Not Even Wrong
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Mon, 29 May 2017 17:07:07 GMTFeedCreatorClass 1.0 dev (specificfeeds.com)GAMBIT
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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 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>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9187This Time It’s For Real
http://www.math.columbia.edu/~woit/wordpress/?p=9180
<p>Several months ago I was <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8844">advertising</a> a “Final draft version” of <a href="http://www.math.columbia.edu/~woit/QM/qmbook.pdf">the book</a> I’ve been working on forever. A month or two after that though, I realized that I could do a more careful job with some of the quantum field theory material, bringing it in line with some standard rigorous treatments (this is all free quantum fields). So, I’ve been working on that for the past few months, today finally got to the end of the process of revising and improving things. My spring break starts today, and I’ll be spending most of it in LA and Death Valley on vacation, blogging should be light to non-existent.</p>
<p>Another big improvement is that there are now some very well executed illustrations, the product of work in TikZ by Ben Dribus. </p>
<p>I’m quite happy with how much of the book has turned out, and would like to think that it contains a significant amount of material not readily available elsewhere, as well as a more coherent picture of the subject and its relationship to mathematics than usual. By the way, while finishing work on the chapter about quantization of relativistic scalar fields, I noticed that Jacques Distler has a very nice <a href="https://golem.ph.utexas.edu/~distler/blog/archives/002943.html">new discussion on his blog of the single-particle theory</a>.</p>
<p>There’s a chance I might still make some more last-minute changes/additions, but the current version has no mistakes I’m aware of. Any suggestions for improvements/corrections are very welcome. Springer will be publishing the book at some point, but something like the current version available now will always remain available on my website</p>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9180Can the Laws of Physics be Unified?
http://www.math.columbia.edu/~woit/wordpress/?p=9129
<p>There’s a new book out this week from Princeton University Press, Paul Langacker’s <a href="http://press.princeton.edu/titles/11054.html">Can the Laws of Physics Be Unified?</a> (surely this is a mistake, but there’s also an ISBN number for a <a href="https://books.google.com/books/about/Can_the_Laws_of_Physics_be_Unified.html?id=LPeJQAAACAAJ">2020 volume with the same name</a> by Tony Zee). It’s part of a <a href="http://press.princeton.edu/catalogs/series/title/princeton-frontiers-in-physics.html">Princeton Frontiers in Physics</a> series, in which all the books have titles that are questions. The other volumes all ask “How…” or “What…” questions, but the question of this volume is of a different nature, and unfortunately the book unintentionally gives the answer you would expect from Hinchcliffe’s rule or Betteridge’s law.</p>
<p>This is not really a popular book, rather is accurately described by the author as “colloquium-level”. Lots of equations, but not much detail explaining exactly what they mean, for that some background is needed. The first two-thirds of the book is a very good summary of the Standard Model. For more details, Langacker has a textbook, <a href="http://www.sns.ias.edu/~pgl/SMB/">The Standard Model and Beyond</a>, which will have a second edition coming out later this year.</p>
<p>The last third of the book consists of two chapters addressing the question of the title, beginning with “What Don’t We Know?”. Here the questions are pretty much the usual suspects:</p>
<ul>
<li>Why the SM spectrum, with its masses and mixing angles?</li>
<li>The hierarchy problem.</li>
<li>The strong CP problem.</li>
<li>Quantum gravity.</li>
<li>Problems rooted in the cosmological model: Baryogenesis, dark matter, dark energy and the CC, </li>
</ul>
<p>In addition, there are problems listed that are only problems if you philosophically think that a good unified model should be more generic than the SM, leading you to ask: why no FCNC? why no EDM?, why no proton decay?</p>
