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Wed, 28 Oct 2020 12:05:59 GMTFeedCreatorClass 1.0 dev (follow.it)Do Particle Physicists Continue to Make Empty Promises?
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/367985519/15156" border=0 width="1" height="1" alt="Story 367985519" title="Story 367985519"> <p>Blogging has been light here, since little worthy of note in math/physics has been happening, and I’ve been busy with teaching, freaking out about the election, and trying to better understand Euclidean spinors. I’ll write soon about the Euclidean spinors, but couldn’t resist today making some comments about two things I’ve seen this week.</p>
<p>Sabine Hossenfelder yesterday had a blog entry/Youtube video entitled <a href="http://backreaction.blogspot.com/2020/10/particle-physicists-continue-to-make.html">Particle Physicists Continue to Make Empty Promises</a>, which properly takes exception to this quote:</p>
<blockquote><p>A good example of a guaranteed result is dark matter. A proton collider operating at energies around 100 TeV will conclusively probe the existence of weakly interacting dark-matter particles of thermal origin. This will lead either to a sensational discovery or to an experimental exclusion that will profoundly influence both particle physics and astrophysics. </p></blockquote>
<p>from a <a href="https://www.nature.com/articles/s41567-020-01054-6">recent article</a> by Fabiola Gianotti and Gian Francesco Giudice in <em>Nature Physics</em>. She correctly notes that</p>
<blockquote><p>They guarantee to rule out some very specific hypotheses for dark matter that we have no reason to think are correct in the first place.</p></blockquote>
<p>A 100 TeV collider can rule out certain kinds of higher-mass WIMPs, but it’s simply untrue that such an exclusion will “profoundly influence both particle physics and astrophysics.” Very few people think such a thing is likely since there’s no evidence for it and no well-motivated theory that predicts it.</p>
<p>Where I part company with Hossenfelder though is that I don’t see much wrong with the rest of the Gianotti/Giudice piece and don’t agree with her point of view that the big problem here is empty promises like this and plans for a new collider. Twenty years ago when I began writing N<em>ot Even Wrong</em>, I started out by writing a chapter about the inherent physical limits that colliders were starting to hit, and the significance of this for the field. It was already clear that getting to higher proton energies than the LHC, or higher lepton energies than LEP was going to be very difficult and expensive. HEP experimentalists are now facing painful and hard choices about the future, which I wrote about in detail here under the title <a href="https://www.math.columbia.edu/~woit/wordpress/?p=10768">Should the Europeans Give Up?</a>. The worldwide experimental HEP community is addressing the problem in a serious way, with the European Strategy Update one aspect, and the US now engaged in a similar <a href="https://snowmass21.org/">Snowmass 2021</a> effort.</p>
<p>Many find it tempting to believe that the answer is simple: just redirect funds from collider physics to non-collider experiments. The problem is that there’s little evidence of promising but unfunded ideas for non-collider experiments. For the last decade there has been no new construction of high energy colliders, with as much money as ever available worldwide for HEP experiments. This should have been a golden age for those with non-collider ideas to propose. This continues to be the case: if you look at the European Strategy Update and Snowmass 2021 efforts, they have seriously focused on finding non-collider ideas to pursue. This should continue to be true, since I see no evidence anyone is going to decide to go ahead with a next generation collider and start spending money building it during the next few years. The bottom line result from the European process was not a decision to build a new collider, but a decision to keep studying the problem, then evaluate what to do in 2026. For the ongoing American process, as far as I know a new US collider is not even a possibility being discussed.</p>
<p>While HEP experiment is facing difficult times because of fundamental physical, engineering and economic limits, the problems of HEP theory are mostly self-inflicted. The decision nearly 40 years ago by a large fraction of the field to orient their research programs around bad ideas that don’t work (SUSY extensions of the Standard Model and string theory unification), then spend decades refusing to acknowledge failure is at the core of the sad state of the subject these days.</p>
<p>About the canniest and most influential HEP theorist around is Nima Arkani-Hamed, and a few days ago I watched an <a href="https://www.facebook.com/imaginescience/videos/the-world-of-thinking-a-conversation-between-nima-arkani-hamed-janna-levin/353045532687868/">interview of him by Janna Levin</a>. On the question of the justification for a new collider, he’s careful to state that the justification is mainly the study of the Higgs. He’s well aware that the failure of the “naturalness” arguments for weak-scale SUSY needs to be acknowledged and does so. He also is well aware that any attempt to argue this failure away by saying “we just need a higher energy collider” won’t pass the laugh test (and would bring Hossenfelder and others down on him like a ton of bricks…).</p>
<p>The most disturbing aspect of the interview is that Levin devotes a lot of time (and computer graphics) to getting Arkani-Hamed to explain his 1998 ideas about “large extra dimensions”, repeatedly telling the audience that he has been given a \$3 million prize for them. <a href="https://arxiv.org/abs/hep-ph/9803315">This paper</a> has by now been cited over 6300 times, and the multi-million dollar business is correct, with the prize citation explaining:</p>
<blockquote><p>Nima Arkani-Hamed has proposed a number of possible approaches to this [<em>hierarchy problem</em>] paradox, from the theory of large extra dimensions, where the strength of gravity is diluted by leaking into higher dimensions, to “split supersymmetry,” motivated by the possibility of an enormous diversity of long-distance solutions to string theory.</p></blockquote>
<p>At the time it was pretty strange that a \$3 million dollar prize was being given for ideas that weren’t working out. It’s truly bizarre though that Levin would now want to make such failed ideas the centerpiece of a presentation to the public, misleading people about their status. The website for the interview also promotes Arkani-Hamed purely in terms of his failures, presented as successes:</p>
<blockquote><p>Nima Arkani-Hamed is one of the leading particle physics phenomenologists of the generation. He is concerned with the relation between theory and experiment. His research has shown how the extreme weakness of gravity, relative to other forces of nature, might be explained by the existence of extra dimensions of space, and how the structure of comparatively low-energy physics is constrained within the context of string theory. He has taken a lead in proposing new physical theories that can be tested at the Large Hadron Collider at CERN in Switzerland,</p></blockquote>
<p>This is part of the overall weird situation of the failed ideas (SUSY/strings) of 40 years ago: they still live on in a dominant position when the subject is presented to the public.</p>
<p>At the same time, the topics Arkani-Hamed is working on now are ones I think are more promising than most of the rest of what is going on in HEP theory. The interview began with a discussion of <a href="https://www.math.columbia.edu/~woit/wordpress/?p=11899">Penrose’s recent Nobel Prize</a>, with Arkani-Hamed explaining Penrose’s fantastic insights about twistor geometry and noting that his own current work involves a fundamental role for twistor space (personally I see some <a href="https://www.math.columbia.edu/~woit/wordpress/?p=11899">other promising directions for using twistor geometry</a>, more to come about this here in the future).</p>
<p>In contrast to Hossenfelder, what I’m seeing these days in HEP physics is not a lot of empty promises (which were a dominant aspect of HEP theory for several decades). Instead, on the experimental side, there’s an honest struggle with implacable difficulties. On the theory side increasingly people have just given up, deciding that it’s better to let the subject die chained to a host of \$3 million prizes for dead ideas than to honestly face up to what has happened.</p>Fri, 23 Oct 2020 23:38:18 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110n441Qvt5f9pn1z8-xSOmNlJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_ofqkgQuZw1yO2020 Physics Nobel Prize
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/362560915/15156" border=0 width="1" height="1" alt="Story 362560915" title="Story 362560915"> <p>The 2020 Physics Nobel Prize was <a href="https://www.nobelprize.org/prizes/physics/2020/summary/">announced this morning</a>, with half going to Roger Penrose for his work on black holes, half to two astronomers (Reinhard Genzel and Andrea Ghez) for their work mapping what is going on at the center of our galaxy. I know just about nothing about the astronomy side of this, but am somewhat familiar with Penrose’s work, which very much deserves the prize.</p>
<p>Penrose is a rather unusual choice for a Physics Nobel Prize, in that he’s very much a mathematical physicist, with a Ph.D. in mathematics (are there other physics winners with math Ph.Ds?). In addition, the award is not for a new physical theory, or for anything experimentally testable, but for the rigorous understanding of the implications of Einstein’s general relativity. While I’m a great fan of the importance of this kind of work, I can’t think of many examples of it getting rewarded by the Nobel prize. I had always thought that Penrose was likely to get a Breakthrough Prize rather than a Nobel Prize, still don’t understand why that hasn’t happened already.</p>
<p>Besides the early work on black holes that Penrose is being recognized for, he has worked on many other things which I think are likely to ultimately be of even greater significance. In particular, he’s far and away the person most responsible for twistor theory, a subject which I believe has a great future ahead of it at the core of fundamental physical theory.</p>
<p>In all his work, Penrose has shown a remarkable degree of originality and creativity. He’s not someone who works to make an advance on ideas pioneered by others, but sets out to do something new and different. His book “The Road to Reality” is a masterpiece, an inspiring original and deep vision of the unity of geometry and physics that outshines the mainstream ways of looking at these questions. </p>
<p>Congratulations to Sir Roger, and compliments to the Nobel prize committee for a wonderful choice!</p>Tue, 06 Oct 2020 15:33:05 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110k7gw0CArcfM06NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_odyE4RFDiep5Quick Links
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/354571105/15156" border=0 width="1" height="1" alt="Story 354571105" title="Story 354571105"> <p>A few quick links:</p>
<ul>
