Short Math Links

Some links of mathematical interest that I’ve recently run across:

  • The life and work of Alexander Grothendieck is one of the great stories of modern mathematics. Winfried Scharlau’s first volume of a biography of Grothendieck, covering the years up to 1948 is now available in English, see here. The third volume, covering Grothendieck’s life after 1970 is only available in German, see here. Leila Schneps is writing a second volume, covering his life and mathematics during the height of his career, from 1948-1970, with chapters appearing as they are written on this page. She is now up to 1952.

    The same page contains links to various wonderful articles about Grothendieck’s mathematics, many by mathematicians who interacted with Grothendieck during his period of greatest mathematical activity.

  • Cédric Villani joins other Fields Medalists with blogs, see here. Villani has just published in France a memoir called Théorème Vivant, a mix of autobiography and description of a collaboration on a mathematics problem. More about the book here, here and here, with a video here.
  • Many of the talks given at this summer’s String-Math 2012 conference are now available as slides or video, see here.
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Simons Foundation and the arXiv

Via the Quantum Pontiff, news that the Simons Foundation will be providing up to \$300,000 in financial support to the arXiv for each of the next five year. Last year, the arXiv announced a \$60K planning grant from Simons. Now the Foundation is stepping in with a much bigger contributions, for details see here.

This kind of support for open-access publication is an excellent way for Simons to use its resources. Perhaps this will be the beginning of a larger effort to buy back control of the math and physics literature from commercial publishers and set up a viable model for making this literature available to all going forward. This may be an expensive undertaking, but Simons (and other math/physics-friendly financiers) have resources on the scale necessary to do this.

Posted in Uncategorized | 22 Comments

Linde on Inflation and the Multiverse

Andrei Linde is one of Yuri Milner’s $3 million dollar men, best known for his “chaotic inflation” version of inflationary theory, as well as being one of the main proponents of anthropic multiverse mania. There’s a long piece based on a conversation with him up now at the Edge web-site.

Much of the piece is just a retread of the usual heavily-promoted ideology of the past 30 years of fundamental physics research: we must have SUSY, so must have supergravity, so must have string theory, so must have the landscape, so must have a multiverse where we can’t predict anything about anything, thus finally achieving success. Linde claims he pretty much had this picture 30 years ago back in 1982, with the string theory component in 1986, with others coming around to his point of view in the last 10 years, partly because of the KKLT work he was co-author of in 2003.

Besides the tired Stanford pseudo-scientific ideology, there’s also a wonderful history of the subject of inflation, from a Moscow point of view, which is rather different than the Western, Alan Guth-oriented, point of view from which the story is often told. Linde’s description of Hawking’s visit to Moscow is not to be missed:

The next morning after I gave a talk at this conference, I found myself at the talk… oh, my God, this is going to be a funny story… I found myself at the talk by Stephen Hawking at Sternberg Institute of Astronomy in Moscow University. I came there by chance because I have heard from somebody that Hawking was giving a talk there. And they asked me to translate. I was surprised. Okay, I will do it. Usually at that time Stephen would give his talk well prepared, which means his student would deliver the talk, and Stephen from time to time would say something, and then the student would stop, and change his presentation and do something else. So Stephen Hawking would correct and guide the student. But in this case they were completely unprepared; the talk was about inflation. The talk was about the impossibility to improve Alan Guth’s inflationary theory.

So they were unprepared, they just finished their own paper on it. As a result, Stephen would say one word, his student would say one word, and then they waited until Stephen would say another word, and I would translate this word. And all of these people in the auditorium, the best scientists in Russia, were waiting, and asking what is going on, what it is all about? So I decided let’s just do it, because I knew what it’s all about. So Stephen would say one word, the student would say one word, and then after that I would talk for five minutes, explaining what they were trying to say.

For about a half an hour we were talking this way and explained to everyone why it was impossible to improve Alan Guth’s inflationary model, what are the problems with it. And then Stephen said something, and his students said: “Andrei Linde recently proposed a way to overcome this difficulty.” I didn’t expect it, and I happily translated it into Russian. And then Stephen said: “But this suggestion is wrong.” And I translated it… For half an hour I was translating what Stephen said, explaining in great detail why what I’m doing is totally wrong. And it was all happening in front of the best physicists in Moscow, and my future in physics depended on them. I’ve never been in a more embarrassing situation in my life.