<p>The last chapter “How will we find out?” lists the usual suspects for ideas about BSM physics: SUSY, compositeness, extra dimensions, hidden sectors, GUTS, string theory. We are told that this is a list of “many promising ideas”. While in general I wouldn’t argue with most of the claims of the book, here I think the author is spouting utter nonsense. The ideas he describes are ancient, many going back 40 years. In many cases they weren’t promising to begin with, introducing a large and complex set of new degrees of freedom without explaining much at all about the SM. Decades of hard work by theorists and experimentalists have not been kind to these ideas. No compelling theoretical models have emerged, and experimental results have been strongly negative, with the LHC putting a large number of nails into the coffins of these ideas. They’re not “promising”, they’re dead. </p>
<p>Langacker does repeatedly point out the problems such ideas have run into, but instead of leaving it at “we don’t know”, he unfortunately keeps bringing up as answer “the multiverse did it”. On page 151 we’re told the most plausible explanation for the CC is “the multiverse did it”, on page 160-163 we’re given “multiverse did it” anthropic explanations for interaction strengths, fermion masses, the Higgs VEV, and the CC. Pages 167-173 are a long argument for “the multiverse did it”. The problem that this isn’t science because it is untestable is dismissed with the argument that it “may well be correct”, and maybe somebody someday will figure out a test. On page 203 we’re told that string theory provides the landscape of vacua necessary to show that “the multiverse did it”.</p>
<p>The treatment of string theory has all of the usual problems: we’re assured that string theory is “conceptually simple”, despite no one knowing what the theory really is. The only problem is that of the “technical details” of constructing realistic vacua. I won’t go on about this, I once wrote a whole book…</p>
<p>In the end, while Langacker expresses the hope that “sometime in the next 10, 50, or 100 years” we will see a successful fully unified theory, there’s nothing in the book that provides any reason for such a hope. There is a lot that argues against such a hope, in particular a lot of argument in favor of giving up and signing up for a multiverse pseudo-scientific endpoint for the field. I suspect the author himself doesn’t realize how much the argument of the book is stacked against his expressed hope and in favor of a negative answer to the title’s question.</p>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9129Reality is Not What It Seems
http://www.math.columbia.edu/~woit/wordpress/?p=9155
<p>This Sunday’s New York Times has a rather hostile<a href="https://www.nytimes.com/2017/03/03/books/review/reality-is-now-what-it-seems-carlo-rovelli.html"> review by Lisa Randall</a> of Carlo Rovelli’s popular book <a href="https://www.penguin.co.uk/books/294669/reality-is-not-what-it-seems/">Reality is Not What It Seems</a>, which has recently come out in English in the US. Rovelli responds with a <a href="https://www.facebook.com/Prof.Rovelli/posts/1622834574408273">Facebook post</a>. Another similar recent book by Rovelli got a much more positive review in the NYT, his <a href="https://www.nytimes.com/2016/03/23/books/review-seven-brief-lessons-on-physics-is-long-on-knowledge.html">Seven Short Lessons on Physics</a>. </p>
<p>I haven’t written about these two books mainly because I don’t think I have anything interesting to say about either of them (although if someone had asked me to review one of them I might have tried to come up with something). They’re aimed very much not at physicists but at a popular audience that doesn’t know much about physics. From the parts I’ve read they seem to do a good job of writing for such an audience, and I noticed nothing that seemed to me either objectionable or particularly unusual. Rovelli’s two slightly different angles on this topic are an interest in the ancient history of speculation about physics and a background in loop quantum gravity rather than HEP theory/string theory. Instead of wading into the controversy over string theory, he just ignores it and writes about what he finds interesting.</p>
<p>I’m not so sure why, since to me this seems harmless if not particularly compelling, but Randall strongly objects to Rovelli’s attempts to draw connections between modern physics and classical philosophy:</p>
<blockquote><p>Wedging old ideas into new thinking is analogous to equating thousand-dollar couture adorned with beads and feathers and then marketed as “tribal fashion” to homespun clothing with true cultural and historical relevance. Ideas about relativity or gravity in ancient times weren’t the same as Einstein’s theory. Art (and science) are in the details. Either elementary matter is extended or it is not. The universe existed forever, or it had a beginning. Atoms of old aren’t the atoms of today. Egg and flour are not a soufflé. Without the appropriate care, it all just collapses.</p></blockquote>