<li>I was sorry to hear of the recent death of Vaughan Jones. A few things about his life and work have started to appear, see <a href="https://terrytao.wordpress.com/2020/09/09/vaughan-jones/">here</a>, <a href="https://news.vanderbilt.edu/2020/09/09/vaughan-jones-preeminent-vanderbilt-mathematician-has-died/">here</a> and <a href="https://www.ams.org/news?news_id=6374">here</a>.</li>
<li>For a wonderful in-depth article about the life of Michael Atiyah written by Nigel Hitchin, see <a href="https://royalsocietypublishing.org/doi/10.1098/rsbm.2020.0001">here</a>.</li>
<li>There are now many new places where you can find talks about math and physics to listen to. For instance, just for math and just at Harvard, there is a series of <a href="https://cmsa.fas.harvard.edu/literature-lecture-series/">Harvard Math Literature</a> talks and Dennis Gaitsgory’s <a href="http://people.math.harvard.edu/~gaitsgde/GLOH_2020/">geometric Langlands office hours</a>.</li>
<li>Breakthrough Prizes were announced today. There’s an argument to be made that the best policy is to ignore them. Weinberg has another 3 million dollars.</li>
<li>For an interview with Avi Loeb about why physics is stuck, see <a href="https://www.salon.com/2020/09/06/physics-is-stuck--and-needs-another-einstein-to-revolutionize-it-physicist-avi-loeb-says/">here</a>.</li>
<li>For an explanation from John Preskill of why quantum computing is hard (which I’d claim has to do with why the measurement problem is hard), see <a href="https://www.amazon.science/blog/amazon-scholar-john-preskill-on-the-aws-quantum-computing-effort">here</a>.</li>
</ul>Thu, 10 Sep 2020 18:38:16 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110kSDw_QL1bxD06NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oRZkU_kFzNeNFall Quantum Mechanics Class
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/353572463/15156" border=0 width="1" height="1" alt="Story 353572463" title="Story 353572463"> <p>I’ll be teaching a course on quantum mechanics this year here at Columbia, from a point of view aimed somewhat at mathematicians, emphasizing the role of Lie groups and their representations. For more details, the course webpage is <a href="http://www.math.columbia.edu/%7Ewoit/QM/fall2020.html">here</a>.</p>
<p>The course is being taught online using Zoom, with 37 students now enrolled. I’ve set things up in my office to try and teach using the blackboard there, and will be interacting with the students mostly via Zoom. As an experiment, I’ve also set up a <a href="https://www.youtube.com/channel/UCdSEKN94Jo1xjUHVyfEfIjg">Youtube channel</a>. If all goes well you should be able to find a livestream of the class there while it’s happening, which is scheduled for 4:10-5:25 Tuesdays and Thursdays, starting tomorrow, September 8. I’ll also try and make sure the recorded livestreams get uploaded and saved at <a href="https://www.youtube.com/playlist?list=PLOaEOh8qMwDLoBJinaH3p31edODHdlb93">this playlist</a>. Unfortunately I won’t be able to interact with people watching on Youtube, should have my hands full trying to get to know the students enrolled here in the course, with only this virtual connection.</p>Mon, 07 Sep 2020 21:56:11 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110lxa1Uf08r2L7V8HZmzB6MmJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oag5YTd7ezhjAMS Open Math Notes
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/353278702/15156" border=0 width="1" height="1" alt="Story 353278702" title="Story 353278702"> <p>The AMS for the last few years has had a valuable project called <a href="https://www.ams.org/open-math-notes">AMS Open Math Notes</a>, a site to gather and make available course notes for math classes, documents of the sort that people sometimes make available on their websites. This provides a great place to go to look for worthwhile notes of this kind (many of them are of very high quality), as well as ensuring their availability for the future. They have an advisory board that evaluates whether submitted notes are suitable.</p>
<p>A couple months ago I submitted the <a href="https://www.math.columbia.edu/~woit/wordpress/?p=11683">course notes I wrote up this past semester for my Fourier Analysis class</a>, and I’m pleased that they were accepted and are now available <a href="https://www.ams.org/open-math-notes/omn-view-listing?listingId=110834">here at the AMS site</a> (and will remain also available <a href="https://www.math.columbia.edu/~woit/fourier-analysis/fouriernotes.pdf">from my website</a>).</p>Sun, 06 Sep 2020 17:42:54 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110mM_Vk22x2P5KpSGW1eS8dIJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_ob_lFWndvTytQuantum Reality
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/352153380/15156" border=0 width="1" height="1" alt="Story 352153380" title="Story 352153380"> <p>Jim Baggott’s new book, <a href="https://global.oup.com/academic/product/quantum-reality-9780198830153">Quantum Reality</a>, is now out here in US, and I highly recommend it to anyone interested in the issues surrounding the interpretation of quantum mechanics. Starting next week I’ll be teaching a course on quantum mechanics for mathematicians (more about this in a few days when I have a better idea how it’s going to work). I’ll be lecturing about the formalism, and for the topic of how this connects to physical reality I’ll be referring the students to this new book (as well as Philip Ball’s <a href="https://www.math.columbia.edu/~woit/wordpress/?p=10522">Beyond Weird</a>).</p>
<p>When I was first studying quantum mechanics in the early-mid 1970s, the main popular sources discussing interpretational issues were uniform triumphalist accounts of how physicists had struggled with these issues and finally ended up with the “Copenhagen interpretation” (which no one was sure exactly how to state, due to diversity of opinion among theorists and Bohr’s obscurity of expression). Everyone now says that the reigning ideology of the time was “shut up and calculate”, but that’s not exactly what I remember. The Standard Model had just appeared, offering up a huge advance and a long list of new questions with powerful methods to attack them. In this context it was was hard to justify spending time worrying about the subtleties of what Copenhagen might have gotten wrong.</p>
<p>In recent decades things have changed completely, with the question of what’s wrong with Copenhagen and how to do better getting a lot of attention. By now a huge and baffling literature about alternatives has accumulated, forming somewhat of a tower of Babel confronting anyone trying to learn more about the subject. Some popular accounts have dealt with this complexity by turning the subject into a morality play, with alternative interpretations portrayed as the Rebel Alliance fighting righteous battles against the Copenhagen Empire. Others accounts are pretty much propaganda for a particular alternative, be it Bohmian mechanics or a many-worlds interpretation.</p>
<p>Instead of something like this, Baggott provides a refreshingly sane and sensible survey of the subject, trying to get at the core of what is unsatisfying about the Copenhagen account, while explaining the high points of the many different alternatives that have been pursued. He doesn’t have an ax to grind, sees the subject more as a “Game of Theories” in which one must navigate carefully, avoiding Scylla, Charybdis, and various calls from the Sirens. One thing which is driving this whole subject is the advent of new technologies that allow the experimental study of quantum coherence and decoherence, with great attention being paid as possible quantum computing technology has become the hottest and best-funded topic around. Whatever you think about Copenhagen, what Bohr and others characterized as inaccessible to experiment is now anything but that.</p>
<p>While one of my least favorite aspects of discussions of this subject is the various ways the terms “real” and “reality” get used, I have realized that one has to get over that when trying to follow people’s arguments, since the terms have become standard sign-posts. What’s at issue here are fundamental questions about physical science and reality, including the question of what the words “real” and “reality” might mean. In <em>Quantum Reality</em>, Baggott provides a well-informed, reliable and enlightening tour of the increasingly complex and contentious terrain of arguments over what our best fundamental theory is telling us about what is physically “real”.</p>Wed, 02 Sep 2020 23:01:25 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110ktww8LCVc_iXawZ12B-dU6Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oa7wGc8VMmn_Funding Priorities
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/349927374/15156" border=0 width="1" height="1" alt="Story 349927374" title="Story 349927374"> <p>The research that gets done in any field of science is heavily influenced by the priorities set by those who fund the research. For science in the US in general, and the field of theoretical physics in particular, recent years have seen a reordering of priorities that is becoming ever more pronounced. As a prominent example, recently <a href="https://www.nature.com/articles/d41586-020-02272-x">the NSF announced</a> that their graduate student fellowships (a program that funds a large number of graduate students in all areas of science and mathematics) will now be governed by the following language:</p>
<blockquote><p>Although NSF will continue to fund outstanding Graduate Research Fellowships in all areas of science and engineering supported by NSF, in FY2021, GRFP will emphasize three high priority research areas in alignment with NSF goals. These areas are Artificial Intelligence, Quantum Information Science, and Computationally Intensive Research. Applications are encouraged in all disciplines supported by NSF that incorporate these high priority research areas.</p></blockquote>
<p>No one seems to know exactly what this means in practice, but it clearly means that if you want the best chance of getting a good start on a career in science, you really should be going into one of</p>
<ul>
<li>Artificial Intelligence</li>
<li>Quantum Information Science</li>
<li>Computationally Intensive Research</li>
</ul>
<p>or, even better, trying to work on some intersection of these topics.</p>
<p>Emphasis on these areas is not new; it has been growing significantly in recent years, but this policy change by the NSF should accelerate ongoing changes. As far as fundamental theoretical physics goes, we’ve already seen that the move to quantum information science has had a significant effect. For example, the IAS PiTP summer program that trains students in the latest hot topics in 2018 was devoted to <a href="https://static.ias.edu/pitp/2018/index.html">From Qubits to Spacetime</a>. The impact of this change in funding priorities is increased by the fact that the largest source of private funding for theoretical physics research, the Simons Foundation, share much the same emphasis. The new Simons-funded Flatiron Institute here in New York has as mission statement</p>
<blockquote><p>The mission of the Flatiron Institute is to advance scientific research through computational methods, including data analysis, theory, modeling and simulation. </p></blockquote>
