Not Even Wrong
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Thu, 20 Jul 2017 18:29:41 GMTFeedCreatorClass 1.0 dev (specificfeeds.com)This Week’s Hype
http://www.math.columbia.edu/~woit/wordpress/?p=9426
<p>Commenter CIP <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9409#comment-226350">pointed out</a> that today’s New York Times has one of the worst examples of string theory hype I’ve seen in a while. Based on <a href="https://arxiv.org/abs/1703.10682">this observation</a> of an expected QFT anomaly effect in a condensed matter system, the NYT has an article <a href="https://www.nytimes.com/2017/07/19/science/mixed-axial-gravitational-anomaly-weyl-semimetals-ibm.html">An Experiment in Zurich Brings Us Nearer to a Black Hole’s Mysteries</a>. Not only is the headline nonsense, but the article ends with</p>
<blockquote><p>The experiment is also a success for string theory, a branch of esoteric mathematics that physicists have used to try to tie gravity into the Standard Model, the laws of physics that describe the other forces in the universe. But string theory has been maligned because it makes predictions that cannot be tested.</p>
<p>Here, Dr. Landsteiner said, string theory was used to calculate the expected anomaly. “It puts string theory onto a firm basis as a tool for doing physics, real physics,” he said. “It seems incredible even to me that all this works, falls all together and can be converted into something so down to earth as an electric current.”</p></blockquote>
<p>There’s no connection at all to string theory here. The NYT seems to have been taken in by string theorist Landsteiner and <a href="https://finance.yahoo.com/news/ibm-scientists-observe-elusive-gravitational-182600873.html">press release hype like this</a>, not noticing that the paper had no mention of string theory in it. The hype is timed to the paper’s <a href="http://www.nature.com/nature/journal/v547/n7663/full/nature23005.html">publication in Nature</a>, where the editor’s summary gets it right, referring to QFT not string theory:</p>
<blockquote><p>Johannes Gooth et al. now provide another intriguing connection to quantum field theory. They show that a condensed-matter analogue of curved space time can add an additional, gravitational component to the chiral anomaly in Weyl semimetals. The work opens the door to further experimental exploration of previously undetected quantum field effects.</p></blockquote>
<p>Someone really should contact the NYT and get them to issue a correction. In particular, any string theorists who care about the credibility of their field should be doing this. </p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9426Various Links
http://www.math.columbia.edu/~woit/wordpress/?p=9373
<p>Some links to things that may be of interest:</p>
<ul>
<li>There’s an excellent <a href="https://fivethirtyeight.com/features/math-has-no-god-particle/">article at FiveThirtyEight</a> about the issue of publicizing math research, taking as example the <a href="http://www.liegroups.org/">Atlas of Lie Groups and Representations</a> project (which will soon be having a <a href="http://www.liegroups.org/workshop2017/workshop/">workshop</a>). This kind of thing generally gets no public attention, while at the same time, one of the results of this research arguably got too much public attention (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=534">here</a>).</li>
<li>There’s a new \$1 million mathematics prize that will be awarded for the first time this fall, together with a $1 million physics prize that was awarded for the first time last year. This is called the <a href="https://futureprize.org/eng">Future Science Prize</a>, and to get it you need to be working in China. Used to be a \$1 million prize was a big deal, now with the \$3 million <a href="https://breakthroughprize.org/">Breakthrough Prizes</a>, a mere million looks like small potatoes.</li>
<li>Another way you could get a measly \$1 million would be to prove (or disprove) the Hodge conjecture. For some inspiration, see Burt Totaro’s new <a href="http://www.ams.org/journals/bull/0000-000-00/S0273-0979-2017-01588-1/home.html">survey of progress on the Tate conjecture</a> (blog entry <a href="https://burttotaro.wordpress.com/2017/06/20/new-review-paper-recent-progress-on-the-tate-conjecture/">here</a>).</li>
<li>4 gravitons has a <a href="https://4gravitons.wordpress.com/2017/06/09/you-cant-smooth-the-big-bang/">nice posting</a> about work by Turok and others about complexified path integrals and cosmology. The issue of the relation between Euclidean and Minkowski signature QFT is one that I think has gotten far too little attention over the years. Now that I’ve finished writing a book with a QFT discussion that sticks to Minkowski space, I’m hoping to work on writing something about the relation to Euclidean space.</li>
<li>There’s an interview with Nima Arkani-Hamed <a href="https://www.pri.org/stories/2017-06-08/physicist-who-always-dreamed-working-us-says-it-s-no-longer-global-center-science">here</a>. His <a href="https://indico.cern.ch/event/617679/contributions/2614659/attachments/1482280/2299162/05-Arkani-Hamed.pdf">talk</a> at the recent <a href="https://indico.cern.ch/event/617679/timetable/#all.detailed">PASCOS 2017</a> conference (real title is second slide “What the Hell is Going On?”) gives his take on the current state of HEP, post failure of the LHC to find SUSY. He’s sticking with his 2004 “Split SUSY” as his “Best Bet”. I’d like to think his inspirational ending claiming that the negative LHC results are forcing people to rethink the foundations of the subject, asking again the question “What is QFT?” reflects reality, but not sure I see much of that.</li>
<li>This year’s LHC startup has been going well, with new a new luminosity record already set, and 6 inverse fb of data already collected. For more, see <a href="http://www.ibtimes.com/cern-lhc-update-large-hadron-collider-breaks-record-circulating-proton-bunches-2561117">here</a>.</li>
<li>Remember that “dark flow” that was supposed to be in the CMB data and evidence for the multiverse (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=5907">here</a>)? Still not there, <a href="https://arxiv.org/abs/1707.00132">according to Planck</a> (via <a href="https://twitter.com/WKCosmo/status/882186467589713921">Will Kinney</a>).</li>
</ul>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9373Last Week’s Hype
http://www.math.columbia.edu/~woit/wordpress/?p=9409
<p>Now back from vacation, more regular blogging should resume imminently. While away, lots of press stories about claims that LIGO could be used to get “evidence for string theory”. As usual, these things can be traced back to misleading statements in a <a href="https://arxiv.org/abs/1704.07392">paper</a> and the associated <a href="http://www.aei.mpg.de/2070241/hints-of-extra-dimensions-in-gravitational-waves">university press release</a>. In this case, there had already been an <a href="https://www.newscientist.com/article/mg23431244-200-gravitational-waves-could-show-hints-of-extra-dimensions/">initial round of hype</a>, <a href="http://backreaction.blogspot.com/2017/05/can-we-use-gravitational-waves-to-rule.html">debunked by Sabine Hossenfelder</a>. The new round seems to have been generated by the June 28 press release. The Guardian has<a href="https://www.theguardian.com/science/2017/jul/05/gravitational-waves-string-theory"> a version of this</a>, but at least there the author found someone to make the obvious point, that this is irrelevant to string theory.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9409This Week’s Hype
http://www.math.columbia.edu/~woit/wordpress/?p=9405
<p>I’m on vacation in Europe, not in any mood to spend more time on this than just to point out that it’s the same usual tedious string theory promotional operation from the same people who have been at this for decades now. We have</p>
<ul>
<li>A PRL publication that has nothing at all to do with string theory, preprint <a href="https://arxiv.org/abs/1702.05490" target="_blank">here</a>. This is about a purely classical pde calculation in coupled EM + gravity.</li>
<li>The researcher’s university puts out a <a href="http://www.cam.ac.uk/research/news/saddle-shaped-universe-could-undermine-general-relativity" target="_blank">press release</a>.</li>
<li>A <a href="https://www.quantamagazine.org/where-gravity-is-weak-and-naked-singularities-are-verboten-20170620/" target="_blank">story then appears</a> where the usual suspects claim this is some sort of vindication for string theory and shows their loop quantum gravity opponents are wrong. There’s a lot of quite good information in the story about the actual classical calculation involved, but no indication of why one might want to be skeptical about the effort to enlist this result in the string vs. loop war.</li>
</ul>
<p>While traveling I’ve seen a couple very good stories about physics online:</p>
<ul>
<li>A <a href="https://www.nytimes.com/2017/06/19/science/cern-large-hadron-collider-higgs-physics.html" target="_blank">summary from Dennis Overbye</a> about the the current status of energy frontier HEP.</li>
<li>An <a href="https://aeon.co/essays/the-quantum-view-of-reality-might-not-be-so-weird-after-all" target="_blank">excellent long article by Philip Ball</a> about quantum mechanics and the measurement problem.</li>
</ul>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9405This Time It’s Really for Real
http://www.math.columbia.edu/~woit/wordpress/?p=9395
<p>Twice now I’ve thought I had a finished version of the <a href="http://www.math.columbia.edu/~woit/QMbook/qmbook.pdf">book I’ve been writing forever</a> (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8844">here</a> and <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9180">here</a>). Each time it turned out that, the way the publishing process was going, I ended up having more time to work on the manuscript and deciding I could do better, especially with some of the basic material about quantum field theory. I do think the latest version has a much improved treatment of the basics of that subject.</p>
