommaso Dorigo had a similar analysis to Butterworth’s up on his blog early on, but was induced to take it down because the release to the press and the associated hullabaloo had not yet taken place.
  • I had been wondering what had happened to the million dollars from the Millenium Prize that Perelman turned down. The Clay Mathematics Institute has recently announced that the money will go to fund, for the next five years, a postdoctoral position at the Institut Henri Poincaré, to be called the Poincaré Chair.
  • A sign of the times: today’s HEP seminar at the IAS was titled “Is SUSY still alive?”. I wasn’t there, so don’t know what the answer was, but clearly the question is now being asked.
  • The Tevatron will shut down on Friday for good, ending an era. There’s an article about this in Science magazine here. Gordon Kane was expecting SUSY to be discovered by this machine, but that didn’t work out, and he’s no fan of Fermilab management:

    But Kane argues that the Tevatron underperformed all along because of weak management at the lab and the Department of Energy, which funds Fermilab. “It could have performed much better and done much more,” he says.

    Reaction to this from Nicholas Samios was:

    “I would not trust a theorist to talk about management,” Samios says.

    • Posted in Uncategorized | 35 Comments

    TEDxFlanders

    Posted on September 25, 2011 by woit

    Tommaso Dorigo and I put on a bit of a show yesterday here in Antwerp at TEDxFlanders, and the results are already available on YouTube (and Tommaso has blog postings here and here). Doing this sort of thing for 1000 people in a venue like the Antwerp Opera House is not at all the sort of thing I’m used to, so I’m glad that it seemed to come out reasonably well.

    Much of this was due to the incredible all-volunteer staff, which put on an ambitious day-long program on a shoe-string (+ crucial help from some sponsors) and pulled it off with only the most minor hitches. Christophe Cop was the “curator” and founding father of TEDxFlanders, and Thomas Goorden led the production team to victory. It was a great pleasure to meet them, many of the other volunteers, and some of the other speakers, as well as to get a chance to enjoy some time in the beautiful city of Antwerp.

    Back to New York (and maybe somewhat more regular blogging) on Tuesday. Hoping to make Dick Gross’s second Eilenberg lecture on Local Langlands at the Columbia math department in the afternoon…

    Posted in Uncategorized | 10 Comments

    No News

    Posted on September 15, 2011 by woit

    I’ve been hearing no interesting news from the LHC recently, about all I’ve learned is that CMS/ATLAS haven’t even decided whether it’s worth combining their latest public data (probably not, what is much more interesting is the large amount of data they are now analyzing separately). So my plan for next week is to travel to Antwerp, where I’ll try and get Tommaso Dorigo drunk and see what I can find out. We’ll both be at TEDx, he’s got more of the story here.

    Adrian Cho has a wonderful long piece in Science (and podcast here) about the sociology of the two big experiments at the LHC. It gives some insight into the process by which a Higgs result is likely to emerge, including the steps being taken to make sure that some group doesn’t “parachute in” at the last moment to try and capture glory. I’m still trying to figure out who gets a Nobel prize if the Higgs is found.

    For some other reading material, there’s John Ellis’s 65th birthday colloquium, an interview with Bianca Dittrich, and yet more evidence that MathOverflow rules.

    Posted in Experimental HEP News | 71 Comments

    How to Win the Nobel Prize

    Posted on September 12, 2011 by woit

    I’m too busy to write much on the blog just this moment, and besides, there’s nothing of great interest I can think of that need’s writing about. So, I’ll take up commenter Shantanu’s suggestion and try and stir up a little trouble with two quick topics related to the Nobel Prize.

  • Norman Dombey recently posted on the arXiv Abdus Salam: A Reappraisal. PART I. How to Win the Nobel Prize which more or less seems to argue that Salam didn’t deserve his 1979 Nobel. He describes a lot of history I didn’t know, but I’m not completely convinced. Part of the argument seems to be that he stole the idea from Weinberg, and didn’t even know the importance of what he had stolen, but my impression was that no one, not even Weinberg, thought very much of the unified electroweak theory at the time. A quick look at the paper in his collected papers that I take to be the 1968 one that justified the Nobel to him appears to discuss the crucial points: a gauge theory with Higgs mechanism.

    Unfortunately I don’t have more time now to look into this history carefully. If someone expert on this history has comments on the Dombey claims, that would be interesting.