<p>In the latest development on this front, the White House <a href="https://www.energy.gov/articles/white-house-office-technology-policy-national-science-foundation-and-department-energy">announced today</a> \$1 billion in funding for artificial intelligence and quantum information science research institutes: </p>
<blockquote><p>“Thanks to the leadership of President Trump, the United States is accomplishing yet another milestone in our efforts to strengthen research in AI and quantum. We are proud to announce that over $1 billion in funding will be geared towards that research, a defining achievement as we continue to shape and prepare this great Nation for excellence in the industries of the future,” said Advisor to the President Ivanka Trump.</p></blockquote>
<p>This includes <a href="https://www.nsf.gov/news/special_reports/announcements/082620.jsp">an NSF component</a> of \$100 million dollars in new funding for five Artificial Intelligence research institutes. One of these will largely be a fundamental theoretical physics institute, to be called the <a href="https://iaifi.org/">NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI)</a>. The theory topics the institute will concentrate on will be</p>
<ul>
<li>Accelerating Lattice Field Theory with AI</li>
<li>Exploring the Multiverse with AI</li>
<li>Classifying Knots with AI</li>
<li>Astrophysical Simulations with AI</li>
<li>Towards an AI Physicist</li>
<li>String Theory Conjectures via AI</li>
</ul>
<p>As far as trying to get beyond the Standard Model, the IAIFI plan is to </p>
<blockquote><p>work to understand physics beyond the SM in the frameworks of string and knot theory.</p></blockquote>
<p>I’m rather mystified by how knot theory is going to give us beyond the SM physics, perhaps the plan is to revive <a href="https://en.wikipedia.org/wiki/Vortex_theory_of_the_atom">Lord Kelvin’s vortex theory</a>.</p>Wed, 26 Aug 2020 15:54:25 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110l9bCbN46A9TqnAxiD9qXc5Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oeX8lipPLhBxStraight Old White Guys and Their Theories of Everything
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/348592021/15156" border=0 width="1" height="1" alt="Story 348592021" title="Story 348592021"> <p>I’m a big fan of Sabine Hossenfelder’s music videos, the latest of which, <a href="https://www.youtube.com/watch?v=5gmtAeqRs14">Theories of Everything</a>, has recently appeared. I also agree with much of the discussion of this <a href="http://backreaction.blogspot.com/2020/08/theories-of-everything-ive-been-singing.html">at her latest blog posting</a> where Steven Evans writes</p>
<blockquote><p>nobody wants to see Peter Woit sing.</p></blockquote>
<p>and Terry Bollinger chimes in:</p>
<blockquote><p>Please, under no circumstances and in no situations, should folks like Peter Woit, Lee Smolin, Garrett Lisi, Sean Carroll, or even John Baez try to spice up their blogs or tweets by adding clips of themselves singing self-composed physics songs.</p>
<p>Trust me, fellow males of the species: However tempted you may be by Sabine’s spectacular success in this arena, it just ain’t gonna work for you!</p></blockquote>
<p>The chorus of Sabine’s song goes:</p>
<blockquote><p>
All you guys with theories of everything<br />
Who follow me wherever I am traveling<br />
Your theories are neat<br />
I hope they will succeed<br />
But please, don’t send them to me
</p></blockquote>
<p>One reason for her bursting into song like this was probably her recent participation in <a href="http://imagination.ucsd.edu/_wp/podcast/theories-of-everything-cosmic-controversies-great-debates-and-scientific-speculations-part-2/">this discussion</a>. I’d like to think (for no good reason) that it had nothing to do with my recently sending her a copy of <a href="http://www.math.columbia.edu/~woit/twistors.pdf">this</a>.</p>
<p>Today brought a <a href="https://www.youtube.com/watch?v=GfRJZbsywPQ">new discussion of theories of everything</a>, by Brian Greene and Cumrun Vafa. When asked by Greene to give a grade to string theory, Vafa said that he would give it a grade of A+, although its grade was less than A on the experimental verification front.</p>
<p>Over the years I’ve been sent more than my fair share of theories of everything, and Sabine is right that they all come from men. In addition, all available evidence is that these men are typically old, straight and white. As someone who <a href="https://www.math.columbia.edu/~woit/wordpress/?p=11899">recently decided he may have an idea about a theory of everything</a>, it has not escaped my attention that pretty much all of these things are nonsense and their authors are, besides being old, straight, white and male, suffering from various degrees of self-delusion.</p>
<p>So, while I’m enthusiastic about new ideas involving twistors and happily continuing to work on them, it’s pretty clear that this is not a good time to be bringing them to market. The elite academic world of Harvard and Princeton theorists that I was trained in has been doing an excellent job of convincing everyone that even the smartest people in the world could not make any progress towards a TOE, and that all claims for such progress from the most respected experts around are not very credible. Best to ignore not just the cranks who fill up your inbox with such claims, but all of them, judging the whole concept to be doomed until the point in the far distant future when an experiment finally provides the clue to the correct way forward. </p>
<p>Given current active social debates, that these kinds of claims are coming from the most unenlightened of all sources (straight old white guys) doesn’t help with trying to get positive attention. Somewhat correlated with the straight old white guy thing though, I’m in a pretty privileged position of being able to keep happily working on what I want to work on, no matter what its market value.</p>
<p>Be warned though, if people don’t pay some more attention, I’m going to start writing songs and singing them here.</p>Fri, 21 Aug 2020 20:16:10 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110lpgrynIGAsczjq7PwYEWiNJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oZ0NBDkVuORrTwistors and the Standard Model
https://api.follow.it/track-rss-story-click/AaY2ldA110k50lVpcY5P331z8-xSOmNlJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oeMJ0nZwBmzx
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/345387299/15156" border=0 width="1" height="1" alt="Story 345387299" title="Story 345387299"> <p>For the past few months I’ve been working on writing up some ideas I’m quite excited about, and the pandemic has helped move things along by removing distractions and forcing me to mostly stay home. There’s now something written that I’d like to publicize, a draft manuscript entitled <a href="https://www.math.columbia.edu/~woit/twistors.pdf">Twistor Geometry and the Standard Model in Euclidean Space</a>, which at some point soon I’ll put on the arXiv. My long experience with both hype about unification in physics as well as theorist’s huge capacity for self-delusion on the topic of their own ideas makes me wary, but I’m very optimistic that these ideas are a significant step forward on the unification front. I believe they provide a remarkable possibility for how internal and space-time symmetries become integrated at short distances, without the usual problem of introducing a host of new degrees of freedom.</p>
<p>Twistor theory has a long history going back to the 1960s, and it is such a beautiful idea that there always has been a good argument that there is something very right about it. But it never seemed to have any obvious connection to the Standard Model and its pattern of internal symmetries. The main idea I’m writing about is that one can get such a connection, as long as one looks at what is happening not just in Minkowski space, but also in Euclidean space. One of the wonderful things about twistor theory is that it includes both Minkowski and Euclidean space as real slices of a complex, holomorphic, geometry. The points in these spaces are best understood as complex lines in another space, projective twistor space. It is on projective twistor space that the internal symmetries of the Standard Model become visible.</p>
<p>The draft paper contains the details, but I should make clear what some of the arguments are for taking this seriously:</p>
<ul>
<li>Unlike other ideas about unification out there, it’s beautiful. The failure of string theory unification has caused a backlash against the idea of using beauty as a criterion for judging unification proposals. I won’t repeat here my usual rant about this. As an example of what I mean about “beauty”, the fundamental spinor degree of freedom appears here tautologically: a point is by definition exactly the $\mathbf C^2$ spinor degree of freedom at that point.</li>
<li>Conformal invariance is built-in. The simplest and most highly symmetric possibility for what fundamental physics does at short distances is that it’s conformally invariant. In twistor geometry, conformal invariance is a basic property, realized in a simple way, by the linear $SL(4,\mathbf C)$ group action on the twistor space $\mathbf C^4$. This is a complex group action with real forms $SU(2,2)$ (Minkowski) and $SL(2,\mathbf H)$ (Euclidean).</li>
<li>The electroweak $SU(2)$ is inherently chiral. For many other ideas about unification, it’s hard to get chiral interactions. In twistor theory one problem has always been the inherent chiral nature of the theory. Here this becomes not a problem but a solution.</li>
</ul>
<p>At the same time I should also make clear that what I’m describing here is very incomplete. Two of the main problems are:</p>
<ul>
<li>The degrees of freedom naturally live not on space-time but on projective twistor space $PT$, with space-time points complex projective lines in $PT$. Standard quantum field theory with fields parametrized by space-time points doesn’t apply and how to work instead on $PT$ is unclear. There has been some work on formulating QFT on $PT$ as a holomorphic Chern-Simons theory, and perhaps that work can be applied here.</li>
<li>There is no idea for where generations come from. Instead of $PT$ perhaps the theory should be formulated on $S^7$ (space of unit length twistors) and other aspects of the geometry there exploited. In some sense, the incarnations of twistors as four complex number or two quaternions are getting used, but maybe the octonions are relevant.</li>
</ul>
<p>What I think is probably most important here is that this picture gives a new and compelling idea about how internal and space-time symmetries are related. The conventional argument has always been that the Coleman-Mandula no-go theorem says you can’t combine internal and space-time symmetries in a non-trivial way. Coleman-Mandula does not seem to apply here: these symmetries live on $PT$, not space-time. To really show that this is all consistent, one needs a full theory formulated on $PT$, but I don’t see a Coleman-Mandula argument that a non-trivial such thing can’t exist.</p>