<p>This version will go off to Springer in a day or so, and they plan to publish it late this year/early next year. I’m setting up a <a href="http://www.math.columbia.edu/~woit/QMbook">web-page for the book</a>, there may be more material there later.</p>
<p>One thing ensuring that I will stop working on this is that in a couple days I’m heading off on vacation, for a two-week or so trip to Europe. Blogging during that time is likely to be light to non-existent. Back around the Fourth of July, and looking forward to thinking about other projects, anything but this book…</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9395The Dangerous Irrelevance of String Theory
http://www.math.columbia.edu/~woit/wordpress/?p=9375
<p>Eva Silverstein has a new preprint out, entitled <a href="https://arxiv.org/abs/1706.02790">The Dangerous Irrelevance of String Theory</a>. The title is I guess intended to be playful, not referring to its accurate description of the current state of string theory, but to the possibility of irrelevant operators having observable effects. </p>
<p>The article is intended to appear in the forthcoming Cambridge University Press volume of contributions to the Munich <a href="http://www.whytrustatheory2015.philosophie.uni-muenchen.de/index.html">“Why Trust a Theory?” conference</a> held back in December 2015. The impetus behind that conference was a December 2014 article in Nature entitled <a href="http://www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535">Scientific method: Defend the integrity of physics</a>. In that article, Ellis and Silk explained the problems with string theory and with the multiverse/string theory landscape.</p>
<p>The organizing committee for the Munich conference was chaired by Richard Dawid, a string theorist turned philosopher who has written a 2013 book, <a href="http://www.math.columbia.edu/~woit/wordpress/?p=5880">String Theory and the Scientific Method</a>. For a fuller discussion of that book, see the linked blog post. To oversimplify, it makes the case that the proper way to react to string theory unification’s failure according to the conventional understanding of the scientific method is to change our understanding of the scientific method. Much of the Munich conference was devoted to discussing that as an issue in philosophy of science.</p>
<p>One aspect of the Munich conference was that it was heavily weighted towards string theorists, with contributions from Dawid, David Gross, Joe Polchinski, Fernando Quevedo, Dieter Lust and Gordon Kane all promoting the idea that string theory was a success. Polchinski explained a computation that shows that string theory is 98.5% likely to be correct, going on to claim that the probability is actually higher: “something over 3 sigma” (i.e. over 99.7%). The only contribution from a physicist that I’ve seen that argued the case for the failure of string theory was that from Carlo Rovelli, see <a href="https://arxiv.org/abs/1609.01966">here</a>. Silverstein’s article says that it was commissioned by Dawid for the proceedings volume, even though she hadn’t been at the meeting. I’m curious whether Dawid commissioned any contributions from string theory critics who weren’t at the meeting.</p>
<p>Silverstein begins her article explaining how physics at a very high energy scale can in principle have observable effects. This of course is true, but the problem with string theory is that, in its landscape version, it has a hugely complicated and poorly understood high energy scale behavior, seemingly capable of producing a very wide range of possible observable effects, none of which have been seen. The article is structured as a defense of string theory, without explaining at all what the criticisms of string theory actually are. The list of references includes 53 items, only one critical of string theory, the Ellis/Silk Nature article. Some of the arguments she makes are:</p>
<ul>
<li>
<blockquote><p>It is sometimes said that theory has strayed too far from experiment/observation. Historically, there are classic cases with long time delays between theory and experiment – Maxwell’s and Einstein’s waves being prime examples, at 25 and 100 years respectively… One thing that is certainly irrelevant to these questions is the human lifespan. Arguments of the sort ‘after X number of years, string theory failed to produce Y result’ are vacuous.</p></blockquote>
<p>I think the comparison to EM or GR is pretty much absurd. For one thing it’s comparing two completely different things: tests of a particular prediction of a theory (EM or GR) that made lots of other testable, confirmed predictions to the case of string theory, where there are no predictions at all. More relevant to the argument over how long to wait for an idea to pay off is that the real question is not the absolute value of the amount of progress, but the derivative: as you study the idea more carefully, do you get closer to testable progress or farther away? I don’t think anybody can serious claim that, 33 years on, we’re closer to a successful string theory unification proposal than we were at the start, back in 1985. I’d argue that the situation is the complete opposite: we have been steadily moving away from such success (and thus entered the realm of failure).
</li>
<li>About supersymmetry Silverstein writes:<br />
<blockquote><p>In my view, the role of supersymmetry is chronically over-emphasized in the field, and hence understandably also in the article by Ellis and Silk. The possibility of supersymmetry in nature is very interesting since it could stabilize the electroweak hierarchy, and extended supersymmetry enables controlled extrapolation to strong coupling in appropriate circumstances. Neither of these facts implies that low-energy supersymmetry is phenomenologically favored in string theory.</p></blockquote>
<p>It is true that Silverstein has never been one of those arguing that the usual string theory scenarios with supersymmetry and 10 or 11 dimensions show that string theory is testable. See for instance her comment <a href="http://www.preposterousuniverse.com/blog/2006/02/04/why-10-or-11/#comment-11331">here</a> back during a “String Wars” discussion in 2006. Her current take on whether string theory implies supersymmetry is just</p>
<blockquote><p>Much further research, both conceptual and technical, is required to obtain an accurate assessment of the dominant contributions to the string landscape.</p></blockquote>
<p>The problem with this is that there so sign of any possibility of progress towards deciding if the string theory landscape implies low-energy SUSY or not (quite the opposite). If you give up the assumptions of SUSY and 10/11 dimensions, you give up what little hope you had of any connection with experiment. She doesn’t mention the LHC at all, especially not the negative results about supersymmetry and extra dimensions that it has produced. The significance of these negative results is not that they disconfirm a strong prediction of string theory, but that they pull the plug on the last remaining hope for connecting standard string theory unification scenarios to anything observable. Pre-LHC string theorists could make an argument that there was good reason to believe in electroweak-scale SUSY, that such a scenario fit in well with string theory unification, and that LHC discovery of SUSY would point a way forward for string theory unification. That argument is now dead. All that’s left is basically the argument that “maybe a miracle will happen and we’ll be vindicated” which in her version is:</p>
<blockquote><p> In principle one could test string theory locally. In practice, this would require discovering a smoking gun signature (such as a low string scale at colliders, or perhaps a very distinctive pattern of primordial perturbations in cosmology), and nothing particularly favors such scenarios currently. </p></blockquote>
</li>
<li>Silverstein’s main argument is basically that string theory is valuable because it leads to the study of models that have various observable signatures that people would not otherwise look for. One example here is supersymmetry, the study of which has had a huge effect on collider physics, strongly shaping the analyses that the experimentalist perform. She gives some detailed other examples from her field of cosmology, in particular about possibly observable non-Gaussianities.<br />
<blockquote><p>String theory participates in empirical science in several ways. In the context of early universe cosmology, on which we have focused in this article, it helped motivate the discovery and development of mechanisms for dark energy and inflation consistent with the mathematical structure of string theory and various thought-experimental constraints. Some of these basic mechanisms had not been considered at all outside of string theory, and some not quite in the form they take there, with implications for effective field theory and data analysis that go well beyond their specifics.</p></blockquote>
<p>I think this is the best argument to be made for “phenomenological” string theory research (as opposed to “formal” string theory, where there are other arguments). Yes, coming up with new models with unexpected observable effects is a valuable enterprise. If your speculative idea generates such things, that’s well and good. The problem though is how to evaluate the situation of a speculative idea that has generated a huge number of such models, none of which has worked out. At what point do you decide that this is an unpromising line of research, better to try just about anything else? Silverstein makes the argument that</p>