<p>She’s also quite critical of the way Rovelli handles the unavoidable problem of writing about a complicated technical subject for the public:</p>
<blockquote><p>The beauty of physics lies in its precise statements, and that is what is essential to convey. Many readers won’t have the background required to distinguish fact from speculation. Words can turn equations into poetry, but elegant language shouldn’t come at the expense of understanding. Rovelli isn’t the first author guilty of such romanticizing, and I don’t want to take him alone to task. But when deceptively fluid science writing permits misleading interpretations to seep in, I fear that the floodgates open to more dangerous misinformation.</p></blockquote>
<p>Here I’m a bit mystified as to why she finds Rovelli any more objectionable than any other similar author (or maybe she doesn’t, and he just happened to be the lucky one to have the first such book she was asked to review in the New York Times). As should be clear from this blog and book reviews that I’ve written, I agree with Randall about a problem that she leads off the review with:</p>
<blockquote><p>Compounding the author’s challenge is the need to distinguish between speculation, ideas that might be verified in the future, and what is just fanciful thinking.</p></blockquote>
<p>However, to me it seemed that Rovelli met this challenge better than many, far better than any of the huge popular literature about supersymmetry, string theory and the multiverse. She may be right that someone not paying careful attention could get the wrong idea from Rovelli about cosmological loop quantum gravity models. It’s equally true though that readers of her own books about extra dimensions, dark matter and the dinosaurs might come away not understanding exactly what the strength of evidence was for those speculations.</p>
<p>On this question of how/whether physicists (here mathematicians are very, very different) make clear what is a solid argument and what is just speculation, another interesting case is that of Nima Arkani-Hamed, who came to prominence in particle theory with Randall, both of them working on extra dimensional models. Both of them got a huge amount of attention for this, from the public and from within physics, although these ideas were always highly speculative and unlikely to work out.</p>
<p>There’s a wonderful new <a href="http://www.theopennotebook.com/2017/02/28/storygram-natalie-wolchovers-visions-of-future-physics/">“Storygram”</a> by George Musser of a great profile by Natalie Wolchover of Arkani-Hamed. It’s all well worth reading, but related to the topic at hand I was struck by the following:</p>
<blockquote><p>Arkani-Hamed considers his tendency to speculate a personal weakness. “This is not false modesty, it’s really a personal weakness, but it’s true, so there’s nothing I can do about it,” he said. “It’s important for me while I’m working on something to be very ideological about it. And then, of course, it’s also important after you are done to forget the ideology and move on to another one.” </p></blockquote>
<p>Arkani-Hamed is an incredibly compelling speaker, but his talks often have struck me as putting forward very strongly some particular speculative point of view, while ignoring some of the obvious serious problems. If you’re not pretty well-informed on the subject, you might get misled… From the quote above he seems to have a fair amount of self-awareness about this. Also interesting in this context is his talk last year at Cornell on <a href="http://www.cornell.edu/video/nima-arkani-hamed-morality-fundamental-physics">The Morality of Fundamental Physics</a>. He gives an inspiring account of the intellectual value system of theoretical physics at its best. On the other hand, he pays no attention to the very real tension between that value system and the way people actually pursue their work, often very “ideologically”. For particle theory in particular and the current situation it finds itself in, this seems to me an important issue for practitioners to be thinking about.</p>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9155Bertram Kostant 1928-2017
http://www.math.columbia.edu/~woit/wordpress/?p=9143
<p>I was sorry to just hear via <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9134#comment-225157">a comment here</a> about the recent death of Bert Kostant, at the age of 88. MIT has a story about him <a href="http://news.mit.edu/2017/bertram-kostant-professor-emeritus-mathematics-dies-0216">here</a>. </p>