<p>What is most bizarre about this proposal is the way in which, by going to Euclidean space-time, you change what is a space-time and what is an internal symmetry. The argument (see <a href="https://www.math.columbia.edu/~woit/wordpress/?p=11865">a recent posting</a>) is that, formulated in Euclidean space, the 4d Euclidean symmetry is broken to 3d Euclidean symmetry by the very definition of the theory’s state space, and one of the 4d $SU(2)$s give an internal symmetry, not just analytic continuation of the Minkowski boost symmetry. There is still a lot about how this works I don’t understand, but I don’t see anything inconsistent, i.e. any obstruction to things working out this way. If the identification of the direction of the Higgs field with a choice of imaginary time direction makes sense, perhaps a full theory will give Higgs physics in some way observably different from the usual Standard Model.</p>
<p>One thing not discussed in this paper is gravity. Twistor geometry can also describe curved space-times and gravitational degrees of freedom, and since the beginning, there have been attempts to use it to get a quantum theory of gravity. Perhaps the new ideas described here, including especially the Euclidean point of view with its breaking of Euclidean rotational invariance, will indicate some new way forward for a twistor-based quantum gravity.</p>
<p><strong>Bonus (but related) links:</strong> For the last few months the CMSA at Harvard has been hosting a <a href="https://cmsa.fas.harvard.edu/literature-lecture-series/">Math-Science Literature Lecture Series</a> of talks. Many worth watching, but one in particular features Simon Donaldson discussing <em>The ADHM construction of Yang-Mills instantons</em> (video <a href="https://youtu.be/Ad1raKFJ_yY">here</a>, slides <a href="https://cmsa.fas.harvard.edu/wp-content/uploads/2020/05/harvard2020.pdf">here</a>). This discusses the Euclidean version of the twistor story, in the context it was used back in the late 1970s to relate solutions of the instanton equations to holomorphic bundles.</p>Tue, 11 Aug 2020 13:13:46 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110k50lVpcY5P331z8-xSOmNlJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oeMJ0nZwBmzxQuantization and Dirac Cohomology
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/344305131/15156" border=0 width="1" height="1" alt="Story 344305131" title="Story 344305131"> <p>For many years I’ve been fascinated by the topic of “Dirac cohomology” and its possible relations to various questions about quantization and quantum field theory. At first I was mainly trying to understand the relation to BRST, and wrote some things here on the blog about that. As time has gone on, my perspective on the subject has kept changing, and for a long time I’ve been wanting to write something here about these newer ideas. Last year I gave a talk at Dartmouth, explaining some of my point of view at the time. Over the last few months I’ve unfortunately yet again changed direction on where this is going. I’ll write about this new direction here in some detail next week, but in the meantime, have decided to make available the <a href="https://www.math.columbia.edu/~woit/qmdirac-dartmouth-printable.pdf">slides from the Dartmouth talk</a>, and a version of the document I was writing on <a href="http://www.math.columbia.edu/~woit/qmdirac.pdf"> Quantization and Dirac Cohomology</a>.</p>
<p>Some warnings:</p>
<ul>
<li>Best to ignore the comments at the end of the slides about applications to Poincaré group representations and BRST. Both of these applications require getting the Dirac cohomology machinery to work in cases of non-reductive Lie algebras. As far as Poincaré goes, I’ve recently come to the conclusion that doing things with the conformal group (which is reductive) is both more interesting and works better. I’ll write more about this next week. For BRST, there is a lot one can say, but I likely won’t get back to writing more about that for a while.</li>
<li>The Quantization and Dirac Cohomology document is kind of a mess. It’s an amalgam of various pieces written from different perspectives, and some lecture notes from a course on representation theory. Some day I hope to find the time for a massive rewrite from a new perspective, but maybe some people will find interesting what’s there now.</li>
</ul>Fri, 07 Aug 2020 22:23:40 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110kaHyybcBZXFTjq7PwYEWiNJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oZ8wOwuivxl1(Imaginary) Time Asymmetry
https://api.follow.it/track-rss-story-click/AaY2ldA110k7WzOhfWV-Q7V8HZmzB6MmJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oc3LNSFq_aSD
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/344000153/15156" border=0 width="1" height="1" alt="Story 344000153" title="Story 344000153"> <p>When people write down a list of axioms for quantum mechanics, they typically neglect to include a crucial one: positivity (or more generally, boundedness below) of the energy. This is equivalent to saying that something very different happens when you Fourier transform with respect to time versus with respect to space. If $\psi(t,x)$ is a wavefunction depending on time and space, and you Fourier transform with respect to both time and space<br />
$$\widetilde{\psi}(E,p)=\frac{1}{2\pi}\int_{-\infty}^\infty \int_{-\infty}^\infty \psi(t,x)e^{iEt}e^{-ipx}dtdx$$<br />
(the difference in sign for $E$ and $p$ is just a convention) a basic axiom of the the theory is that, while $\widetilde{\psi}(E,p)$ can be non-zero for all values of $p$, it must be zero for negative values of $E$.</p>
<p>This fundamental asymmetry in the theory also becomes very apparent if you want to “Wick rotate” the theory. This involves formulating the theory for complex time and exploiting holomorphicity in the time variable. One way to do this is to inverse Fourier transform $\widetilde{\psi}(E,p)$ in $E$, using a complex variable $z=t+i\tau$:<br />
$$\widehat{\psi}(z,p)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty \widetilde{\psi}(E,p)e^{-iEz} dE$$<br />
The exponential term in the integral will be<br />
$$e^{-iE(t+i\tau)}=e^{-iEt}e^{E\tau}$$<br />
which (since $E$ is non-negative) will only have good behavior for $\tau <0$, i.e. in the lower-half $z$-plane. Thinking of Wick rotation as involving analytic continuation of wave-functions from $z=t$ to $z=t+i\tau$, this will only work for $\tau <0$: there is a fundamental asymmetry in the theory for (imaginary) time.</p>
<p>If you decide to define a quantum theory starting with imaginary time and Wick rotating (analytically continuing) back to real, physical time at the end of a calculation, then you need to build in $\tau$ asymmetry from the beginning. One way this shows up in any formalism for doing this is in the necessity of introducing a $\tau$-refection operation into the definition of physical states, with the Osterwalder-Schrader positivity condition then needed in order to ensure unitarity of the the theory.</p>
<p>Why does one want to formulate the theory in imaginary time anyway? A standard answer to this question is that path integrals don’t actually make any sense in real time, but in imaginary time often become perfectly well-defined objects that can be thought of as expectation values in a statistical mechanical system. For a somewhat different answer, note that even for the simplest free particle theory, when you start calculating things like propagators you immediately run into integrals that involve integrating a function with a pole, for instance integrating over $E$ integrals with a term<br />
$$\frac{1}{E-\frac{p^2}{2m}}$$<br />
Every quantum mechanics and quantum field theory textbook has a discussion of what to do to make sense of such calculations, by defining the integral involved as a specific limit. The imaginary time formalism has the advantage of being based on integrals that are well-defined, with the ambiguities showing up only when one analytically continues to real time. Whether or not you use imaginary time methods, the real time objects getting computed are inherently not functions, but boundary values of holomorphic functions, defined of necessity as limits as one approaches the real axis.</p>
<p>A mathematical formalism for handling such objects is the theory of hyperfunctions. I’ve started writing up some notes about this, see <a href="http://www.math.columbia.edu/~woit/hyperfunctions.pdf">here</a>. As I find time, these should get significantly expanded. </p>
<p>One reason I’ve been interested in this is that I’ve never found a convincing explanation of how to deal with Euclidean spinor fields. Stay tuned, soon I’ll write something here about some ideas that come from thinking about that problem.</p>Thu, 06 Aug 2020 18:44:03 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110k7WzOhfWV-Q7V8HZmzB6MmJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oc3LNSFq_aSDYesterday’s Hype
https://api.follow.it/track-rss-story-click/AaY2ldA110m5HaCGpD945XawZ12B-dU6Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_obcXp7n6n2io
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/342492460/15156" border=0 width="1" height="1" alt="Story 342492460" title="Story 342492460"> <p>Every summer CERN runs a <a href="https://summerstudent.web.cern.ch/home">summer student programme</a>, designed to bring in a group of students to participate in scientific activities at CERN and provide lectures for them about the basics and latest state of the field of high energy physics. Because of the COVID situation, this summer they have not been able to bring students in, but are providing instructional lectures and Q and A’s. <a href="https://summerstudent.web.cern.ch/lectures-2020">This year’s sessions</a> are based on having students follow materials from last year’s lectures, followed by a Q and A to answer their questions.</p>
<p>One of the topics the students are presented is <a href="https://summerstudent.web.cern.ch/lectures-2019/what-is-string-theory">What is String Theory?</a>, and you can watch the 2019 video or <a href="https://indico.cern.ch/event/817571/attachments/1865556/3110483/CERN-SummerSchool-2019.pdf">look at the slides</a>. Timo Weigand’s presentation can be accurately described as pure, unadulterated hype, with not a hint of the existence of any significant problem with ideas presented. In the <a href="https://videos.cern.ch/record/2725650">Q and A yesterday</a>, Weigand did come up with a new piece of “evidence for string theory”: it “predicts” no continuous spin representations.</p>
<p>I can’t begin to understand why anyone thinks it’s all right for CERN to subject impressionable students to this kind of thing. Someone, not me, should be complaining to the organizers and to CERN management.</p>
<p>This is unfortunately now an all too common example of what passes for “Sci Comm” in much of the field of fundamental physics: endless repetition of old discredited arguments in favor of a failed theory, coupled with pretending not to know about what is wrong with these arguments. The field that was once one of the greatest examples of the power of the human mind and the strength of the scientific method has become something very different and quite dangerous: all-too-visible ammunition for those who want to make the case that scientists are as deluded and tribalistic as anyone else, so not to be trusted.</p>Sat, 01 Aug 2020 15:23:04 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110m5HaCGpD945XawZ12B-dU6Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_obcXp7n6n2ioWhat is "Spin”?