<blockquote><p>Whether empirical or mathematical, constraints on interesting regions of theory space is valuable science. In this note we focus on string theory’s role in the former.</p>
<p>Since information theory is currently all the rage, it occurred to me that we can phrase this in that language. Information is maximized when the probabilities are equal for a set of outcomes, since one learns the most from a measurement in that case. The existence of multiple consistent theoretical possibilities implies greater information content in the measurements. Therefore, theoretical research establishing this (or constraining the possibilities) is directly relevant to the question of what and how much is learned from data. In certain areas, string theory plays a direct role in this process.</p></blockquote>
<p>The problem here is that of what is an “interesting region of theory space”. At this point the failures of string theory unification strongly indicate that it’s not such an interesting region. It seems likely that we’d be better off if most theorists focusing on phenomenology of this failed program were to pick something else to work on.</li>
</ul>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=93752018 US HEP Budget
http://www.math.columbia.edu/~woit/wordpress/?p=9361
<p>HEPAP has been meeting the past couple days, with presentations available <a href="https://science.energy.gov/hep/hepap/meetings/201706/">here</a>. Much of the discussion is about the President’s 2018 budget proposal recently submitted to Congress, which contains drastic cuts to all sorts of programs, including for support of scientific research. In particular the proposal is to cut the total NSF budget from \$7.5 billion to \$6.65 billion (-11.3%), and the DOE science budget from \$5.4 billion to \$4.47 billion (-17%).</p>
<p>At the DOE, for HEP physics, the cut would be from \$825 million to \$673 million (-18.5%). For topics less popular with the new administration the cuts are even larger, e.g. a 43% cut for biological and environmental research. </p>
<p>At the NSF (numbers with respect to FY 2016), the proposed cut for DMS (Mathematics) is 10.3%, for Physics 8.5% (-\$23.6 million) and for Astronomy 10.3%. The FY 2016 budget number for Physics was \$277 million, of which \$13.2 million went to HEP theory.</p>
<p>Budget cuts on this scale would be extreme and unheard of, requiring shutting down major planned experimental projects. For some sorts of spending, this sort of cut is painful but manageable, but cutting out 18.5% of the spending on an experimental apparatus under construction may likely mean you don’t have an experiment anymore.<br />
The HEPAP presentations are from people working for DOE/NSF and under orders to plan for these cuts and not complain about them, so I think don’t reflect at all what the real implications of such cuts would be. </p>
<p>There’s a summary of discussion <a href="https://science.energy.gov/~/media/hep/hepap/pdf/201706/Lankford-Day2.pdf">here</a>, including a discussion of last year’s <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8998">HEP theory letter</a>. It sounds like nothing much has been done about that, and it may not get much attention given the current situation.</p>
<p>It’s important though to keep in mind that this budget proposal may very well already be dead on arrival at Congress. Take a look at slide 22 of <a href="https://science.energy.gov/~/media/hep/hepap/pdf/201706/lsuter_communication_activites.pdf">this presentation</a> that reports that of the staffers and representatives asked about (a preliminary version of) this, only 8.4% were in favor. In recent years the US budgeting process has been quite dysfunctional, with actual budget numbers only appearing at the last minute of an opaque process leading not to a budget but to a “Continuing Resolution”. I doubt anyone has any idea what is going to happen this year, with the passing of something close to this budget probably one of the least likely eventualities. Physicists and mathematicians up in arms about these proposed budget cuts need to keep in mind the context: this budget is an extremely radical proposal of an unparalleled sort, with even larger cuts aimed at groups that are far needier than scientists (for one random example, food stamps are to be cut by 25.3%). Yes, scientists should be organizing to fight this budget, but the impacts on them and their research are one of the less important reasons for doing so.</p>
<p>I’m setting all comments to go to moderation. If you just want to rant pro or con about the awful situation the US is now in, please do it elsewhere. If you have any actual information about the effects of this on the physics and math communities as the budget process gets underway, that would be worthwhile and interesting. Two people tweeting about this are <a href="https://twitter.com/KyleCranmer/with_replies">Kyle Cranmer</a> and <a href="https://twitter.com/physicsmatt/with_replies">Matthew Buckley</a>.</p>
<p><strong>Updates</strong>: Details of the DOE HEP budget proposal are <a href="https://science.energy.gov/~/media/budget/pdf/sc-budget-request-to-congress/fy-2018/FY_2018_SC_HEP_Cong_Budget.pdf">here</a>. It explains that about 20-25% of the research positions funded by DOE at all levels would be eliminated. There would be an “extended shutdown of the Fermilab accelerator complex”.<br />
About 1/3 of DOE HEP theory funding would be eliminated, but it would be replaced by an equal amount of funding for quantum information science as a subfield of HEP. Looks like someone in the Trump administration is a great believer in “It From Qubit”…</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9361Multiverse Politics
http://www.math.columbia.edu/~woit/wordpress/?p=9349
<p>The <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9289">political campaign for the multiverse</a> continues today with a <a href="http://nautil.us/issue/48/chaos/the-inflated-debate-over-cosmic-inflation">piece by Amanda Gefter at Nautilus</a>. It’s a full-throated salvo from the Linde-Guth side of the multiverse propaganda war they are now waging, with Linde dismissing Steinhardt’s criticism as based on “a total ignorance of what is going on”. All of the quotes for the article are on the pro-multiverse side. There is a new argument from them I’d never heard before: Guth comes up with this one:</p>
<blockquote><p>You can create a universe from nothing—you can create infinite universes from nothing—as long as they all add up to nothing. Not only is that a deep insight, it also creates a testable prediction. “Eternal inflation certainly predicts that the average density of all conserved quantities should be zero,” Guth says. “So if we ever became convinced that the universe has a nonzero density of electric charge or angular momentum, eternal inflation would no longer be an option.”</p></blockquote>
<p>The article is subtitled “Why the majority of physicists are on one side of a recent exchange of letters”. One way to interpret this claim is just that 33 is more than 3, but the reason for this is clear: while Guth, Kaiser, Linde and Nomura decided to go on a political campaign, drumming up signatures on their letter, Ijjas, Loeb and Steinhardt didn’t do this, but instead put together a <a href="http://physics.princeton.edu/~cosmo/sciam/">website discussing the scientific issues</a>.</p>
<p>Where the majority of physicists stand on the Guth-Linde claims is an interesting question, one that I don’t think is addressed anywhere by hard numbers. My anecdotal data is that the majority of those I’ve ever talked to about this don’t think the Guth-Linde multiverse claims are science, but don’t see any reason to waste their time arguing with pseudo-science. They hope it will just go away by itself, as it becomes ever clearer that the multiverse is, scientifically, an empty idea.</p>
<p>Unfortunately, I don’t see this going away and I think it’s now doing very serious damage to physics and its public image. There’s a political campaign now being waged, and one side is very determined to win and putting a lot of energy into doing so. Those on the other side need to step up and make themselves heard. </p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9349A Few Quick Items
http://www.math.columbia.edu/~woit/wordpress/?p=9340
<p>I’ve had little time for blogging, and coincidentally, there seems to be little to blog about recently. Here though are a few quick items:</p>
<ul>
<li>Several people had asked me about <a href="https://arxiv.org/abs/1703.00543">this paper about the CC</a>, and I had to tell them that this was not something I could evaluate. Luckily, Sabine Hossenfelder has read it and thought about it carefully, and discusses the problems with this sort of thing <a href="http://backreaction.blogspot.com/2017/05/does-parametric-resonance-solve.html">here</a>. The physics community owes her a great debt.</li>
<li>The LHC is back in business, with intensity starting to ramp up. You can follow progress <a href="https://lpc.web.cern.ch/lumiplots_2017_pp.htm">here</a>. This summer should see release of more results based on last year’s run, results from this year’s run likely will not appear until early next year.</li>
<li>Inference magazine has a thoughtful <a href="http://inference-review.com/article/higgs-on-the-moon">piece in the latest issue</a> by Adam Falkowski (AKA Jester) about prospects for the future of HEP physics. The same issue also has a <a href="http://inference-review.com/article/natural-physics">piece by Aurélien Barrau</a> about the implications of the failure to find the “natural” physics some expected SUSY to provide.</li>