  • One way to win the prize is to do revolutionary work. This year’s prize will be announced October 4, and for the past few years I haven’t had much in the way of thoughts about obvious candidates. After reading Richard Panek’s The 4% Universe early this year and learning more of the story of the discovery of the acceleration of the universe, I’m pretty sure that sooner or later there will be a Nobel Prize for that, maybe this year. Those better informed than me can speculate about what the exact names will be that will go on the prize.
    • Posted in Uncategorized | 57 Comments

    Imagine There’s No God Particle

    Posted on September 5, 2011 by woit

    It’s easy if you try (as John Lennon would say).

    The LHC is back in business after a technical stop, getting ready to collide protons for the next couple months, perhaps reaching an integrated luminosity of about 5 inverse femtobarns. This is a factor of four higher than the luminosity used in most analyses that have been made public so far, and the latest projections are that this should allow an exclusion of a Higgs over the entire expected mass range at 95% confidence level, if such a particle really doesn’t exist.

    My pre-LHC predictions (see here) of five years ago have held up well, and nothing yet has changed my view that a Higgs particle scenario and a no-Higgs scenario are equally likely. The best argument for a Higgs in the mass range of 114-145 GeV is that it’s the simplest way anyone has found of making the Standard Model work, and explains a range of precision electroweak measurements.

    The best argument against the Higgs is that elementary linear scalar fields are problematic (since not asymptotically free) and esthetically displeasing (not geometrical and constrained by symmetries, so lead to lots of undetermined parameters, mainly for the Yukawas that determine the masses of all fermions). By analogy with the theory of superconductivity though, one can imagine that the Higgs makes a good low-energy effective theory (a la Landau-Ginzburg), even if there’s a more interesting fundamental theory, which may require going to a smaller distance scale (a la BCS theory). As the allowed Higgs mass range has narrowed though, I’m starting to think that there may be something to the argument that it’s implausible that the mass would end up being in the hardest mass range for colliders to examine. More likely it’s just not there, and the hardest range is the last one to fall to experiment.

    By the way, I was interviewed about this on a Wired podcast (see here), not sure how it turned out. I don’t think I said anything surprising or controversial.

    The imminent arrival of an experimental result deciding the issue of the SM Higgs has focused attention on what the implications will be, and here’s what I’ve been thinking:

    If the SM Higgs is found, there will be rejoicing at first at CERN and within the physics community, and an appropriately proud announcement to the public. Debate will begin on who gets the Nobel: experimentalists? which of the 6000+ people at LHC/CMS/ATLAS? or theorists? Anderson/Higgs/Englert/Brout/Guralnik/Hagen/Kibble, or ? I gather Brout is no longer with us, maybe this will have to wait until the list gets down to three by attrition. Probably the best case would be for Weinberg/Salam, but they already were rewarded for the SM. Maybe the Swedes could make Weinberg’s a double. The LHC experimentalists would have an active research program for many years trying to measure the Higgs properties. Theorists though would face the gloomy prospect that these would just agree with the SM. We’d be stuck pretty much where we have been for thirty years: no clues as to how to do better than the SM.

    What though if the SM Higgs gets ruled out? CERN may consider this an embarassment, but it’s actually a far more exciting result, one even more worthy of the Nobel than finding the long-sought particle. SUSY enthusiasts will claim this means it’s a SUSY Higgs, and model builders will get to work on constructing more complicated models designed to explain the result by making the Higgs even harder to see (Matt Strassler is starting to write about such models here). My guess would be though that no Higgs means the argument from esthetics was right, so adding in more scalar fields in some complex pattern isn’t a very plausible explanation of the null result.

    A commenter here pointed out that this possibility was discussed during the debate over the SSC, when it was argued that, in the case of no Higgs, you would need a 40 TeV machine to look at W/Z scattering, to get information about what was really going on. The LHC should be capable of quite high luminosity, which may compensate for its lower energy in such searches, see a recent discussion here.

    My own very vague favorite idea has always been that, non-perturbatively, there’s something important we’re missing in our understanding of gauge symmetry in chiral gauge theories and that this may hold the secret to the mystery of electroweak symmetry breaking. While this idea has been a motivation for research I’ve been pursuing in recent years, I can’t claim to have made any progress on it. My second real blog posting here was about this, back in 2004, leading to a torrent of abuse. Maybe if there’s no Higgs, SUSY and extra dimensions are gone, this could become a legitimate question in the eyes of mainstream theorists.

    You-hoo-oo-oo-oo, you may say I’m a dreamer
    But I’m not the only one…

    Update: It seems that I’m definitely not the only one inspired by John Lennon recently, with CIP beating me to this a while ago.