https://api.follow.it/track-rss-story-click/AaY2ldA110krGa9JXf4UpE6NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oUlRDoniyfxq
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/339933205/15156" border=0 width="1" height="1" alt="Story 339933205" title="Story 339933205"> <p>The explanation for the lack of blogging here the past month is mostly that I haven’t seen any news worth blogging about. It took only a little bit of self-control to not do things like make snarky comments about recent conferences on <a href="https://indico.cern.ch/event/929434/timetable/">string theory</a> and <a href="http://perimeterinstitute.ca/video-library/collection/quantum-gravity-2020">quantum gravity</a>.</p>
<p>Today I noticed a <a href="https://twitter.com/astroliz_/status/1286013599392108544">discussion on Twitter</a> of the perennial question about what “spin” means in quantum theory, with some of the tweets included this highly appropriate meme: <a href="https://www.math.columbia.edu/~woit/wordpress/wp-content/uploads/2020/07/spin.jpg"><img class="size-medium wp-image-11812 aligncenter" src="https://www.math.columbia.edu/~woit/wordpress/wp-content/uploads/2020/07/spin-289x300.jpg" alt="" width="289" height="300" srcset="https://www.math.columbia.edu/~woit/wordpress/wp-content/uploads/2020/07/spin-289x300.jpg 289w, https://www.math.columbia.edu/~woit/wordpress/wp-content/uploads/2020/07/spin.jpg 640w" sizes="(max-width: 289px) 100vw, 289px" /></a></p>
<p>I thought it might be worth while to make a stab at explaining what “spin” really is. For a much more detailed version, I wrote <a href="http://www.math.columbia.edu/~woit/QMbook">a book</a>. But this post is much shorter…</p>
<p>Picking a particular point and a particular direction (say the z-direction), the angular momentum $J_z$ is defined to be the “generator” of rotations about that point, around the z-axis. This means that when you do such a rotation by an angle $\theta$, for any observable (function of position and momentum) $F$<br />
$$\frac{dF}{d\theta}|_{\theta=0}=\{J_z, F\}$$<br />
where the bracket is the Poisson bracket (50/50 chance the sign here is correct). A short calculation shows<br />
$$J_z=r_xp_y-r_yp_x$$<br />
which is often given as the definition. $J_z$ is itself an observable, which you can say is the angular momentum about the z-axis of a point particle with x,y coordinates of its position and momentum given by $r_x,r_y,p_x,p_y$. In classical physics $J_z$ can take on any values.</p>
<p>In quantum mechanics, observables are operators acting on states, and $J_z$ becomes the operator $\widehat{J}_z$ which (with an additional factor of $-i$ to get unitary transformations) generates rotations on states. This means (using units such that $\hbar=1$)<br />
$$\frac{d}{d\theta}\ket{\psi(\theta)}=-i\widehat J_z \ket{\psi(\theta)}$$<br />
You can solve this differential equation and see that if you rotate a state by an angle $\theta$ about the $z$ axis, you get<br />
$$\ket{\psi(\theta)}=e^{-i{\widehat J}_z\theta}\ket{\psi(0)}$$<br />
States that are eigenvectors of ${\widehat J}_z$ are supposed to be the ones with a well-defined value of the classical observable $J_z$, given by the eigenvalue.</p>
<p>One finds experimentally that the observed values of $J_z$ are given by<br />
$$\frac{n}{2}$$<br />
Unlike the classical case, as expected this number is quantized (that’s why they call it quantum mechanics…), but the factor of $2$ is unexpected. Since a rotation by $2\pi$ should bring the state back to itself, one expects that<br />
$$e^{-iJ_z2\pi}=1$$<br />
so $J_z$ should be an integer. If one finds a state with $J_z=\frac{1}{2}$, rotating it by an angle $2\pi$ changes its sign. This is weird, but the sign of a state isn’t itself something you can measure.</p>
<p>Looking more closely at the operator $\widehat{J}_z$ for quantum systems, one finds that for some states it has exactly the same relation to position and momentum as in classical physics<br />
$$\widehat{J}_z=\widehat{r}_x\widehat{p}_y-\widehat{r}_y\widehat{p}_x$$<br />
When states are given by a wavefunction depending on spatial coordinates, one can show that this is just the expected action by infinitesimal rotation of the spatial coordinates. In this case rotation by $2\pi$ doesn’t change the state, and $J_z$ has integral (not half-integral) values.</p>
<p>For many quantum systems though, there is an extra term:<br />
$$\widehat{J}_z=\widehat{r}_x\widehat{p}_y-\widehat{r}_y\widehat{p}_x+\widehat{S}_z$$<br />
and it is this extra term $\widehat {S}_z$ that is the “spin” observable. When states are given by wavefunctions, what the equation above is telling you is that when you act on a state by a rotation, you get not just the expected induced action from the rotation on spatial coordinates, but also an extra term. A natural guess is that, as in the meme, a point particle is really a ball of some new stuff, with $\widehat {S}_z$ the effective extra term caused by the positions and momenta of the new stuff.</p>
<p>For an elementary particle such as an electron, experimentally one finds that $\widehat S_z$ has eigenvalues $\pm 1/2$, which explains why one sees half-integral quantization. As the meme says, there is no viable physical model of rotating stuff that would give this result. Something very different is going on.</p>
<p>So far I’ve stuck to talking about rotations about the z-axis, but one also should consider rotations about other axes. The problem is that more sophisticated mathematics is needed, since the generators of rotations around different axes don’t commute (doing the rotations in the opposite order gives a different result). The mathematics needed is that of the representation theory of the rotation group $SO(3)$ and its double-cover $SU(2)$. From this representation theory one learns that the only consistent possibilities are given by putting together copies of a “spin n/2” representation for $n=0,1,2,\cdots$. These are $n+1$-dimensional vector spaces, on which $\widehat{S}_z$ acts with eigenvalues<br />
$$\frac{-n}{2}, \frac{-n +2}{2},\cdots,\frac{n-2}{2},\frac{n}{2}$$<br />
The case $n=0$ is that of $\widehat{S}_z=0$, and the simplest non-trivial case is the $n=1$ case which gives $\widehat{S}_z$ for the electron.</p>
<p>So, the “spin 1/2” characteristic of the electron is something completely new, unrelated to anything in classical mechanics. If you describe the electron by a wavefunction, it will take values not in the complex numbers, but in pairs of complex numbers, with rotations acting on the pairs by the spin-1/2 representation (also known as the “spinor” representation). Besides the non-classical physical behavior, the geometry is also non-classical, with the spinor representation something that cannot be described by the usual formalism of vectors and tensors.</p>
<p>Another reason I haven’t been writing much on the blog this past month is that I’ve been working on writing up something about twistors. I’ll write about twistors in detail here when this is done, but one thing they do is give a picture of space-time geometry in which spinors are fundamental, not vectors. A fundamental idea of twistor theory is that a point in space-time is a complex two-plane inside complex four-space. In twistor theory the answer to the question of where the spinor degree of freedom at a point comes from is tautological: the two complex dimensional spinor degree of freedom at a point IS the point.</p>
<p>Bonus link for those who have gotten this far. A <a href="https://indico.cern.ch/event/932053/contributions/3917549/attachments/2065716/3466659/Personnel-Jun2020-FG.pdf">presentation by CERN director Fabiola Gianotti</a>, which comes off a bit differently than news reports saying CERN is going ahead with FCC. On page 5</p>
<blockquote>
<ul>
<li>Strategy gives a direction for future collider(s) at CERN (FCC). Prudent: feasibility study first.</li>
<li>Intensified accelerator R&D to prepare alternatives if FCC feasibility study fails.</li>
<li>No consensus in European community on which type of Higgs factory(linear or circular).</li>
</ul>
</blockquote>
<p>Page 9 lists three “first priorities” for the feasibility study:</p>
<blockquote>
<ul>
<li>find funds for the tunnel</li>
<li>[Be sure] no show-stoppers for ~100 km tunnel in Geneva region</li>
<li> magnet technology [are the FCC-hh magnets feasible?]; how to minimise environmental impact</li>
</ul>
</blockquote>Thu, 23 Jul 2020 20:23:01 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110krGa9JXf4UpE6NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oUlRDoniyfxqHEP News
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/329231973/15156" border=0 width="1" height="1" alt="Story 329231973" title="Story 329231973"> <p>The CERN Council is meeting today and tomorrow, and should approve the <a href="https://www.math.columbia.edu/~woit/wordpress/?p=10768">long-awaited 2020 update of the European Strategy for Particle Physics</a>. There will be a <a href="https://webcast.web.cern.ch/event/i924500">live webcast of the open part of the Council meeting on Friday</a>.</p>
<p>My understanding is that the most difficult and contentious decision, that of how and whether to go forward with a new energy frontier collider, has been put off until 2026, when there will be a new update. In the meantime, design work will emphasize studies for the leading contender: a new large circular electron-positron machine. Studies of a linear collider design (CLIC) will continue at a reduced rate. New work will begin on the possibility of a muon collider, as well as other advanced accelerator technologies that might someday be usable.</p>