<li>Hironaka has recently put on his website <a href="http://www.math.harvard.edu/~hironaka/pRes.pdf">a document</a> intended to give a proof of resolution of singularities in characteristic p. For some background and links to explanations of what this is about, see <a href="https://mathoverflow.net/questions/269651/hironakas-proof-of-resolution-of-singularities-in-positive-characteristics">mathoverflow</a>. Evidently Hironaka has been working on this proof for quite a few years, this is the first complete version to be made public. Sometime in the next few months it should become clear whether this proof will really work, as experts get a chance to go through it carefully. If it does work, it will be a remarkable story, especially since Hironaka is now 86.</li>
<li>Maybe I’m the last one to find this out, but for quite a few years now MIT has been making public detailed course materials including lecture notes from many courses in <a href="https://ocw.mit.edu/courses/find-by-topic/#cat=mathematics">mathematics</a> and <a href="https://ocw.mit.edu/courses/find-by-topic/#cat=science&subcat=physics">physics</a>.</li>
</ul>
<p><strong>Update</strong>: For the obligatory Multiverse Mania item, see this <a href="https://www.edge.org/conversation/martin_rees-curtains-for-us-all">interview with Lord Martin Rees</a>. Rees is rather proud of himself for leading the field of theoretical physics to embrace Multiverse Mania, quoting Frank Wilczek as claiming at the end of a conference that:</p>
<blockquote><p>five years ago we were a beleaguered minority, whereas now, he and I and others had led many other people into the wilderness.</p></blockquote>
<p>Besides his belief in the multiverse, he also believes this is what we have in our future:</p>
<blockquote><p>I don’t think Elon Musk is realistic when he imagines sending people a hundred at a time for normal life because Mars is going to be far less clement than living at the South Pole, and not many people want to do that. I don’t think there will be many ordinary people who want to go, but there will be some crazy pioneers who will want to go, even if they have one-way tickets.</p>
<p>The reason that’s important is the following: Here on Earth, I suspect that we are going to want to regulate the application of genetic modification and cyborg techniques on grounds of ethics and prudence. This links with another topic I want to come to later about the risks of new technology. If we imagine these people living as pioneers on Mars, they are out of range of any terrestrial regulation. Moreover, they’ve got a far higher incentive to modify themselves or their descendants to adapt to this very alien and hostile environment.</p>
<p>They will use all the techniques of genetic modification, cyborg techniques, maybe even linking or downloading themselves into machines, which, fifty years from now, will be far more powerful than they are today. The posthuman era is probably not going to start here on Earth; it will be spearheaded by these communities on Mars.</p></blockquote>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9340GAMBIT
http://www.math.columbia.edu/~woit/wordpress/?p=9334
<p>The <a href="http://lhcp2017.physics.sjtu.edu.cn/">LHCP 2017 conference</a> was held this past week in Shanghai, and among the results announced there were new negative results about SUSY from <a href="https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults#conference_notes_with_full_2015">ATLAS</a> with both ATLAS and CMS now reporting for instance limits on gluino masses of around 2 TeV. The LHC has now ruled out the existence of SUSY particles in the bulk of the mass range that will be accessible to it (recall for instance that pre-LHC, gluino mass limits were about 300 GeV or so).</p>
<p>Over the years there has been an ongoing effort to produce “predictions” of SUSY particle masses, based on various sorts of assumptions and various experimental data that might be sensitive to the existence of SUSY particles. One of the main efforts of this kind has been the <a href="http://mastercode.web.cern.ch/mastercode/">MasterCode collaboration</a>. <a href="https://arxiv.org/abs/0808.4128">Back in 2008</a> before the LHC started up, they were finding that the “best fit” for SUSY models implied a gluino at something like 600-750 GeV. As data has come in from the LHC (and from other experiments, such as dark matter searches), they have periodically released new “best fits”, with the gluino mass moving up to stay above the increasing LHC limits. </p>
<p>I’ve been wondering how efforts like this would evolve as stronger and stronger negative results came in. The news this evening is that they seem to be evolving into something I can’t comprehend. I haven’t kept track of the latest MasterCode claims, but back when I was following them I had some idea what they were up to. Tonight a large collaboration called GAMBIT released a series of papers on the arXiv, which appear to be in the same tradition of the old MasterCode fits, but with a new level of complexity. The <a href="https://arxiv.org/abs/1705.07908">overall paper</a> is 67 pages long and has 30 authors, and there are eight other papers of length totaling over 300 pages. The collaboration has <a href="http://gambit.hepforge.org/">a website</a> with lots of other material available on it. I’ve tried poking around there, and for instance reading a <a href="http://live.iop-pp01.agh.sleek.net/2017/02/26/when-supercomputers-go-over-to-the-dark-side/">Physics World article about GAMBIT</a>, but I have to confess I remain baffled.</p>
<p>So, the SUSY phenomenology story seems to have evolved into something very large that I can’t quite grasp anymore, perhaps a kind reader expert in this are can explain what is going on.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9334This Month’s Hype
http://www.math.columbia.edu/~woit/wordpress/?p=9319
<p>It seems that a couple of the authors of the recent <a href="https://blogs.scientificamerican.com/observations/a-cosmic-controversy/">Cosmic Controversy</a> letter (discussed <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9289">here</a>) are going on a campaign to embarrass the 29 physicists who were convinced to sign their letter. Andrei Linde has gone to <a href="http://motls.blogspot.com/2017/05/why-testability-criticisms-of-inflation.html#comment-3300742156">Lubos Motl’s blog</a> to thank him for his blog entry which lauded Linde as having eaten from the biblical tree of knowledge and which denounced his critics as imbeciles. To deal with Linde, Ijjas, Steinhardt and Loeb have added a new webpage to their website called <a href="http://physics.princeton.edu/~cosmo/sciam/index.html#facts">Fact Checking</a>. It lists the four “predictions” of inflation claimed to agree with experiment by Linde et al. and gives four references to papers published by Linde touting different “predictions” for the same quantities, predictions not agreeing with experiment.</p>
<p>This month’s Scientific American has a remarkable cover story, <a href="https://www.scientificamerican.com/article/can-quantum-mechanics-save-the-cosmic-multiverse/">The Quantum Multiverse</a> from one of the other four letter authors, Yasunori Nomura. I’ve seen some fairly bizarre stories about fundamental physics in Scientific American over the years, but this one sets a new standard for outrageous nonsense, and I’m wondering whether it too may cause some of the 29 co-signers of the letter co-authored by Nomura to question the wisdom of joining with him and Linde. Nomura is well known for a definite prediction based on the multiverse: in 2009 he co-authored <a href="https://arxiv.org/abs/0910.2235">a paper</a> claiming that the multiverse predicted the Higgs mass would be 141 GeV +/- 2 GeV. This played a major role in the film <a href="http://www.math.columbia.edu/~woit/wordpress/?p=6308">Particle Fever</a>. That three years later the Higgs was discovered at 125 GeV seems to have had no effect on his multiverse enthusiasm.</p>
<p>The new SciAm cover story is not about anything new, but is based on <a href="https://arxiv.org/abs/1104.2324">a 6 year old paper by Nomura</a> discussed <a href="http://www.math.columbia.edu/~woit/wordpress/?p=3723">here</a>. At the time I wrote about this “I’m having trouble making sense of any of these papers” and quoted Lubos’s evaluation: “They’re on crack”. Nothing I’ve seen about this over the past six years seems to me to make any sense at all, including the new SciAm cover story, which just seems even more content-free and meaningless than previous efforts to explain this “multiverse interpretation of quantum mechanics”. On the obvious question: how would you test this, Nomura just has this to say:</p>
<blockquote><p>Evidence so far indicates that the cosmos is flat, but experiments studying how distant light bends as it travels through the cosmos are likely to improve measures of the curvature of our universe by about two orders of magnitude in the next few decades. If these experiments find any amount of negative curvature, they will support the multiverse concept because, although such curvature is technically possible in a single universe, it is implausible there. Specifically, a discovery supports the quantum multiverse picture described here because it can naturally lead to curvature large enough to be detected, whereas the traditional inflationary picture of the multiverse tends to produce negative curvature many orders of magnitude smaller than we can hope to measure.</p></blockquote>
<p>This paragraph manages to put together three different misleading and unsupported claims:</p>
<ul>
<li>“If these experiments find any amount of negative curvature, they will support the multiverse concept because, although such curvature is technically possible in a single universe, it is implausible there.” This is just nonsense. </li>
<li>“the traditional inflationary picture of the multiverse tends to produce negative curvature many orders of magnitude smaller than we can hope to measure”. What is the inflationary multiverse “prediction” for negative curvature? As far as I can tell it’s compatible with pretty much any level we might observe.</li>