<p>Kostant was a major figure in the field of representation theory, and perhaps the leading one during the second half of the twentieth century among those with a serious interest in the relations between representation theory and quantum theory. These relations have for a long time now been a deep source of fascination to me, and Kostant’s work has had a great impact on how I think about the subject.</p>
<p>I’ll just list here some of his major papers that I’ve spent significant amounts of time with, characterized by a few major themes:</p>
<p><strong>Borel-Weil-Bott, Lie algebra cohomology, BRST and Dirac cohomology</strong></p>
<ul>
<li><a href="https://www.jstor.org/stable/1970237">Lie algebra cohomology and the generalized Borel-Weil theorem</a>. This paper has had a huge influence. Some notes from my graduate course discussing this and Borel-Weil-Bott are <a href="http://www.math.columbia.edu/~woit/LieGroups-2012/borelweilbott.pdf">here</a>.</li>
<li><a href="http://www.sciencedirect.com/science/article/pii/0003491687901783">Symplectic reduction, BRS cohomology and infinite-dimensional Clifford algebras</a> (with Shlomo Sternberg). If you really want to understand the mathematics underlying the BRST method, this is the place to start.</li>
<li><a href="https://arxiv.org/abs/math/0208048">Dirac cohomology for the Dirac operator</a>. For the context of this and a lot more about the subject, see the <a href="http://www.springer.com/us/book/9780817632182">book by Huang and Pandzic</a>.</li>
</ul>
<p><strong>Quantization of the dual of a Lie algebra, W-algebras</strong></p>
<p>The dual of a Lie algebra is a Poisson manifold, and you can ask what happens when you quantize this. For semisimple Lie algebra, reduction with respect to the nilradical is an idea that Kostant pursued, with two examples the following two papers. Applied to loop groups, this is a central idea of the geometric Langlands program. The theory of W-algebras is also an outgrowth of this.</p>
<ul>
<li><a href="https://eudml.org/doc/142586">On Whittaker vectors and representation theory</a>.</li>
<li>Quantization and representation theory, in the volume <a href="https://books.google.com/books?id=KvgvyFgrW10C&pg=PA287&lpg=PA287&dq=%22quantization+and+representation+theory%22+kostant&source=bl&ots=ZhYl_17HL_&sig=XlK4TUfbZRMCkXP6UVtF74HAXvI&hl=en&sa=X&ved=0ahUKEwippuCU8qvSAhVK92MKHZQWAywQ6AEIQjAG#v=onepage&q=%22quantization%20and%20representation%20theory%22%20kostant&f=false">Representation theory of Lie groups</a>.</li>
</ul>
<p><strong>Geometric quantization theory and co-adjoint orbits</strong></p>
<p>Starting around 1970 Kostant did a great deal of work developing the theory of “geometric quantization” and the idea of quantizing co-adjoint orbits to get representations (other figures to mention in this context are Kirillov and Souriau). Some of his papers on this are: </p>
<ul>
<li><a href="http://link.springer.com/chapter/10.1007%2Fb94535_20">Orbits, symplectic structures and representation theory</a>.</li>
<li><a href="http://www.mathunion.org/ICM/ICM1970.2/Main/icm1970.2.0395.0406.ocr.pdf">Orbits and quantization theory</a>. 1970 ICM talk.
</li>
<li>Quantization and unitary representations. In <a href="http://link.springer.com/book/10.1007%2FBFb0079063">Lecture notes in Mathematics 170</a>.</li>
</ul>
<p>All of the three general themes above are closely intertwined, and the relations between them indicate that there is still a lot more to be understood about how quantum theory and representation theory are related, with Kostant’s work undoubtedly playing a large role in developments to come.</p>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9143Various News
http://www.math.columbia.edu/~woit/wordpress/?p=9134
<p>First some mathematics items:</p>
<ul>
<li>Igor Shafarevich, one of the great figures of twentieth century algebraic geometry and algebraic number theory, died this past weekend at the age of 93. Besides his many contributions to mathematics research, he was also a remarkably lucid expositor. His two volume <a href="http://www.springer.com/la/book/9783642579080">Basic Algebraic Geometry</a> is a wonderful introduction to that subject, his survey volume <a href="http://www.springer.com/us/book/9783540251774">Basic Notions of Algebra</a> emphasizes the connections to geometry, and his volume on number theory (with Borevich) struck the AMS reviewer as <a href="http://projecteuclid.org/euclid.bams/1183527219">“delectable”</a>.
<p>Shafarevich was also known for his religiously-motivated nationalistic views which to many were distressingly anti-Semitic. In the spirit of respect for the recently deceased, I’ll just link to a quite interesting recent discussion (very sympathetic to Shafarevich) of the issue by David Mumford <a href="http://www.dam.brown.edu/people/mumford/blog/2016/Shaf.html">here</a> (and ruthlessly delete attempts to argue about this in the comment section).