<p>There will be some move in the direction of the US program, which has abandoned the energy frontier, including more participation in the US and Japanese neutrino programs. A “scientific diversity program”, Physics Beyond Colliders, will receive new support. This program will try and come up with new experiments that don’t require a new energy frontier machine. For more about it, see <a href="https://arxiv.org/abs/1902.00260">this CERN report</a> and <a href="https://www.nature.com/articles/s41567-020-0838-4">this article in Nature</a>.</p>
<p>In other news from CERN, work on the LHC should start resuming this summer, with the ongoing LS2 extended by a few months because of the COVID shutdown, so beams back in the LHC late next summer. There likely will be no significant new data coming from the LHC during 2021. The extended shutdown may provide the time for magnet quench training needed to bring the machine to its design energy of 7 TeV/beam.</p>Thu, 18 Jun 2020 18:23:43 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110mPOWymSVP-g7V8HZmzB6MmJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_ob_yuN8lQAygHEP Theory Job Situation
https://api.follow.it/track-rss-story-click/AaY2ldA110k42aIdweBZdauOb4R2Z5gEJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oQiKgxjzG8m2
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/328903368/15156" border=0 width="1" height="1" alt="Story 328903368" title="Story 328903368"> <p>Way back in the 1980s and 1990s I was, for obvious personal reasons, paying close attention to the job situation for young HEP theorists. They were not good at all: way more talented young theorists than jobs, many if not most Ph.D.s who wanted to continue in the field unhappily spending many years in various postdocs before giving up and doing something else. By the later part of the 1990s I had found a satisfying permanent position in math, so this problem seemed much less interesting. When I was writing “Not Even Wrong” I did spend quite a bit of time gathering numbers to try and quantify the problem, and wrote about them in the book. </p>
<p>Since then I haven’t paid a lot of attention to the HEP theory job situation, hoped that it might have gotten a bit better as the wave of physicists hired during the 1960s hit retirement age, opening up some permanent positions. Today someone sent me a <a href="https://www.facebook.com/angi.smay/posts/10157132547853715">link to a personal statement on Facebook</a> (sorry, but you need to login to a Facebook account to see this) from a young theorist (<a href="https://www.mpp.mpg.de/en/news/news/detail/angnis-schmidt-may-leitet-neue-forschungsgruppe/">Angnis Schmidt-May</a>) who has recently decided to leave the field, for reasons that she explains. These include:</p>
<blockquote><p> We are put in competition with each other from day one, and only very few of us will be given prestigious positions in the end. Most of us never see a permanent contract, keep jumping from place to place and eventually need to find a second career after having sacrificed our entire 20s and 30s to academia. After having made it through the worst part of this and more or less securing my career, it still made me sick to see young physicists entering this spiral. I felt terrible about encouraging them to continue on this path because it is impossible to tell who will make it in the end and who will end up miserable with regrets…</p>
<p>Science itself is severely suffering from the poor working conditions and lack of genuine career prospects. I personally found it extremely hard to focus on the science while constantly being worried about the duration and location of my next contract. #PublishOrPerish. Interactions with and among colleagues are often dominated by the drive to “show off”. Very few people focus on removing misunderstandings or ask honest questions in order to fill their knowledge gaps. The general atmosphere is dominated by doubt instead of trust. We constantly need to outshine our peers. Better to demonstrate superficial knowledge of broad subjects than to focus on the details of a deep problem. Your next result needs to be “groundbreaking”, otherwise you’re out of a job. But produce it and have it published at least one year before your contract ends because that’s when you need to apply for a new one. Science has become a show…</p>
<p>I see absolutely no chance that any of the above will change any time soon.
</p></blockquote>
<p>She also makes important points about the personal cost of this system:</p>
<blockquote><p>During the last 10 years, I was forced to constantly move around, losing contact to people who meant a lot to me and not being able to establish new lasting relationships.</p></blockquote>
<p>Sadly, it seems pretty much nothing at all has changed in the last 30-40 years, and I continue to believe this is one reason the subject has been intellectually stagnant during this period. About the only positive suggestion I can make for anyone who wants to try and do anything about this is to take a look at the analogous job situation in mathematics. My knowledge of this is mostly anecdotal, but my impression is that while, like most academic fields, the career path for a new math Ph.D. is not easy, the situation is not at all as bad as the one in HEP theory described above.</p>
<p><strong>Completely Off-Topic</strong>: Xenon1T has reported <a href="https://science.purdue.edu/xenon1t/?p=1474">new results</a> today. This seems to me unlikely to be new physics (extraordinary claims require extraordinary evidence), so if you want to follow this story, you should be<a href="http://resonaances.blogspot.com/2020/06/hail-xenon-excess.html"> consulting Jester</a>, not me.</p>Wed, 17 Jun 2020 15:13:16 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110k42aIdweBZdauOb4R2Z5gEJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oQiKgxjzG8m2Feynman Lectures on the Strong Interactions
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/328332470/15156" border=0 width="1" height="1" alt="Story 328332470" title="Story 328332470"> <p>Available at the arXiv this evening is something quite fascinating. Jim Cline has posted <a href="https://arxiv.org/abs/2006.08594">course notes from Feynman’s last course, given in 1987-88 on QCD</a>. There are also some audio files of a few of the lectures available <a href="http://www.physics.mcgill.ca/~jcline/Feynman/">here</a>. The course was interrupted by Feynman’s final illness, with the last lecture given just a couple weeks before Feynman’s death in February of 1988. There’s an introduction to the notes by Cline in which he explains more about the course and how the notes came to be.</p>
<p>The course was given over thirty years ago, and many textbooks have appeared since then, but it seems to me this has held up well as an excellent place for a student to go to learn the subject.</p>Tue, 16 Jun 2020 01:25:17 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110m1GNfwD_Zt5nawZ12B-dU6Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_odgtjsj8HwyBAn Advertisement for Representation Theory
https://api.follow.it/track-rss-story-click/AaY2ldA110m8cq_0nlSidh4qXtCBZOA-Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oZTrCGzyyDgO
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/326546127/15156" border=0 width="1" height="1" alt="Story 326546127" title="Story 326546127"> <p>There’s a new article at Quanta today promoting representation theory, Kevin Hartnett’s <a href="https://www.quantamagazine.org/the-useless-perspective-that-transformed-mathematics-20200609/">The ‘Useless’ Perspective that Transformed Mathematics</a>. Representation theory is a central, unifying theme in modern mathematics, one that deserves a lot more attention than it usually gets, with undergraduate math majors often not exposed to the subject at all. My <a href="https://www.math.columbia.edu/~woit/QMbook/">book on quantum mechanics</a> is very much based on the idea that the subject is best understood in terms of representation theory. Unfortunately, physics students typically get even less exposure to representation theory than math students.</p>
<p>While I think the article is a great idea, and well-worth reading, I do have two quibbles, one minor and one major. The minor quibble is that one example given of a group, the real numbers with multiplication, is not quite right: you need to remove the element 0, since it has no inverse. If the group law is the additive one, then the real number line with nothing removed truly is a group.</p>
<p>The major quibble is with the theme of the article that a group representation can be thought of as a simplification of something more complicated, the group itself. This is a good way of thinking about one aspect of the use of representation theory in number theory, where representations provide a tractable way to get at the much more complicated structure of the absolute Galois group of a number field. The <a href="https://vimeo.com/148780725">talk by Geordie Williamson</a> linked to in the article (slides <a href="http://people.mpim-bonn.mpg.de/geordie/BMS.pdf">here</a>) explains this well, but Williamson also gets right the more general context, where the group can be easy to understand, the representations complicated. For a simple example of this, in the case of the circle group $S^1$ the group is very easy to understand, its representation theory (the theory of Fourier series) is much more complicated (and much more interesting).</p>