Then the talk was over, and I said: “I translated, but I disagree,” and I explained why. And then I told Stephen: “Would you like me to explain it to you in greater detail?” and he said, “Yeah.” And then he rode out from this place, and we found some room, and for about two or three hours all the people in Sternberg Institute were in panic because the famous British scientist just disappeared, nobody knew where to.

During that time, I was near the blackboard, explaining what was going on there. From time to time, Stephen would say something, and his student would translate: “But you did not say that before.” Then I would continue, and Stephen would again say something, and his student would say again the same words: “But you did not say that before.” And after we finished, I jumped into his car and they brought me to their hotel. We continued the discussion, which ended by him showing me photographs of his family, and we became friends. He later invited me to a conference in Cambridge, in England, which was specifically dedicated to inflationary theory. So that’s how it all started. It was pretty dramatic.

Addressing the question of “what evidence is there for any of this?”, here’s what Linde has to say:

Usually I answer in the following way: If we do not have this picture, then we cannot explain many strange coincidences, which occur around us. Like why vacuum energy is so immensely small, incredibly small. Well, that is because we have many different vacua, and in those vacua where vacuum energy is too large, galaxies cannot form. In those vacua, where energy density is negative, the universe rapidly collapses, and in our vacuum the energy density is just right, and that is why we live here. That’s the anthropic principle. But you cannot use anthropic principle if you do not have many possibilities to choose from. That’s why multiverse is so desirable, and that’s what I consider experimental evidence in favor of multiverse.

So, the main experimental evidence for the multiverse is that an anthropic argument works. Some might not find this completely convincing.

About 5 years ago, the field of “string cosmology” was quite active, with even a graduate-level textbook appearing. My impression (contrast the tone of this review, with those of 5 years earlier) is that there’s much less interest in this area during recent years, since it became obvious that no predictions about physics were going to emerge from it. Late this year or early next year the Planck experiment will finally report what it sees in the CMB. I’m curious to know whether Linde and other string cosmology proponents have any predictions for what Planck will tell us.

Update: The Annenberg Foundation funds Annenberg Learner, a site designed to provide information to high school teachers. Their Physics course includes a unit from Stanford’s Shamit Kachru, which is pretty much pure hype, unadulterated by any skepticism that string theory might not be the way the world works. Physicists may have lost interest in string cosmology, seeing it as a failure, but that’s no reason not to teach it to high school students…

Update: Historian of science Helge Kragh has a new article Criteria of Science, Cosmology, and Lessons of History discussing the Multiverse, philosophy of science, and the dubious use of historical analogies. About the Multiverse: “it explains a lot but predicts almost nothing”.

Update: Tonight’s arXiv listings include The Top 10500 Reasons Not to Believe in the Landscape from Tom Banks, which starts off with:

The String Landscape is a fantasy.

He goes on to claim co-credit with Linde for the anthropic explanation for the value of the CC (in inflationary models), as well as to argue that it is wrong:

Linde and I were the first to suggest an anthropic explanation for the value of the c.c. based on inflationary models [2], but within the context of the string landscape, or most any contemporary view of global EI [i.e., Eternal Inflation], I don’t think anthropic reasoning leads to good phenomenology.

Posted in Multiverse Mania | 38 Comments

Bill Thurston, 1946-2012

Bill Thurston passed away yesterday, at the age of 65, after a battle with melanoma. Thurston was for many years the dominant figure in the study of 3 dimensional topology and geometry, winning a Fields medal for this work in 1982. His “Geometrization Conjecture” classifying the topology of 3 manifolds was finally proved by Perelman as part of his work on the Poincaré Conjecture.

For an exposition of some of his work, see The Geometry and Topology of Three-manifolds, which exists as a set of unpublished notes here, and a book covering the first few chapters of the notes here. Thurston was sometimes criticized for not writing up full proofs of his results, making it difficult for others entering the field (and sometimes students were advised not to enter the field since Thurston was so good the danger was he would just solve all open problems). He wrote a truly wonderful essay On Proof and Progress in Mathematics, responding to this and laying out part of his vision of how to do mathematics.