</li>
<li>The AMS Notices has a <a href="http://www.ams.org/publications/journals/notices/201703/rnoti-p197.pdf">set of articles in honor of Andrew Wiles and his work</a>, which include some great explanations of the mathematics, as well as a long in-depth interview.</li>
<li>For another detailed interview with a mathematician, see Quanta magazine for a <a href="https://www.quantamagazine.org/20170221-mathematical-truth-sylvia-serfaty-interview/">piece by Siobhan Roberts</a> about Sylvia Serfaty of the Courant Institute.</li>
</ul>
<p>On the physics front, there’s:</p>
<ul>
<li>For his contribution to the Why Trust a Theory? conference (see <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8132">here</a> and <a href="http://www.math.columbia.edu/~woit/wordpress/?p=8149">here</a>), Helge Kragh has a <a href="https://arxiv.org/abs/1702.05648">new paper</a> which examines the question of whether history of science can help evaluate recent claims about the need to change the way theories are assessed. He sees in the unsuccessful “vortex theory” of the late nineteenth century an analog of string theory, with many of the same claims and justifications for lack of success. He quotes as a typical example of the enthusiasm of the time:<br />
<blockquote><p>I feel that we are so close with vortex theory that – in my moments of greatest optimism – I imagine that any day, the final form of the theory might drop out of the sky and land in someone’s lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory of anything we have had before and that … when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory!</p></blockquote>
<p>but then explains that this is actually a quote from Witten, with “string” replaced by “vortex”.</li>
<li>Scientifc American this month has an <a href="https://www.scientificamerican.com/article/cosmic-inflation-theory-faces-challenges/">article</a> (also available <a href="https://www.cfa.harvard.edu/~loeb/sciam3.pdf">here</a>) about the problems with the theory of inflation. The authors end by pointing out the dangers to science of multiverse inflationary scenarios (which they call the “multimess”):<br />
<blockquote><p>Some scientists accept that inflation is untestable but refuse to abandon it. They have proposed that, instead, science must change by discarding one of its defining properties: empirical testability. This notion has triggered a roller coaster of discussions about the nature of science and its possible redefinition, promoting the idea of some kind of nonempirical science. </p>
<p>A common misconception is that experiments can be used to <em>falsify</em> a theory. In practice, a failing theory gets increasingly immunized against experiment by attempts to patch it. The theory becomes more highly tuned and arcane to fit new observations until it reaches a state where its explanatory power diminishes to the point that it is no longer pursued. The explanatory power of a theory is measured by the set of possibilities it excludes. More immunization means less exclusion and less power. A theory like the multimess does not exclude anything and, hence, has zero power. Declaring an empty theory as the unquestioned standard view requires some sort of assurance outside of science. Short of a professed oracle, the only alternative is to invoke authorities. History teaches us that this is the wrong road to take. </p></blockquote>
</li>
<li>Nautilus has an <a href="http://cosmos.nautil.us/short/139/what-dark-matter-needs-are-new-kinds-of-experiments">article by Juan Collar</a> about the increasing skepticism about Wimps as dark matter candidates, and the interest in alternatives.</li>
</ul>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9134A Big Bang in a Little Room
http://www.math.columbia.edu/~woit/wordpress/?p=9107
<p>There’s a <a href="https://www.wsj.com/articles/searching-for-god-at-the-center-of-the-big-bang-1487364733">review in today’s Wall Street Journal</a> by me of Zeeya Merali’s <a href="http://www.hachettebookgroup.com/titles/zeeya-merali/a-big-bang-in-a-little-room/9780465065912/">A Big Bang in a Little Room</a>. If their version is behind a paywall you might find also find it elsewhere (for instance <a href="https://secure.marketwatch.com/story/searching-for-god-at-the-center-of-the-big-bang-2017-02-17">here</a>). I’ll reproduce parts of the review below with some comments more appropriate for the blog venue. As always, the editors at the WSJ did an excellent job of improving the first draft I sent them.</p>
<p>Merali has a website about the book <a href="http://www.thelittlebangtheory.com/">here</a>, and last week Nature published <a href="http://www.nature.com/nature/journal/v542/n7640/full/542164a.html">this review by Andreas Albrecht</a>. Albrecht criticizes the book for “sloppy interplay between science and religion”, but I think he misses the important point that the most serious problem here is the sloppiness about what is science and what isn’t. When physics journals decide to publish articles like <a href="http://www.worldscientific.com/doi/abs/10.1142/S0217732306020834">this one</a>, it’s not surprising that science writers make the mistake of taking them seriously and writing about them (Merali’s first chapter is about this paper).</p>
<p>Here are some extracts from the review, with some comments:</p>
<blockquote><p>What happened at the Big Bang—or before—is an irresistible question but one that, for now, as science, lies in the realm of the purely speculative.</p>