<p>As Williamson explains, a good way to think about what is going on is that representation theory does simplify something by linearizing it, but it’s not the group, it’s a group action. When people talk about the importance of the study of “symmetry” in mathematics, physics, and elsewhere, they often make the mistake of only paying attention to the symmetry groups. The structure you actually have is not just a group (the abstract “symmetries”), but an action of that group on some other object, the thing that has symmetries. When you talk about “rotational symmetry” you have a rotation group, but also something else: the thing that is getting rotated. Representation theory is the linearization of this situation, often achieved by going from the group action on an object to the corresponding group action on some version of functions on the object. Once linearized, the group action becomes a problem in linear algebra, with the group elements represented as matrices, which act on the vectors of the linearization.</p>
<p>To further add to the confusion, “symmetry” is often described in popular accounts as meaning “invariance”. In typical examples given, “invariance” just means that you have a group action, since the group is taking elements of the set to other elements of the set (e.g. rotations not of an arbitrary object, but of a sphere). In representation theory, you have a different notion of invariance. For instance, for the representation of rotations on functions on the sphere, the constant functions are a one-dimensional invariant subspace, giving a trivial representation. But, there are lots of more interesting invariant subspaces of higher dimensions. These are the irreducible representations on the sets of spherical harmonics.</p>Tue, 09 Jun 2020 21:23:18 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110m8cq_0nlSidh4qXtCBZOA-Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oZTrCGzyyDgOThe Week’s Anti-Hype
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<img src="https://api.follow.it/rssubscribers/rss_show_story_count/322811887/15156" border=0 width="1" height="1" alt="Story 322811887" title="Story 322811887"> <p>I never thought I would see this happen: a university PR department correcting media hype about its research. You might have noticed <a href="https://www.math.columbia.edu/~woit/wordpress/?p=11747#comment-236286">this comment here a week ago</a>, about a flurry of media hype about neutrinos and parallel universes. A <a href="https://www.cnn.com/2020/05/27/world/neutrino-research-anita-scn-trnd/index.html">new CNN story</a> does a good job of explaining where the nonsense came from. The main offender was <a href="https://www.newscientist.com/article/mg24532770-400-we-may-have-spotted-a-parallel-universe-going-backwards-in-time/">New Scientist</a>, which got the parallel universe business somehow from Neil Turok and from <a href="https://arxiv.org/abs/1803.11554">here</a>.</p>
<p>The ANITA scientists and their institution’s PR people were not exactly blameless, having participated in a 2018 publicity campaign to promote the idea that they had discovered not a parallel universe, but supersymmetry. They reported an observation <a href="https://arxiv.org/abs/1803.05088">here</a>, which led to lots of dubious speculative theory papers, such as <a href="https://arxiv.org/abs/1809.09615">this one about staus</a>. The University of Hawaii in December 2018 put out a press release announcing that <a href="https://www.hawaii.edu/news/2018/12/10/antarctica-physics-discovery/">UH professor’s Antarctica discovery may herald new model of physics</a>. One can find all sorts of stories from this period about how this was evidence for supersymmetry, see for instance <a href="http://nautil.us/issue/65/in-plain-sight/have-balloons-and-ice-broken-the-standard-model">here</a>, or <a href="https://www.livescience.com/63692-standard-model-broken-supersymmetry-new-physics.html">here</a>.</p>
<p>It’s great to see that the University of Hawaii has tried to do something at least about the latest “parallel universe” nonsense, putting out last week a press release entitled <a href="https://www.hawaii.edu/news/2020/05/21/media-incorrectly-connects-uh-research/">Media incorrectly connects UH research to parallel universe theory</a>. CNN quotes a statement from NASA (I haven’t seen a public source for this), which includes:</p>
<blockquote><p>Tabloids have misleadingly connected NASA and Gorham’s experimental work, which identified some anomalies in the data, to a theory proposed by outside physicists not connected to the work. Gorham believes there are more plausible, easier explanations to the anomalies.</p></blockquote>
<p>The public understanding of fundamental physics research and the credibility of the subject have suffered a huge amount of damage over the past few decades, due to the overwhelming amount of misleading, self-serving BS about parallel universes and failed speculative ideas put out by physicists, university PR departments and the journalists who mistakenly take them seriously. I hope this latest is the beginning of a new trend of people in all these categories starting to fight hype, not spread it.</p>Wed, 27 May 2020 16:47:59 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110l6_QHAVls7jB4qXtCBZOA-Jrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_ofYclvR_ZDozOral Histories
https://api.follow.it/track-rss-story-click/AaY2ldA110m2nYP35KVnCU6NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oawDfUyaBUcH
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/322031975/15156" border=0 width="1" height="1" alt="Story 322031975" title="Story 322031975"> <p>I recently ran across <a href="https://www.aip.org/history-programs/niels-bohr-library/oral-histories/44286">a recent interview with Mary K. Gaillard</a>, which encouraged me to look again at the <a href="https://www.aip.org/history-programs/niels-bohr-library/oral-histories">AIP’s oral histories site</a>. For a review of her autobiographical book, see <a href="https://www.math.columbia.edu/~woit/wordpress/?p=7938">here</a>.</p>
<p>She has the following comments on the current state of HEP theory:</p>
<blockquote><p><strong>Zierler:</strong></p>
<p>What do you see as the future of theoretical physics? Where is the field headed?</p>
<p><strong>Gaillard:</strong></p>
<p>Well, I think it’s headed towards insanity [laugh] by itself. I mean, no, if we don’t have experiments, people can let their imaginations run wild, and invent anything without it being verified or disproven. So I think it—I mean, if we want to understand more about what happens at higher energies, we have to have higher energy colliders. I don’t think—well, cosmology is tied to particle physics, and that’s probably something from—I mean, there is a lot of data coming from cosmology. And there is some data that will be coming from very low energy precision physics. But I don’t think that theory by itself—it needs to be kept in line by [laugh] experiments.</p>
<p>…</p>
<p><strong>Zierler:</strong></p>
<p>And so what advice do you have sort of globally for people entering the field in terms of the kinds of things they should study, and the way they should study those things?</p>
<p><strong>Gaillard:</strong></p>
<p>That’s a [laugh]—actually, I often advise people to go into astro-particle physics just because I think that it has more promise of getting data because I don’t—I mean, I strongly believe you can’t go forward without good data, and unless—well, of course, if they do have another generation of colliders, that would be great. I just don’t know if that’s going to happen…</p></blockquote>
<p>Another very recent interview I found interesting was <a href="https://www.aip.org/history-programs/niels-bohr-library/oral-histories/44270">that of Vipul Periwal</a>. Periwal arrived as a Ph.D. student at Princeton around the time I was on my way out, starting his career right about when string theory hit in late 1984. He worked as a string theorist for quite a few years, ending up in a tenure-track faculty position at Princeton, but then left the HEP field completely, starting a new career in biology. Here are some extracts from his interview:</p>
<blockquote><p><strong>Zierler:</strong></p>
<p>And what was David [Gross]’s research at this point? What was he pursuing?</p>
<p><strong>Periwal:</strong></p>
<p>String theory. He was just 100 percent in string theory. Right? They just did the heterotic string, and so everyone was — every seminar at Princeton at that time was all string theory. It was all string theory. Curt was working on it, David was working on it. Edward was working on it. Larry Yaffe was probably the only person — no, two people, Larry Yaffe and Ian Affleck were not doing string theory. Not that they couldn’t, but they just would not do it.</p>
<p>…</p>
<p><strong>Zierler:</strong></p>
<p>So you mean, despite at this point all of the work on string theory, there were still existential questions about what string theory was, that remained to be answered?</p>
<p><strong>Periwal:</strong></p>
<p>There still are.</p>
<p><strong>Zierler:</strong></p>
<p>Yeah.</p>
<p><strong>Periwal:</strong></p>
<p>No one has ever figured out what is string theory. I mean, if you go ask all the eminent string theorists, none of them can answer for you this one simple question. Can you show me a consistent string theory, where supersymmetry is broken?</p>
<p>…</p>
<p><strong>Zierler:</strong></p>
<p>Was it good for your research? Was it a good time for you [<em>his postdoc at the IAS</em>]?</p>
<p><strong>Periwal:</strong></p>