<li>“the quantum multiverse picture described here because it can naturally lead to curvature large enough to be detected.” I can’t find anywhere a calculation of the negative curvature expected by the “quantum multiverse picture”, and I don’t believe any such calculation is possible.</li>
</ul>
<p>Given some of the outrageous hype I’ve seen in recent years in respectable publications, it’s gotten rather hard to shock me with this sort of thing, but I do find this Scientific American cover story shocking.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9319A Cosmic Controversy
http://www.math.columbia.edu/~woit/wordpress/?p=9289
<p>A couple months ago Scientific American published <a href="https://www.scientificamerican.com/article/cosmic-inflation-theory-faces-challenges/">an article by Ijjas, Steinhardt and Loeb</a> (also available <a href="https://www.cfa.harvard.edu/~loeb/sciam3.pdf">here</a>), which I discussed a bit <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9134">here</a>. One aspect of the article was its strong challenge to multiverse mania, calling it the “multimess” and accusing multiverse explanations of being untestable and unscientific. </p>
<p>Yesterday Scientific American published, under the title <a href="https://blogs.scientificamerican.com/observations/a-cosmic-controversy/">A Cosmic Controversy</a>, a rebuttal signed by 33 physicists, together with a response from the authors, who have also set up <a href="http://physics.princeton.edu/~cosmo/sciam/">a webpage giving further details of their response</a>. Undark has an article covering this: <a href="https://undark.org/2017/05/09/a-debate-over-cosmic-inflation-and-editing-at-scientific-american-gets-heated/">A Debate Over Cosmic Inflation (and Editing at Scientific American) Gets Heated</a>.</p>
<p>As Ijjas, Steinhardt and Loeb point out on their webpage, the story of this letter is rather unusual. It was written by David Kaiser and three physicists well-known for their outspoken promotion of the multiverse (Guth, Linde and Nomura). Evidently these authors decided they needed reputational support on their side, and sought backing from other prominent names in the field (I’m curious to know who may have refused to sign if asked…). Their letter starts out with a claim to represent the “dominant paradigm in cosmology” and notes the large number of papers and researchers involved in studying inflation.</p>
<p>If you read carefully both sides (IS&L and GKL&N) of this, I think you’ll find that they are to a large degree speaking past each other, with a major problem that of imprecision in what one means by “inflation”. To the extent that there is a specific identifiable scientific disagreement, it’s about whether Planck data confirms predictions of the “simplest inflationary models.” IS&L write:</p>
<blockquote><p>The Planck satellite results—a combination of an unexpectedly small (few percent) deviation from perfect scale invariance in the pattern of hot and colds spots in the CMB and the failure to detect cosmic gravitational waves—are stunning. For the first time in more than 30 years, the simplest inflationary models, including those described in standard textbooks, are strongly disfavored by observations.</p></blockquote>
<p>whereas GKL&N respond:</p>
<blockquote><p>there is a very simple class of inflationary models (technically, “single-field slow-roll” models) that all give very similar predictions for most observable quantities—predictions that were clearly enunciated decades ago. These “standard” inflationary models form a well-defined class that has been studied extensively. (IS&L have expressed strong opinions about what they consider to be the simplest models within this class, but simplicity is subjective, and we see no reason to restrict attention to such a narrow subclass.) Some of the standard inflationary models have now been ruled out by precise empirical data, and this is part of the desirable process of using observation to thin out the set of viable models. But many models in this class continue to be very successful empirically.</p></blockquote>
<p>I take this as admission that IS&L are right that some predictions of widely advertised inflationary models have been falsified. Of course, if these had worked they would have been heavily promoted as “smoking gun” proof of inflation, as was demonstrated by the BICEP2 B-mode fiasco. After BICEP2 announced (incorrectly) evidence for B-modes, Linde claimed this was a “smoking gun” for inflation (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=7715">here</a>) and the New York Times had a <a href="https://www.nytimes.com/2014/03/18/science/space/detection-of-waves-in-space-buttresses-landmark-theory-of-big-bang.html?_r=0">front page story</a> about the “smoking gun” confirmation of inflation vindicating the ideas of Guth and Linde. A couple months later, before the BICEP2 result was shown to be mistaken, Guth, Linde and Starobinsky were awarded the $1 million Kavli Prize in Astrophysics.</p>
<p>GKL&N don’t mention the sorry story of the BICEP2 B-modes, what they have to say about this is</p>
<blockquote><p>the levels of B-modes, which are a measure of gravitational radiation in the early universe, vary significantly within the class of standard models…</p>
<p>The B-modes of polarization have not yet been seen, which is consistent with many, though not all, of the standard models.</p></blockquote>
<p>About the IS&L “unexpectedly small (few percent) deviation from perfect scale invariance” all GKL&N have to say is </p>
<blockquote><p>The standard inflationary models… predict the statistical properties of the faint ripples that we detect in the cosmic microwave background (CMB). First, the ripples should be nearly “scale-invariant”</p></blockquote>
<p>This doesn’t seem to address at all the IS&L claims, which they make in more detail as</p>
<blockquote><p>The latest Planck data show that the deviation from perfect scale invariance is tiny, only a few percent, and that the average temperature variation across all spots is roughly 0.01 percent. Proponents of inflation often emphasize that it is possible to produce a pattern with these properties. Yet such statements leave out a key point: inflation allows many other patterns of hot and cold spots that are not nearly scale-invariant and that typically have a temperature variation much greater than the observed value. In other words, scale invariance is possible but so is a large deviation from scale invariance and everything in between, depending on the details of the inflationary energy density one assumes. Thus, the arrangement Planck saw cannot be taken as confirmation of inflation.</p></blockquote>
<p>GKL&N argue for three other confirmed predictions of inflationary models:</p>
<blockquote><p>Second, the ripples should be “adiabatic,” meaning that the perturbations are the same in all components: the ordinary matter, radiation and dark matter all fluctuate together. Third, they should be “Gaussian,” which is a statement about the statistical patterns of relatively bright and dark regions. Fourth and finally, the models also make predictions for the patterns of polarization in the CMB, which can be divided into two classes, called E-modes and B-modes. The predictions for the E-modes are very similar for all standard inflationary models</p></blockquote>
<p>On these issues I don’t see anything from IS&L and would love to hear from an expert.</p>
<p>The main issue here comes down to the question of the flexibility vs. rigidity of inflationary models. Is the inflationary paradigm rigid enough to make solid predictions, or so flexible that it can accommodate any experimental result? GKL&N are making the case for the former, IS&L for the latter, and they point out the following quote from Guth himself:</p>
<blockquote><p>when asked via email if they could name any pro-inflation scientists who believe that the theory is nonetheless untestable, the trio pointed to a video of a 2014 panel during which Loeb asks Guth directly whether it’s possible to do an experiment that would falsify inflation.</p>
<p>“Well, I think inflation is a little too flexible an idea for that to make sense,” Guth replied.</p></blockquote>
<p>A fair take on all this would be to note that it’s a complicated situation, and I doubt I’m the only one who would like to see an even-handed technical discussion of exactly what the “simplest” models are and a comparison of their predictions with the data. Claims to the public from one group of experts that Planck data says one thing, from others claiming it says the opposite are generating confusion here rather than clarity about the science.</p>
<p>I’m strongly on the side of IS&L on one issue, that of the danger of theories that invoke the multiverse as untestable explanation. I don’t think though that they make a central issue clear. The simple inflationary models whose “predictions” for Planck data are being discussed involve a single inflaton field, with no understanding of how this is supposed to couple to the rest of physics. One is told that eternal inflation implies a multiverse with different physics in different universes, but in a single inflaton model this physics should just depend on a single parameter, and such a theory should be highly predictive (once you know one mass, all others are determined). What’s really going on is that there is no connection at all between the simple single field models that GKL&N and IS&L are arguing about, and the widely promoted completely unpredictive string theory landscape models (involving large numbers of inflaton-type fields with dynamics that is not understood).</p>