My first encounter with Thurston was in the early eighties, when I was a physics graduate student at Princeton. I was working on the problem of defining the topological charge of a lattice gauge field, and it became clear that one approach to do this would require computing the volumes of “spherical tetrahedra”, the 3d analog of the problem of computing the areas of spherical triangles. I’d had some experience trying to talk to mathematicians about the problem I was working on, with the usual result a baffling response about principal bundles, sections, characteristic classes, and all sorts of what seemed to be abstract nonsense (which later on of course I learned was the right way to think about the problem…). So, I was pretty convinced that mathematicians were uniformly experts in a lot of abstract, high-powered technology, surely no longer conversant with the kind of more concrete formulas of the mathematics of earlier centuries.

This was before the days of the internet, so the answer to my problem couldn’t be found via Google, and a bit of library research got me nowhere. So, I stopped by to see a friend who was a math grad student and asked him my volume question. He said that while he didn’t know, he knew someone who could surely help me, and took me over to the math lounge, where Thurston could often be found. After I asked my question, Thurston immediately knew the answer, explained it to me on the blackboard, and gave me the proper reference of where to read more (you break them up in a certain way and then get an answer in terms of things called Schläfli functions, see here). I realized that my views of how much the best research mathematicians knew about concrete calculations and lore from previous centuries had been rather naive.

Thurston’s death at such a relatively young age is a loss for us all. My condolences to his family, including his son Dylan, a very talented topologist in his own right, who has been my colleague here for the last several years.

Update: Terry Tao has more about Thurston and his work here.

Update: More here, here and here. Also worth the time is seeing what he had to say on MathOverflow.

Update: Jordan Ellenberg has something here.

Update: The New York Times has an obituary here.

Update: There’s a Cornell site here, Scientific American has a piece by Evelyn Lamb here, John Horgan here.

Update: Jonah Sinick has put together a memorial slideshow here.

Posted in Obituaries | 15 Comments

This Week’s Hype

The Higgs suggests that there could be more dimensions of space-time than we previously thought.

From a New Yorker piece this week (subscription required) about Joe Incandela of CMS and the Higgs discovery.

Even the famed New Yorker fact-checkers are no match for extra-dimensional hype. Will someone tell them they’ve been had?

Posted in This Week's Hype | 38 Comments

LHC News

The LHC is operating well, hitting record peak luminosities, with integrated luminosity for the year over 11 fb-1. By the end of the year there may be 25 fb-1 per experiment or so. Current plan seems to be to update the results on the Higgs in December, much like last year, so there may not be much news until then.

This week the LHC Machine Advisory Committee was meeting, slides here. The current schedule has this proton run ending mid-December. After a heavy-ion run early next year, the machine will go into a long shutdown starting in March, with main goal to fix the magnet interconnections and commission the machine to run at nearly design energy, 6.5 TeV/beam. First beams at this energy will not be until April 2015, with maybe 20-25 fb-1 of integrated luminosity in the first year’s run.

With no sign of SUSY so far, and little reason to believe it will show up in the rest of the 2012 data since nothing has shown up already, the rallying cry of SUSY enthusiasts is now “Wait Until 2015”, or, maybe more like 2016, since early 2016 may be when analyses of a significant amount of 6.5 TeV data start to appear. I’d been wondering whether David Gross has been getting discouraged at the prospect of having to pay off on his SUSY bets. Someone asked him this recently, with the results here on YouTube. He says he’s still willing to take 50/50 bets on SUSY, but “with the right conditions”, which are 50 fb-1 of analyzed data/experiment (he says this will be “years from now I think”, roughly 2017 maybe if all goes well), and he adds “then we need a judge, because it won’t be so obvious I think”. So, it looks like it’s going to be quite a while before we get to see Gross pay up…

Posted in Experimental HEP News | 30 Comments

SUSY 2012, and Strassler on the String Wars

This post was originally going to be just about the latest SUSY exclusion results announced at SUSY 2012 and their significance, but I realized there’s nothing much new to say, and it would be tedious to just write the same things. ATLAS new results are here, including some using this year’s 8 TeV data. As before, not a hint of SUSY in the CMS or ATLAS data. Now that the expected places to find SUSY have shown nothing, emphasis is on how to search more obscure corners of the 100 + parameter space of the theory which are accessible at the LHC, but hard to study. For a good recent survey of this effort, see Matt Reece’s recent presentation here.