<p>In “A Big Bang in a Little Room,” science writer Zeeya Merali turns the question around, asking instead whether physicists can create a “baby universe,” born in its own Big Bang. Indeed, one prominent theorist she interviews has suggested that our own universe might be a baby universe created by a “physicist hacker,” with the complex pattern of fundamental particle masses intended as some sort of message to us. thereby learning more about the beginnings of the “old” one.</p></blockquote>
<p>The reference here is to Andrei Linde and <a href="https://arxiv.org/abs/hep-th/9110037">this 1991 paper</a>.</p>
<blockquote><p>[Merali] explains that her interest in this topic is tied up with her religious beliefs: If we ourselves could play God and create a new universe, wouldn’t that creation amount to a theological discovery, showing the likelihood that some higher intelligence was responsible for the Big Bang? She structures her narrative around interviews with prominent theoretical physicists; they mostly discuss science, but religious questions sometimes play a role, with often fascinating results. While some refuse to engage, she gets others to discuss such topics as the relation of the laws of physics to God’s happiness, the possibility of a physical “consciousness field,” and what the quantum mechanics of the Big Bang might indicate about the possibility of life after death and resurrection.</p></blockquote>
<p>Don Page is the one interested in God’s happiness, Abhay Ashtekar in the “consciousness field”, and Andrei Linde in resurrection.</p>
<blockquote><p>Mr. Linde is the central figure in this story, and Ms. Merali describes him as “a showman: bombastic, passionate, and fueled by the certain belief that inflation theory, which he helped to invent, is correct.” While Ms. Merali takes all of this seriously, there are very good reasons why most physicists don’t. Readers of “A Big Bang in a Little Room” would be well-advised to enjoy the ride but stay skeptical. Inflationary models can to some degree be confronted with observation and tested (a topic covered in other books but not this one).</p></blockquote>
<p>About the string theory landscape:</p>
<blockquote><p>Ms. Merali gives a disturbing version of this, contemplating the possibility that “string theory and inflation may be conspiring against us in such a way that we may never find evidence for them, and just have to trust in them as an act of faith.” </p></blockquote>
<p>This comes after an explanation of the anthropic multiverse point of view from HEP experimentalist Greg Landsberg, where he adds the twist of anthropics explaining why the string scale is at such high energy, and thus unobservable. The full paragraph in the book is</p>
<blockquote><p>In other words, the physics of string theory and inflation may be conspiring against us in such a way that we may never find evidence for them, and just have to trust in them as an act of faith. The multiverse truly works in mysterious ways!</p></blockquote>
<p>If that paragraph doesn’t make a scientist’s blood run cold and see the danger physics is facing, I don’t know what will. I end the review with</p>
<blockquote><p>In an era where “post-truth” was the word of the year, scientists and science writers need to make clear that science is not a species of theological or philosophical speculation and not about belief or entertainment value. Legitimate scientific claims are those that can be backed up with evidence, and unfortunately the wonderful and exciting story told well here contains none at all. </p></blockquote>
<p>My concern about the topic of the book is that it’s <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9053">Fake Physics</a>, not that religion is motivating the author (and likely motivating the Templeton Foundation to fund this project). A book about the religious views of physicists would be an interesting one that I’d certainly read, and the material in this book on that topic is quite interesting. One of the odder twists here is that the two blurbs from physicists promoting the book are from Sean Carroll and Martin Rees, with Carroll writing </p>
<blockquote><p>So you want to make your own universe. Zeeya Merali’s new book won’t quite give you an instruction kit—but it’s the closest thing we have at the moment. A fun and mind-expanding ride through modern ideas of how universes come to be.</p></blockquote>
<p>I don’t see how you can be devoted to fighting for science against religiously-driven pseudoscience, and think that this book is one you’d like to see be the public face of what “modern ideas” about cosmology are.</p>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9107Various Links
http://www.math.columbia.edu/~woit/wordpress/?p=9110
<p>The Columbia Math department has been doing extremely well in recent years, with some wonderful mathematicians joining the department. A couple items first involving some of them:</p>
<ul>
<li>Kevin Hartnett at Quanta Magazine has a <a href="https://www.quantamagazine.org/20170209-the-fight-to-fix-symplectic-geometry/">great article</a> about developments in the field of technical issues in the foundations of symplectic topology. This explains work by my colleague Dusa McDuff, who together with Katrin Wehrheim has been working on such issues, trying to resolve questions raised by fundamental work of Kenji Fukaya and collaborators. For technical details, two places to start looking are <a href="https://arxiv.org/abs/1701.07821">here</a> and <a href="https://arxiv.org/abs/1508.01844">here</a>.