<p>I think IS&L made a mistake by not pointing this out, and that Guth, Linde, Nomura and some of the signers of their letter (e.g. Carroll, Hawking, Susskind, Vilenkin) have long been guilty of promoting the defeatist pseudo-scientific idea that “evidence for inflation is evidence for a multiverse with different physics in each universe, explaining why we can’t ever calculate SM parameters”. By defending the predictivity of “inflation” while ignoring the “different physics in different parts of the multiverse” question, I think many signers of the GKL&N letter were missing a good opportunity to make common cause with IS&L on defending their science against an ongoing attack from some of their fellow signatories.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9289Some Quick Items
http://www.math.columbia.edu/~woit/wordpress/?p=9301
<p>A few quick items, I may use this posting to add a couple more later, the next posting will discuss today’s letter to Scientific American about inflation.</p>
<ul>
<li>Today’s <a href="https://indico.cern.ch/event/632309/">LHCC meeting at CERN</a> had reports from the LHC machine and experiments. About two weeks to go before collisions and data-taking start again.</li>
<li>Physics Today has a <a href="http://physicstoday.scitation.org/doi/10.1063/PT.3.3551">report this month on the LHeC proposal</a>, something that has not gotten as much attention as it deserves. This is a proposal to collide protons and electrons, by building a new electron machine and a detector at a collision point with the LHC beam. Unlike proposals for a 100 TeV proton-proton machine that are getting a lot of attention, this would not push the energy frontier, but it would cost a great deal less (estimate is half a billion to a billion, vs. multiple tens of billions for the 100 TeV machine). In a few years when the question of a follow-on machine to the LHC starts to get very pressing, this idea and the HE-LHC idea (higher field magnets in the LHC tunnel, maybe doubling the energy) may get a lot more attention as the only financially viable ways forward.</li>
<li>The Université de Montpelier today has started to make accessible about 18,000 pages of its <a href="https://grothendieck.umontpellier.fr/">archive of Grothendieck’s mathematical writings</a>. For anyone interested in Grothendieck’s work, this should keep you busy for a while…</li>
</ul>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9301Theories of Everything
http://www.math.columbia.edu/~woit/wordpress/?p=9282
<p>I’ve written a review for the <a href="http://blog.physicsworld.com/2017/05/02/the-may-2017-issue-of-physics-world-is-now-out/">latest issue of Physics World</a> of a short new book by Frank Close, entitled <a href="https://profilebooks.com/theories-of-everything-ideas-in-profile.html">Theories of Everything</a>. You can read the review <a href="http://www.math.columbia.edu/~woit/PWMay17reviews-woit.pdf">here</a>.</p>
<p>As I discuss in the review, Close explains a lot of history, and asks the question of whether we’re in an analogous situation to that of the beginning of the 20th century, just before the modern physics revolutions of relativity and quantum theory. Are the cosmological constant and the lack of an accepted quantum theory of gravity indications that another revolution is to come? I hope to live long enough to find out…</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9282Why String Theory is Still Not Even Wrong
http://www.math.columbia.edu/~woit/wordpress/?p=9280
<p>John Horgan recently sent me some questions, and has put them and my answers up at his Scientific American site, under the title <a href="https://blogs.scientificamerican.com/cross-check/why-string-theory-is-still-not-even-wrong/">Why String Theory is Still Not Even Wrong</a>. My thanks to him for the questions and for the opportunity to summarize my take on various issues.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9280Two Pet Peeves
http://www.math.columbia.edu/~woit/wordpress/?p=9222
<p>I was reminded of two of my pet peeves while taking a look at the appendix A of <a href="https://arxiv.org/abs/1704.05067">this paper</a>. As a public service to physicists I thought I’d go on about them here, and provide some advice to the possibly confused (and use some latex for a change).</p>
<p><strong>Don’t use the same notation for a Lie group and a Lie algebra</strong>.</p>
<p>I noticed that Zee does this in is “Group Theory in a Nutshell for Physicists”, but thought it was unusual. It seems other physicists do this too (same problem with Ramond’s “Group Theory: a physicist’s survey”, the next book I checked). The argument seems to be that this won’t confuse people, but, personally, I remember being very confused about this when I first started studying the subject, in a course with Howard Georgi. Taking a look at Georgi’s book for that course (first edition) I see that what he does is basically only talk about Lie algebras. So, the fact that I was confused about Lie groups vs. Lie algebras wasn’t really his fault, since he was not talking about the groups.</p>
<p>The general theory of Lie groups and Lie algebras is rather complicated, but (besides the trivial cases of translation and U(1)=SO(2) groups) many physicists only need to know about two Lie groups and one Lie algebra, and to keep straight the following facts about them. The groups are</p>
<ul>
<li>SU(2): the group of two by two unitary matrices with determinant one. These can be written in the form<br />
$$\begin{pmatrix}<br />
\alpha & \beta\\<br />
-\overline{\beta}& \overline{\alpha}<br />
\end{pmatrix}$$<br />
where \(\alpha\) and \(\beta\) are complex numbers satisfying \(\alpha^2+\beta^2=1\), and thus parametrizing the three-sphere: unit vectors in four real dimensional space.
</li>
<li>SO(3): the group of three by three orthogonal matrices with determinant one. There’s no point in trying to remember some parametrization of these. Better to remember that a rotation by a counter-clockwise angle theta in the plane is given by<br />
$$\begin{pmatrix}<br />
\cos\theta & -\sin\theta\\<br />
\sin\theta & \cos\theta<br />
\end{pmatrix}$$<br />
and then produce your rotations in three dimensions as a product of rotations about coordinate axes, which are easy to write down. For instance a rotation about the 1-axis will be given by<br />
$$\begin{pmatrix}<br />
1&0&0\\<br />
0&\cos\theta & -\sin\theta\\<br />
0&\sin\theta & \cos\theta<br />
\end{pmatrix}$$
</li>
</ul>
<p>The relation between these two groups is subtle. Every element of SO(3) corresponds to two elements of SU(2). As a space, SO(3) is the three-sphere with opposite points identified. Given elements of SO(3), there is no continuous way to choose one of the corresponding elements of SU(2). Given an element of SU(2), there is an unenlightening impossible to remember formula for the corresponding element of SO(3) in terms of \(\alpha\) and \(\beta\), but to really understand what’s going on, you need to identify points in \(\mathbf R^3\) with traceless two by two self-adjoint matrices by for instance<br />
$$(x_1,x_2,x_3)\leftrightarrow x_1\sigma_1 +x_2\sigma_2+x_3\sigma_3=\begin{pmatrix} x_3&x_1-ix_2\\x_1+ix_2&-x_3\end{pmatrix}$$<br />
Then the SO(3) rotation corresponding to an element of SU(2) is given by<br />
$$\begin{pmatrix} x_3&x_1-ix_2\\x_1+ix_2&-x_3\end{pmatrix}\rightarrow \begin{pmatrix}<br />
\alpha & \beta\\<br />
-\overline{\beta}& \overline{\alpha}<br />
\end{pmatrix}\begin{pmatrix} x_3&x_1-ix_2\\x_1+ix_2&-x_3\end{pmatrix} \begin{pmatrix}<br />
\alpha & \beta\\<br />
-\overline{\beta}& \overline{\alpha}<br />
\end{pmatrix}^{-1}$$</p>
<p>Since most of the time you only care about two Lie groups, you mostly only need to think about two possible Lie algebras, and luckily they are actually the same, both isomorphic to something you know well: \(\mathbf R^3\) with the cross product. In more detail you have</p>
<ul>
<li>su(2) or \(\mathfrak{su}(2)\): Please don’t use the same notation as for the Lie group SU(2). These are traceless self-adjoint two by two complex matrices, identified with \(\mathbf R^3\) as above except for a factor of two.<br />
$$(x_1,x_2,x_3)\leftrightarrow \frac{1}{2}\begin{pmatrix} x_3&x_1-ix_2\\x_1+ix_2&-x_3\end{pmatrix}$$<br />
Under this identification, the cross-product corresponds to the commutator of matrices.</p>
<p>You get elements of the group SU(2) by exponentiating elements of its Lie algebra.
</li>
<li>so(3) or \(\mathfrak{so}(3)\): Please don’t use the same notation as for the Lie group SO(3). These are antisymmetric three by three real matrices, identified with \(\mathbf R^3\) by
<p>$$(x_1,x_2,x_3)\leftrightarrow \begin{pmatrix}<br />
0&-x_3&x_2\\<br />
x_3&0 & -x_1\\<br />
-x_2&x_1&0<br />
\end{pmatrix}$$<br />
Under this identification, the cross-product corresponds to the commutator of matrices.</p>
<p>You get elements of the group SO(3) by exponentiating elements of its Lie algebra.
</li>
</ul>
<p>If you stick to non-relativistic velocities in your physics, this is all you’ll need most of the time. If you work with relativistic velocities, you’ll need two more groups (either of which you can call the Lorentz group) and one more Lie algebra, these are</p>
<ul>
<li>SL(2,C): This is the group of complex two by two matrices with determinant one, i.e. complex matrices<br />
$$\begin{pmatrix}<br />
\alpha & \beta\\<br />
\gamma& \delta<br />
\end{pmatrix}$$<br />
satisfying \(\alpha\delta-\beta\gamma=1\). That’s one complex condition on four complex numbers, so this is a space of 6 real dimensions. Best to not try and visualize this; besides being six-dimensional, unlike SU(2) it goes off to infinity in many directions.</li>
<li>SO(3,1): This is the group of real four by four matrices M of determinant one such that<br />
$$M^T\begin{pmatrix}-1&0&0&0\\<br />
0&1&0&0\\<br />
0&0&1&0\\<br />
0&0&0&1\end{pmatrix}M=\begin{pmatrix}-1&0&0&0\\<br />
0&1&0&0\\<br />
0&0&1&0\\<br />
0&0&0&1\end{pmatrix}$$<br />
This just means they are linear transformations of \(\mathbf R^4\) preserving the Lorentz inner product.