    Update: On the topic of this posting, see Slava Rychkov’s talk that just appeared on the arXiv. From the summary:

    We have seen many impressive new physics limits set at this conference. But, have we ever truly believed in the models that are being pushed away? Z-prime, CMSSM, split SUSY, to name a few? I myself certainly never believed in these. Take Z-prime. In spite of what you may have heard, this is a completely unmotivated extension of the SM. It solves nothing of its problems and has nothing to do with Naturalness. Same for split SUSY, anathema to Naturalness. CMSSM is the only victim on the list for which I feel sorry, but we can’t give up on SUSY just because this straightjacketed version of it failed.

    Another early casualty has been the Large Extra Dimensions scenario. But again, this was hardly a bona fide solution to the hierarchy problem. The mechanism which cuts off the Higgs mass quadratic divergence has not been concretely specified. It’s only because the idea was so original that we ever gave it the benefit of the doubt. Now with LHC limits on the (4+n)-dimensional Planck scale already a factor two above the Tevatron limits, it’s basically gone. The truth is, apart from SUSY, there are only two other motivated scenarios for TeV-scale physics: strong EWSB and Composite Higgs. I mentioned some of the signals expected in these models. Unlike CMSSM, they typically require much higher luminosity to be seen.

    Posted in Favorite Old Posts, Uncategorized | 89 Comments

    Knocking on Heaven’s Door

    Posted on September 4, 2011 by woit

    Lisa Randall’s new book is about to come out, it’s entitled Knocking on Heaven’s Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World. It turns out that it’s really two books in one, both of which are much better and more clearly written than her previous effort, Warped Passages. One reason might be help from well-known novelist Cormac McCarthy who is thanked (together with Lubos Motl) for extensive feedback during the book’s writing.

    One of the books here is not surprising, it’s somewhat of an update of the earlier book, emphasizing the story of the LHC. This includes a very detailed explanation of the history of the LHC and how it works, together with a wonderful and clear examination of the design of the ATLAS and CMS detectors, as well as the physics they are looking for. All in all, this is about the best popular-level explanation of what is going on at the LHC that I’ve seen, up-to-date as of a few months ago.

    The second book inside the book is of much wider scope. Randall’s prominence as a scientist has brought her into contact with a wide range of people (Bill Clinton’s endorsement is on the book’s cover), including artists, government officials, financiers, technologists, and a wide range of thinkers of different sorts. She has taken on the role of a public face of physics, and has written a book which is in part a very general defense of science and the materialist, rationalist world-view that modern science is based on. Her experiences with non-scientists are reflected in how she writes about a range of topics, including the notion of beauty in science, the question of how to analyze risk, the relation of religion and science and much more. Her discussions of these topics are uniformly sensible, although rather conventional and unsurprising.

    In the end though, the book left me somewhat uncomfortable. Understandably, Randall is overly enthusiastic about the prospects of Randall-Sundrum models, describing them as “an idea that probably stands as good a chance as any of being right” (most theorists would assign a much higher probability to SUSY). She writes that, if correct, the LHC is expected to see KK gravitons at a mass of around 1 TeV. Recently limits on masses of such particles have been pushed up to nearly 2 TeV. These extra-dimensional models were considered interesting but not especially plausible by most theorists pre-LHC. Like SUSY, they’re starting to be ruled out by the LHC, a process which may take a while until their defenders finally admit that the expected signals just aren’t there.

    The time period of Randall’s career roughly corresponds to my own (she’s a few years younger), and, as she acknowledges, her field of model-building throughout this career has been dominated by string theory-inspired SUSY and extra dimensional models. These were never very convincing, and they are now biting the dust. From the experimental side, this is an inspirational story of the triumph of the scientific method and the huge achievements of the LHC machine and detectors, but from the theoretical side, the story of this period is darker and much less inspirational. It’s not something that makes the best topic for a defense of how science is conducted.

    One odd thing about the book is the title, which for Randall carries a positive meaning that she acknowledges doesn’t correspond to the very dark one of the Bob Dylan song from the soundtrack of the Sam Peckinpah film. It’s a beautiful song, but one not about finding truth, but about getting shot in the gut and facing death, hopefully not relevant to particle physics in the LHC era:

    Mama, put my guns in the ground
    I can’t shoot them anymore.
    That long black cloud is comin’ down
    I feel like I’m knockin’ on heaven’s door.

    Posted in Book Reviews | 14 Comments