<p>The Hartnett story does an excellent job of showing one aspect of how research mathematics is done. Due to the complexity of the arguments needed, it’s not unusual for early papers in a new field to not be completely convincing to everyone, with unresolved questions about whether proofs really are airtight. The way things are supposed to work, and how they worked here, is that as researchers better understand the subject proofs are improved, details better understood and problems fixed. Along the way there may be disagreements about whether the original arguments were incomplete or not, but almost always people end up agreeing on the final result.</p>
<p>Also featured in the article is another of my Columbia colleagues, Mohammed Abouzaid, who provides characteristically wise and well thought out remarks on the story.</li>
<li>Via Chandan Dalawat, I learned of an interesting <a href="https://www.youtube.com/watch?v=RORBT2m7zo0">CIRM video interview</a> with another colleague, Michael Harris. The same site has this <a href="https://www.youtube.com/watch?v=kq_T0Yq-oVQ">interview with Dusa McDuff</a>, as well as a variety of other interviews in <a href="https://www.youtube.com/playlist?list=PLBNfdZUo7fyo8ySMOZSbPIfWN5Kv9BEuC">English</a> and <a href="https://www.youtube.com/playlist?list=PLBNfdZUo7fyoKyb2vQfM3A7hQHr5NrGoJ">French</a>.</li>
</ul>
<p>For some other non-Columbia related links:</p>
<ul>
<li>The 70th birthday of Alain Connes is coming up soon, and will be celebrated with a series of <a href="http://www.connes70.fudan.edu.cn/">public lectures and conferences on noncommutative geometry</a> in Shanghai.<br />
This year will be the last series of lectures by Connes at the College de France. They’re appearing online <a href="http://www.college-de-france.fr/site/alain-connes/course-2016-2017.htm">here</a>, and I highly recommend them. He’s taking the opportunity to start the series with a general overview of the point of view about the relationship of geometry and quantum theory that he has been developing for many years.</li>
<li>For employment trends in theoretical particle physics, there are some updated graphs of data gleaned from the particle theory jobs rumor mill created by Erich Poppitz and available <a href="https://www.physics.utoronto.ca/~poppitz/Jobs94-08">here</a>. In terms of total number of jobs, there has been some recovery in the past couple years, with about 15 jobs/year, above the 10 or so common since the 2008 financial crisis (before 2008 numbers were higher, 20-25). As always, an important thing to keep in mind about this field is that this number of permanent jobs/year is a small fraction of the number of Ph.Ds. in the subject being produced each year at US universities.