</li>
</ul>
<p>The relation between SO(3,1) and SL(2,C) is much the same as the relation between SO(3) and SU(2). Each element of SO(3,1) corresponds to two elements of SL(2,C). To find the SO(3,1) group element corresponding to an SL(2,C) group element, proceed as above, removing the “traceless” condition, so identifying \(\mathbf R^4\) with self-adjoint two by two matrices as follows<br />
$$(x_0,x_1,x_2,x_3)\leftrightarrow\begin{pmatrix} x_0+x_3&x_1+ix_2\\x_1-ix_2&x_0-x_3\end{pmatrix}$$<br />
The SO(3,1) action on \(\mathbf R^4\) corresponding to an element of SL(2,C) is given by<br />
$$\begin{pmatrix} x_0+x_3&x_1+ix_2\\x_1-ix_2&x_0-x_3\end{pmatrix}\rightarrow \begin{pmatrix}<br />
\alpha & \beta\\<br />
\gamma & \delta<br />
\end{pmatrix}\begin{pmatrix} x_0+x_3&x_1+ix_2\\x_1-ix_2&x_0-x_3\end{pmatrix} \begin{pmatrix}<br />
\alpha & \beta\\<br />
\gamma& \delta<br />
\end{pmatrix}^{-1}$$</p>
<p>As in the three-dimensional case, the Lie algebras of these two Lie groups are isomorphic. The Lie algebra of SL(2,C) is easiest to understand (please don’t use the same notation as for the Lie group, instead consider sl(2,C) or \(\mathfrak{sl}(2,C)\)), it is all complex traceless two by two matrices, i.e. matrices of the form<br />
$$\begin{pmatrix}a&b\\<br />
c&-a\end{pmatrix}$$</p>
<p>For the isomorphism with the Lie algebra of SO(3,1), go on to pet peeve number two and then consult a relativistic QFT book to find some form of the details.</p>
<p><strong>Keep track of the difference between a Lie algebra and its complexification</strong></p>
<p>This is a much subtler pet peeve than pet peeve number one. It really only comes up in one place, when physicists discuss the Lie algebra of the Lorentz group. They typically put basis elements \(J_j\) (infinitesimal rotations) and \(K_j\) (infinitesimal boosts) together by taking complex linear combinations<br />
$$A_j=J_j+iK_j,\ \ B_j=J_j-iK_j$$<br />
and then note that the commutation relations of the Lie algebra simplify into commutation relations for the \(A_j\) that look like the \(\mathfrak{su}(2)\) commutation relations and the same ones for the \(B_j\). They then announce that<br />
$$SO(3,1)=SU(2) \times SU(2)$$<br />
Besides my pet peeve number one, even if you interpret this as a statement about Lie algebras, it’s not true at all. The problem is that the Lie algebras under discussion are real Lie algebras, you’re just supposed to be taking real linear combinations of their elements. When you wrote down the equations for \(A_j\) and \(B_j\), you “complexified”, getting elements not of \(\mathfrak{so}(3,1)\), but what a mathematician would call the complexification \(\mathfrak{so}(3,1)\otimes C\). Really what has been shown is that<br />
$$ \mathfrak{so}(3,1)\otimes C = \mathfrak{sl}(2,C) + \mathfrak{sl}(2,C)$$</p>
<p>It turns out that when you complexify the Lie algebra of an orthogonal group, you get the same thing no matter what signature you start with, i.e.<br />
$$ \mathfrak{so}(3,1)\otimes C =\mathfrak{so}(4)\otimes C =\mathfrak{so}(2,2)\otimes C$$<br />
all of which are two copies of \(\mathfrak{sl}(2,C)\). The Lie algebras you care about are what mathematicians call different “real forms” of this and they are different for different signature. What is really true is<br />
$$\mathfrak{so}(3,1)=\mathfrak{sl}(2,C)$$<br />
$$\mathfrak{so}(4)=\mathfrak {su}(2) + \mathfrak {su}(2)$$<br />
$$\mathfrak{so}(2,2)=\mathfrak{sl}(2,R) +\mathfrak{sl}(2,R)$$</p>
<p>For details of all this, see <a href="http://www.math.columbia.edu/~woit/QM/qmbook.pdf">my book</a>.</p>
<p>Note: Posting this and heading home for the evening, haven’t checked some signs, and tomorrow morning will likely make some typographical improvements. If you want to check the signs, please do….</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9222Quick Links
http://www.math.columbia.edu/~woit/wordpress/?p=9217
<p>A few quick items:</p>
<ul>
<li>I was very sorry to hear recently of the death of David Goss (obituary <a href="http://www.legacy.com/obituaries/dispatch/obituary.aspx?n=david-mark-goss&pid=184946410&fhid=8669">here</a>), a mathematician specialist in function fields who was at Ohio State. David had a side interest in physics and was a frequent e-mail correspondent. From what I recall I first heard from him in 2004 soon after the blog started, with my first reaction when I saw the subject and From line that of wondering why David Gross wanted to discuss that particular article about physics with me.
<p>Over the years he often sent me links to things I hadn’t heard about, with always sensible comments about them and other topics. I had the pleasure of meeting him a couple years ago, when he came to Columbia to drop off his son, who is now a student here. My condolences to his family and friends.</li>
<li>The AMS has a wonderful relatively new repository of mostly expository documents called <a href="https://www.ams.org/open-math-notes">Open Math Notes</a>. The quality of these seems to uniformly be high, and this is a great new service to the community. I hope it will grow and thrive with more contributions.</li>
<li>Peter Scholze has now finished his series of talks at the IHES about his ongoing work on local Langlands, the talks are available <a href="https://www.youtube.com/playlist?list=PLx5f8IelFRgEBJSiTdHD7-WNmPfw9fL89">here</a>.</li>
<li>Jean-Francois Dars and Ann Papillault have a web-site called <a href="http://llx.fr/site/histoires-courtes/">Histoire Courtes</a>, with short pieces in French, many of which are about <a href="http://llx.fr/site/tag/mathematiques/">math</a> and <a href="http://llx.fr/site/tag/physique/">physics</a> research.</li>
<li>The LHC is starting to come to life again after a long technical stop. Machine checkout next week, <a href="https://docs.google.com/spreadsheets/d/1F1fpmpyg2m6bD6G4L7fRmTXJPOheVIR_1GwwQMhpzgQ/">recommissioning with beam during May</a>, physics starts again in June.</li>
<li>There’s a new book out with string theory predictions from Gordon Kane, called <a href="http://iopscience.iop.org/book/978-1-6817-4489-6">String Theory and the Real World</a>. Kane has been writing popular pieces about string theory predictions for at least 20 years, with a 1997 piece in Physics Today telling us that string theory was “supertestable”, with a gluino at 200-300 GeV. Over the years, his gluino mass predictions have moved up many times, as the older predictions get falsified. I don’t have a copy of the new book, but at <a href="https://books.google.com/books?id=PJCNDgAAQBAJ">Google Books</a> you can read some of it. From the pages available there I see that<br />
<blockquote><p>the compactified M-theory example we will examine below predicts that gluinos will have masses of about 1.5 TeV…<br />
The bottom line is that with about 40 inverse fb of data the limits on gluinos are just at the lower range of expected masses at the end of 2016.</p></blockquote>
<p>Right around the time the book was published, results released at Moriond (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9187">here</a>) claimed exclusion of gluinos up to about 2 TeV. Assumptions may be somewhat different than Kane’s, but I suspect his 1.5 TeV gluino is now excluded.</li>
</ul>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9217The Social Bubble of Physics
http://www.math.columbia.edu/~woit/wordpress/?p=9207
<p>Sabine Hossenfelder is on a tear this week, with two excellent and highly provocative pieces about research practice in theoretical physics, a topic on which she has become the field’s most perceptive critic.</p>
<p>The first is in this month’s Nature Physics, entitled <a href="http://www.nature.com/articles/nphys4079.epdf?author_access_token=dMVHpyeLS-NjURH8w2YMvdRgN0jAjWel9jnR3ZoTv0P_mUIBWwidhH-m_DEyWfyPEmxrqKJGmG1wRPAvM7TmEnWiQAKO043-f7r3iLjOmZMvLKGZFIOVANQT2nh0ZdPz">Science needs reason to be trusted</a>. I’ll quote fairly extensively so that you get the gist of her argument:</p>
<blockquote><p>But we have a crisis of an entirely different sort: we produce a huge amount of new theories and yet none of them is ever empirically confirmed. Let’s call it the overproduction crisis. We use the approved methods of our field, see they don’t work, but don’t draw consequences. Like a fly hitting the window pane, we repeat ourselves over and over again, expecting different results.</p>
<p>Some of my colleagues will disagree we have a crisis. They’ll tell you that we have made great progress in the past few decades (despite nothing coming out of it), and that it’s normal for progress to slow down as a field matures — this isn’t the eighteenth century, and finding fundamentally new physics today isn’t as simple as it used to be. Fair enough. But my issue isn’t the snail’s pace of progress per se, it’s that the current practices in theory development signal a failure of the scientific method…</p>
<p>If scientists are selectively exposed to information from likeminded peers, if they are punished for not attracting enough attention, if they face hurdles to leave a research area when its promise declines, they can’t be counted on to be objective. That’s the situation we’re in today — and we have accepted it.</p>
<p>To me, our inability — or maybe even unwillingness — to limit the influence of social and cognitive biases in scientific communities is a serious systemic failure. We don’t protect the values of our discipline. The only response I see are attempts to blame others: funding agencies, higher education administrators or policy makers. But none of these parties is interested in wasting money on useless research. They rely on us, the scientists, to tell them how science works.</p>
<p>I offered examples for the missing self-correction from my own discipline. It seems reasonable that social dynamics is more influential in areas starved of data, so the foundations of physics are probably an extreme case. But at its root, the problem affects all scientific communities. Last year, the Brexit campaign and the US presidential campaign showed us what post-factual politics looks like — a development that must be utterly disturbing for anyone with a background in science. Ignoring facts is futile. But we too are ignoring the facts: there’s no evidence that intelligence provides immunity against social and cognitive biases, so their presence must be our default assumption…</p>
<p>Scientific communities have changed dramatically in the past few decades. There are more of us, we collaborate more, and we share more information than ever before. All this amplifies social feedback, and it’s naive to believe that when our communities change we don’t have to update our methods too.</p>
<p>How can we blame the public for being misinformed because they live in social bubbles if we’re guilty of it too?