<p>I don’t think I did particularly interesting research. I did — I mean, I did okay, but I’m not particularly proud of anything I did there, except for one little paper I wrote, in which [laughs] — see, this is called the contrarian part — is I showed — people were very excited about the large N limit, so I took this toy model, and I showed that in the large N limit, it actually produced something nonanalytic, as in like, you could not, in any order of 1 over an expansions, ever see what the answer was that was exact at N equals infinity. So, in other words, it was to me a cautionary tale. Like, you think you’re doing large N and then getting an intuition for finite N. But here’s this very simple model where you can do the calculation exactly, and you can do all your 1 over N expansion as far as you want, and it’ll never tell you [laughs] about what’s going to happen at N equals infinity. But you know, it’s a — at this point, string theory was already at that time pretty much a sociological thing.</p>
<p><strong>Zierler:</strong></p>
<p>What do you mean “sociological”?</p>
<p><strong>Periwal:</strong></p>
<p>So, it’s something that was borne home to me gradually, that there’s no experimental proof. Like, are you a good physicist or a bad physicist? Who’s going to tell? How do you know? Right?</p>
<p><strong>Zierler:</strong></p>
<p>Yeah.</p>
<p><strong>Periwal:</strong></p>
<p>I mean, I’d go and give a talk somewhere, and I remember this very clearly. I went and gave a talk at SUNY Stony Brook, what’s now called, I guess, Stony Brook University. And at the end of the talk, I was talking to one of the faculty there who’d invited me. And he said, “So, what does XYZ think of this work?” And I was just taken aback. I was like, wait, you’re a physicist. I’m a physicist. Why do we need to know what XYZ thinks of this?</p>
<p><strong>Zierler:</strong></p>
<p>Yeah.</p>
<p><strong>Periwal:</strong></p>
<p>Right? That’s what I mean by sociology.</p>
<p><strong>Zierler:</strong></p>
<p>I see. It’s as much about what a certain group of peers thinks about the theory.</p>
<p><strong>Periwal:</strong></p>
<p>Yeah, and this really perturbed me. As far as I was concerned, after the string perturbation theory diverges thing, I was not interested in doing perturbative calculations. So, what the solution was that people did was: okay, we’ll work on various supersymmetric theories where there is no higher contribution, and under the assumption that there is supersymmetry, you can use holomorphicity to deduce things from the structure of the fact that there’s so much supersymmetry. And this really bothered me, as in okay, there’s this really amazingly beautiful structure, and lots of very pretty mathematical results that are coming out — mathematical results that are suggested by these correlations. But I just don’t get — as a physicist, I don’t to want to have to worry about, “What does XYZ think about what I’m doing?”</p>
<p><strong>Zierler:</strong></p>
<p>Yeah, because you’re pursuing a truth, and it’s either true or it’s not. It doesn’t really matter what other people think about it.</p>
<p><strong>Periwal:</strong></p>
<p>Right. I really don’t care. I mean, no matter how much I respect — and I do — Edward, or David, or whoever, I really don’t need to know what they think about my work. Right? I just — anyhow —</p>
<p><strong>Zierler:</strong></p>
<p>How does that attitude serve you in an academic setting, though? Right?</p>
<p><strong>Periwal:</strong></p>
<p>It doesn’t.</p>
<p><strong>Zierler:</strong></p>
<p>How does that attitude affect you in terms of tenure considerations and things like that?</p>
<p><strong>Periwal:</strong></p>
<p>Yeah, so when I was — no, so I actually — I mean, when I was — well, I have no — I’m really stupid sociologically, as in, I have no instinct for self-preservation. So, I could see I had role models in front of me of how people with tenure…</p>
<p><strong>Zierler:</strong></p>
<p>Succeeded.</p>
<p><strong>Periwal:</strong></p>
<p>…succeed, not just getting tenure at Princeton, but getting tenure at very good places after Princeton, too. And I paid zero attention to all this. So, while I was at Princeton, I tried doing some lattice gauge theory.</p></blockquote>
<p>With this attitude, it’s not surprising that in Periwal didn’t get tenure at Princeton. He didn’t soon get job offers elsewhere in HEP theory, and decided in 2001 better to try another field than keep going in the one he was in. The interview ends with:</p>
<blockquote><p>
<strong>Zierler:</strong></p>
<p>Alright. So, really, the last question. What does the big breakthrough moment look like for you? How would you conceptualize this in terms of putting all of this together? What does that big breakthrough look like?</p>
<p><strong>Periwal:</strong></p>
<p>If I could make a prediction that was clinically testable, that would make me very happy.</p>
<p><strong>Zierler:</strong></p>
<p>Do you think you’ll get there? It’s the thing that motivates you.</p>
<p><strong>Periwal:</strong></p>
<p>Yeah. I want — you know, I said this once. We had someone visiting when I was managing the physics seminar at Princeton once, as an assistant professor. So, this guy asked me, “So, Vipul, what are you working on?” And I was very jaundiced at that time about making a prediction. So, I said, “Well, lattice gauge theory,” which, you know, nobody at Princeton did lattice gauge theory. You were all supposed to be doing string theory. I said, “Yeah, I want a number before I die.” [laughs] People are looking at me like, “What kind of lunatic is this?” But you know, a number. That would be nice.</p></blockquote>
<p>Looking through the old interviews, I found one of very personal interest, that of <a href="https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4812">Gerald Pearson</a>, who worked with my grandfather Gaylon Ford at Bell Labs. Some of his stories mentioned work with my grandfather (whose main expertise was in the design and construction of vacuum tubes) at Bell Labs during the 1930s. During this period both studied at Columbia, where my grandfather got a master’s degree in physics.</p>
<blockquote><p><strong>Pearson:</strong></p>
<p>Gaylon Ford worked with Johnson. When Kelly was head of the tube department, he worked in that area. And then they had a big shakeup after which the job was no longer available. Much against his desires, he came over to work with us.</p>
<p>…</p>
<p><strong>Hoddeson:</strong></p>
<p>In 1938 you were moved over from Johnson’s group into Becker’s. In fact, you and Sears seem to have changed places.</p>
<p><strong>Pearson:</strong></p>
<p>Before that took place, I remember Johnson called me into his office one day and he wanted to know if I would like to work on… well, Buckley had sent a memorandum asking for temperature regulators for buried cable. Johnson wanted to know if I would like to work in this area. Of course, no one likes to change their jobs but I said, “Fine” and we agreed that I would spend a portion of my time on this problem and that’s where thermistors came from. This continued on and it was very successful. Then it was decided that the work fit in better with Becker’s area than it did with Johnson’s. And, well you asked me about Ford. He was the one who was brought from the tube shop to work on this. And then he later went to work on something else.</p>
<p><strong>Hoddeson:</strong></p>
<p>Let’s see if we can date that time. Ford wasn’t working with you yet. Ford is here with you in 1934. But this move didn’t take place until ’38.</p>
<p><strong>Pearson:</strong></p>
<p>Yes, that’s what I was saying. He first came over to work on change of resistance with temperature. And he was working with a sulfide compound. And then, let’s see, what happened to him. He went someplace else and Johnson called me into his office and asked me if I would like to carry on Ford’s work and we agreed that I should do it part time and still work on noise. But I said I didn’t want to work with sulphur, it smelled too bad. I said if I work in that area, I’m going to use some other materials. So I made a study of that. First I worked on boron and then on a combination of oxides. A lot of my patents are on such materials and devices. These devices are still used today in the buried cable system as volume regulators.</p></blockquote>Sun, 24 May 2020 16:16:02 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110m2nYP35KVnCU6NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oawDfUyaBUcHFinal Fourier Analysis Notes
https://api.follow.it/track-rss-story-click/AaY2ldA110kLAh2mu4-fjk6NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oRsoESdoqBRV
<img src="https://api.follow.it/rssubscribers/rss_show_story_count/320544775/15156" border=0 width="1" height="1" alt="Story 320544775" title="Story 320544775"> <p>Our semester here at Columbia is finally over, and I’ve put the lecture notes on Fourier analysis that I wrote up in one document <a href="https://www.math.columbia.edu/~woit/fourier-analysis/fouriernotes.pdf">here</a>. A <a href="https://www.math.columbia.edu/~woit/wordpress/?p=11683">previous blog posting</a> explained the origin of the notes: they cover the second half of this semester’s course, from the point at which the course became an online course due to the COVID-19 situation.</p>
<p>Not much blogging going on here, mainly since everyone staying home seems to have kept news of much interest to a minimum. </p>Tue, 19 May 2020 03:18:18 GMThttps://api.follow.it/track-rss-story-click/AaY2ldA110kLAh2mu4-fjk6NAX1_5kxdJrrc4NnA57E12CUZTVS_YALR39lnjt6QowTKTCcIdhdI24M9rPM_oRsoESdoqBRV