SUSY 2012 featured a plenary talk by Gordon Kane, promoting his string theory “predictions”. As usual, the gluino is right around the corner. Back in 2000, it was supposed to be around 250 GeV, with SUSY discovery at the Tevatron in 2001-3 (see here). Last summer the “prediction” was 600 GeV, just above the 500 GeV limits. Last December, the gluino discovery was imminent, by summer 2012. The latest news is that the gluino mass prediction is now 1 TeV, just above the 800 GeV limits according to Kane. You can watch the gluino move by comparing the same “prediction” plot on slide 22 here and slide 34 here. Kane now claims in bold face that “String/M theory prediction is that no gluino signal expected so far” (page 35) referring (I think) to this paper, which seems to say nothing of the kind. This is just getting more and more bizarre.

Matt Strassler (described here as “the chief US theoretician”) has rarely been critical of string theory hype (although he did in a comment refer to Kane’s claims as “garbage and propaganda”), preferring to see prominent blogging critics of string theory and SUSY hype as the bigger problem to deal with. Today though he took a dramatic and rather admirable step, with a posting about string theory that starts off with:

…the theory’s been spectacularly over-hyped, and the community’s political control of high-energy physics in many U.S. physics departments has negatively impacted many scientific careers, including my own.

He goes on to cast himself as a lonely moderate surrounded by two teams of extremists, arguing that

it is high time the ball were grabbed by the referee and placed quietly in the middle of the field where it belongs.

His refereed position in the middle of the field would have acknowledgement that “string theory cannot be tested at present, and that situation might continue for a very long time, perhaps centuries”, while lauding string theory for providing a range of important insights into other problems than unification. This refereed position seems to me already pretty much the mainstream position of string theorists I know. My problems with it are that it still allows the heavy promotion of a failed idea (string unification as “our best bet”, even if mysteriously “hard to test”), and the over-hype problem is also prevalent among discussion of string theory applications to other parts of physics.

Strassler gives an interesting example of how some ideas from string theory ended up providing inspiration for advances in amplitude calculations, although the main heros of the tale are the phenomenologists who have done the hard work behind these advances (see his exchange with the anonymous “dude” in the comments).

Oddly enough, what seems to have motivated Strassler to take this new public stand are the recent $3 million prizes awarded to his colleagues down the road at Princeton. He devoted this recent posting to attacking me and Nature News for quoting me about the prizes, but ended up agreeing with some of my concerns, specifically:

What upsets me is that there is a long, long list of deserving scientists, some of whom have received little recognition despite their important work, and some of whom could really use some research money and/or time off from teaching — and Milner overlooked them all…

Philanthrophy needs to be done with the consent and participation of the beneficiaries; otherwise it generally fails, and sometimes it causes complete disasters. For instance, you can completely destabilize an organization that is functioning well if you just hand one of its members a million dollar check without understanding the implications…

Anyway, as far as I can tell, the Milner prize is one thing our field didn’t really need. I can think of a few things we really do desperately need, at least in the U.S.

It’s pretty clear where Strassler thinks the money should have gone:

we have too many string theorists teaching at the top U.S. universities, and not enough theorists doing other aspects of high-energy physics, including Standard Model predictions…

He explained in the earlier posting that he has been trying to raise private money for an LHC Institute, but that this has failed because of the recession. I don’t know any details of this, but I do know that about five years ago he and Arkani-Hamed were proposing something like this to the NSF, with the two of them as co-directors. This foundered not because of the recession but because reviewers didn’t much like the idea of giving a lot of new money to well-funded theorists at Princeton and Rutgers, largely to retool string theory groups into LHC phenomenology groups.

That proposal advertised the likelihood of discovery of SUSY or something equally dramatic about a year after first beams at the LHC, with a large group of theorists needed to sort out the “LHC Inverse Problem” of how one was going to figure out the underlying physics responsible for the confusing plethora of non-SM signals the LHC would be seeing. Perhaps a reason for finding it hard to get funding for a theory LHC institute these days is not the recession, but the lack of any such advertised signal. On the other hand, with $12 million of cash in their pockets now, the IAS theorists should be able to themselves privately fund the proposed Arkani-Hamed/Strassler center, if they still think this a good idea.

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’t Hooft on Cellular Automata and String Theory

Gerard ’t Hooft in recent years has been pursuing some idiosyncratic ideas about quantum mechanics; for various versions of these, see papers like this, this, this and this. His latest version is last month’s Discreteness and Determinism in Superstrings, which starts with cellular automata in 1+1 dimensions and somehow gets a quantized superstring out of it (there are also some comments about this on his web-site here).