</p></blockquote>
<p>There’s a lot of food for thought in the whole article, and it raises the important question of why the now long-standing dysfunctional situation in the field is not being widely acknowledged or addressed.</p>
<p>For some commentary on one aspect of the article by Chad Orzel, see <a href="https://www.forbes.com/sites/chadorzel/2017/04/06/why-are-there-too-many-papers-in-theoretical-physics/#460cc6a737ee">here</a>.</p>
<p>On top of this, <a href="http://backreaction.blogspot.com/2017/04/dear-dr-b-why-do-physicist-worry-so.html">yesterday’s blog entry at Backreaction</a> was a good explanation of the black hole information paradox, coupled with an excellent sociological discussion of why this has become a topic occupying a large number of researchers. That a large number of people are working on something and they show no signs of finding anything that looks interesting has seemed to me a good reason to not pay much attention, so that’s why I’m not that well-informed about exactly what has been going on in this subject. When I have thought about it, it seemed to me that there was no way to make the problem well-defined as long as one lacks a good theory of quantized space-time degrees of freedom that would tell one what was going on at the singularity and at the end-point of black hole evaporation.</p>
<p>Hossenfelder describes the idea that what happens at the singularity is the answer to the “paradox” as the “obvious solution”. Her take on why it’s not conventional wisdom is provocative:</p>
<blockquote><p>What happened, to make a long story short, is that Lenny Susskind wrote a dismissive paper about the idea that information is kept in black holes until late. This dismissal gave everybody else the opportunity to claim that the obvious solution doesn’t work and to henceforth produce endless amounts of papers on other speculations.</p>
<p>Excuse the cynicism, but that’s my take on the situation. I’ll even admit having contributed to the paper pile because that’s how academia works. I too have to make a living somehow.</p>
<p>So that’s the other reason why physicists worry so much about the black hole information loss problem: Because it’s speculation unconstrained by data, it’s easy to write papers about it, and there are so many people working on it that citations aren’t hard to come by either. </p></blockquote>
<p>I hope this second piece too will generate some interesting debate within the field.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9207Some Math and Physics Interactions
http://www.math.columbia.edu/~woit/wordpress/?p=9197
<p>Quanta magazine has a <a href="https://www.quantamagazine.org/20170404-quantum-physicists-attack-the-riemann-hypothesis/">new article</a> about physicists “attacking” the Riemann Hypothesis, based on the publication <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.130201">in PRL</a> of <a href="https://arxiv.org/abs/1608.03679">this paper</a>. The only comment from a mathematician evaluating relevance of this to a proof of the Riemann Hypothesis basically says that he hasn’t had time to look into the question.</p>
<p>The paper is one of various attempts to address the Riemann Hypothesis by looking at properties of a Hamiltonian quantizing the classical Hamiltonian xp. To me, the obvious problem with an attempt like this is that I don’t see any use of deep ideas about either number theory or physics. The set-up involves no number theory, and a simple but non-physical Hamiltonian, with no use of significant input from physics. Without going into the details of the paper, it appears that essentially a claim is being made that the solution to the Riemann Hypothesis involves no deep ideas, just some basic facts about the analysis of some simple differential operators. Given the history of this problem, this seems like an extraordinary claim, backed by no extraordinary evidence.</p>
<p>I suspect that the author of the Quanta article found no experts in mathematics willing to comment publicly on this, because none found it worth the time to look carefully at the article, since it showed no engagement with the relevant mathematical issues. A huge amount of effort in mathematics over the years has gone into the study of the sort of problems that arise if you try and do the kind of thing the authors of this article want to do. Why are they not talking to experts, formulating their work in terms of well-defined mathematics of a proven sort, and referencing known results?</p>
<p>Maybe I’m being overly harsh here, this is not my field of expertise. Comments from experts on this definitely welcome (and those from non-experts strongly discouraged).</p>
<p>While these claims about the Riemann Hypothesis at Quanta look like a bad example of a math-physics interaction, a few days ago the magazine published something much more sensible, a piece by IAS director Robbert Dijkgraaf entitled <a href="https://www.quantamagazine.org/20170330-how-quantum-theory-is-inspiring-new-math/">Quantum Questions Inspire New Math</a>. Dijkgraaf emphasizes the role ideas coming out of string theory and quantum field theory have had in mathematics, with two high points mirror symmetry and Seiberg-Witten duality. His choice of mirror symmetry undoubtedly has to do with the <a href="http://www.math.ias.edu/sp/mirrorsymmetry">year-long program</a> about this being held by the mathematicians at the IAS. His characterizes this subject as follows:</p>
<blockquote><p>It is comforting to see how mathematics has been able to absorb so much of the intuitive, often imprecise reasoning of quantum physics and string theory, and to transform many of these ideas into rigorous statements and proofs. Mathematicians are close to applying this exactitude to homological mirror symmetry, a program that vastly extends string theory’s original idea of mirror symmetry. In a sense, they’re writing a full dictionary of the objects that appear in the two separate mathematical worlds, including all the relations they satisfy. Remarkably, these proofs often do not follow the path that physical arguments had suggested. It is apparently not the role of mathematicians to clean up after physicists! On the contrary, in many cases completely new lines of thought had to be developed in order to find the proofs. This is further evidence of the deep and as yet undiscovered logic that underlies quantum theory and, ultimately, reality.</p></blockquote>
<p>I very much agree with him that there’s an underlying logic and mathematics of quantum theory which we have not fully understood (my <a href="http://www.math.columbia.edu/~woit/QM/qmbook.pdf">book</a> is one take on what we do understand). I hope many physicists will take the search for new discoveries along these lines to heart, with progress perhaps flowing from mathematics to physics, which could sorely use some new ideas about unification.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9197New LHC Results
http://www.math.columbia.edu/~woit/wordpress/?p=9187
<p>This week results are being presented by the LHC experiments at the <a href="https://indico.in2p3.fr/event/13763/other-view?view=standard">Moriond</a> (twitter <a href="https://twitter.com/search?f=tweets&vertical=default&q=moriond">here</a>) and <a href="https://indico.cern.ch/event/550030/timetable/">Aspen</a> conferences. While these so far have not been getting much publicity from CERN or in the media, they are quite significant, as first results from an analysis of the full dataset from the 2015+2016 run at 13 TeV, This is nearly the design energy (14 TeV) and a significant amount of data (36 inverse fb/experiment). The target for this year’s run (physics to start in June) is another 45 inverse fb and we’ll not start to hear about results from that until a year or so from now. For 14 TeV and significantly larger amounts of data, the wait will be until 2021 or so.</p>
<p>The results on searches for supersymmetry reported this week have all been negative, further pushing up the limits on possible masses of conjectured superparticles. Typical limits on gluino masses are now about 2.0 TeV (see <a href="https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/SUSY/ATLAS_SUSY_Summary/ATLAS_SUSY_Summary.pdf">here</a> for the latest), up from about 1.8 TeV last summer (see <a href="https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/SUSY/ATLAS_SUSY_Summary/ATLAS_SUSY_Summary_201609.pdf">here</a>). ATLAS results are being posted <a href="https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults">here</a>, and I believe CMS results will appear <a href="https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS">here</a>.</p>
<p>This is now enough data near the design energy that some of the bets SUSY enthusiasts made years ago will now have to be paid off, in particular Lubos Motl’s bet with Adam Falkowski, and David Gross’s with Ken Lane (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=7160">here</a>). A major question now facing those who have spent decades promoting SUSY extensions of the Standard Model is whether they will accept the verdict of experiment or choose a path of denialism, something that I think will be very damaging for the field. The situation last summer (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8708">here</a>) was not encouraging, maybe we’ll soon see if more conclusive data has any effect. </p>
<p>If the negative news from the LHC is getting you down, for something rather different and maybe more promising, I recommend the coverage of the latest developments in neutrino physics <a href="https://neutel11.wordpress.com/">here</a>.</p>
Thu, 20 Jul 2017 18:29:41 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9187