<p>The numbers for distribution of subfields separate out “string theory” and lattice gauge theory. There have always been few jobs in lattice gauge theory, appear to be no hires in that subject for the past two years. I’m putting “string theory” in quotes, because it’s very hard these days to figure out what counts as “string theory”. With Poppitz’s choice of what to count, hiring in string theory has recovered a bit, now around 25% of the total for the past two years, up from more like 15% typical since 2006 (earlier on the numbers in some years were around 50%). </li>
<li>As pointed out here by commenter Shantanu, on Wednesday John Ellis gave a talk on <a href="http://pirsa.org/displayFlash.php?id=17020013">Where is particle physics going?</a> at Perimeter. I’d characterize Ellis’s answer to the question as “farther down the blind alley of supersymmetry”. He spins the failure to find SUSY so far at the LHC as some sort of positive argument for SUSY. The question session was dominated by questions about SUSY, with Ellis taking the attitude that there’s no reason to worry about the failure so far of the fine-tuning argument for SUSY, all you need to do is “ratchet up your pain threshold”. I fear that’s some sort of general advice where this line of research is going.
<p>About the failure to find any evidence for SUSY wimps that were supposed to explain dark matter, Ellis explained that he had been working on this idea for 34 years, first writing about it in 1983, so with that much invested in it, he’s not about to give up now.</li>
</ul>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9110Perfectoid Woodstock
http://www.math.columbia.edu/~woit/wordpress/?p=9103
<p>Every year in Tucson the Arizona Winter School takes place, with a five day program on some topic in arithmetic geometry aimed mainly at advanced graduate students, designed to get them involved in current research-level topics. This year’s topic (<a href="http://swc.math.arizona.edu/index.html">Perfectoid Spaces</a>) is drawing a huge number of people there next month, with about 450 participants expected (in the past numbers were more like 100). This should be a veritable Woodstock of arithmetic geometry, with no one I’ve talked to quite able to figure this out, thinking that there probably weren’t 450 people worldwide interested at all in arithmetic geometry. It seems everyone in the field will be there and then some.</p>
<p>Peter Scholze is the opening and closing act. The other lecturers who will take the stage have started to put lecture notes for their lectures on the school website.</p>
<p>Some are dubious that there really are 400 or so students in the world with the background necessary to understand this material. See for example <a href="http://mathoverflow.net/questions/260330/a-roadmap-for-understand-perfectoid-spaces">MathOverflow</a> where nfdc23 isn’t very encouraging to a student who doesn’t know any rigid analytic geometry, but plans to attend the AWS. In any case, I hear Tucson is quite nice in March.</p>
<p>At some kind of other end of the spectrum of such things, a couple months later experts will gather in Germany to discuss this field (see <a href="https://www.simonsfoundation.org/mathematics-and-physical-science/simons-symposia/p-adic-hodge-theory-2017/">here</a>). Also for about five days, at the Schloss Elmau Luxury Spa and Cultural Hideaway, the sort of place heads of state go for G7 meetings. Rooms run $600 a night or so, but in this case the tab is being picked up by the Simons Foundation. Sorry, by invitation only.</p>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9103Math and Physics Social Media
http://www.math.columbia.edu/~woit/wordpress/?p=9098
<p>In the current situation, getting back to finding interesting news about math and/or physics to think about seems like a good idea, but I’ve been having trouble coming up with such news. Besides blogs, many of them listed on the right-hand margin of this one, I also follow some people on Twitter and on Google+. There are quite a few well-known physicists on Twitter at this point. On any given day you can learn something interesting from, for instance, <a href="https://twitter.com/FrankWilczek">Frank Wilczek</a> or <a href="https://twitter.com/preskill">John Preskill</a> (or see an <a href="https://twitter.com/preskill/status/827622415135936512">epic</a> <a href="https://twitter.com/FrankWilczek/status/827624066882297856">throwdown</a> between them). </p>
<p>I’m sure there are many other mathematicians and physicists on social media that I’m not aware of, and open here to hearing suggestions. Part of the problem is that I’m now so old I figure I don’t even know what social media sites are out there. I hear there’s this thing called Facebook, but also that it’s now over as far as the younger generation is concerned. So, if you have a suggestion about where to find high quality news about math or physics on social media, whether it’s on Twitter, Google+, Facebook, Live Journal, Instagram, Pinterest, Snapchat, Yik Yak, Grindr or something else I’ve never heard of, please let us all know in the comments.</p>
Mon, 29 May 2017 17:07:07 GMThttp://www.math.columbia.edu/~woit/wordpress/?p=9098