Personally I find it difficult to get at all interested in this (for reasons I’ll try and explain in a moment), but those who are interested might like to know that ’t Hooft has taken to explaining himself and discussing things with his critics at a couple places on-line, including Physics StackExchange, and Lubos Motl’s blog. If you want to discuss ’t Hooft’s ideas, best if you use one of these other venues, where you can interact with the man himself.

One of ’t Hooft’s motivations is a very common one, discomfort with the non-determinism of the conventional interpretation of quantum mechanics. The world is full of crackpots with similar feelings who produce reams of utter nonsense. ’t Hooft is a scientist though of the highest caliber, and as with some other people who have tried to do this sort of thing, I don’t think what he is producing is nonsense. It is, however, extremely speculative, and, to my taste, starting with a very unpromising starting point.

Looking at the results he has, there’s very little of modern physics there, including pretty much none of the standard model (which ’t Hooft himself had a crucial role in developing). If you’re going to claim to solve open problems in modern physics with some radical new ideas, you need to first show that these ideas reproduce the successes of the estabished older ones. From what I can tell, ‘t Hooft may be optimistic he can get there, but he’s a very long way from such a goal.

Another reason for taking very speculative ideas seriously, even if they haven’t gotten far yet, is if they seem to involve a set of powerful and promising ideas. This is very much a matter of judgement: what to me are central and deep ideas about mathematics and physics are quite different than someone else’s list. In this case, the central mathematical structures of quantum mechanics fit so well with central, deep and powerful insights into modern mathematics (through symmetries and representation theory) that any claim these should be abandoned in favor of something very different has a big hurdle to overcome. Basing everything on cellular automata seems to me extremely unpromising: you’re throwing out deep and powerful structures for something very simple and easy to understand, but with little inherent explanatory power. That’s my take on this, those who see this differently and want to learn more about what ’t Hooft is up to should follow the links above, and try discussing these matters at the venues ’t Hooft is frequenting.

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Short Items

  • There’s an interview with the CERN director here.
  • John Preskill and others at the Caltech Institute for Quantum Information and Mattter now have a blog here.
  • The usual summer workshop on math and physics at Stony Brook is now running at the Simons Center, see videos of talks here. Videos of talks from the Simons Symposium this spring in the Virgin Islands on knot homologies and BPS states are now available here.
  • Last month there was a CBMS conference on Unitary Representations of Reductive Groups in Boston, with David Vogan the main speaker. For a nice set of survey lectures and others, see here. If you find the Vogan conference too old-school, a workshop on categorical representation theory this coming week organized by David Ben-Zvi may be more to your liking, lecture notes starting to appear here.
  • The only thing stopping me so far from ordering a copy of Francis Farley’s novel Catalysed Fusion is that it looks like it is only available in ebook form, and I’ve until now avoided those and stuck to paper. According to an article in the Telegraph:

    …a steamy new novel written by a retired physicist lifts the lid on the organisation’s studious exterior to reveal an altogether more glamorous lifestyle of wild nights, adrenalin-fuelled sports and romantic trysts…

    Prof Farley describes a group of young researchers whose groundbreaking work and racy private lives intertwine as they enjoy the high life at Switzerland’s top ski resorts and France’s best beaches.

    Prof Farley revealed that he even based a character on himself – Ivan, a physicist and crack glider pilot who is married to a former stripper and sets up a new lab on a nudist Mediterranean island.

    He told the Daily Telegraph: “We were well paid, we had diplomatic status, no taxes. We got tax-free petrol and drinks and we went out and enjoyed life…

    “We worked hard and then some people would go home to their families but there were lots of little floozies about and other men had a roving eye, and so did some of the women.”

    Perhaps things have changed a bit since the eighties in Geneva….

  • Text books for graduate students on SUSY and string theory are coming fast and furious these days. Next month will see Peter West’s Introduction to Strings and Branes, a few months ago there was String Theory and Particle Physics: An Introduction to String Phenomenology by Ibanez and Uranga. Even more recent is Freedman and Van Proeyen’s Supergravity, which now has one review on Amazon (from “Dan”):

    This is a must-buy for every high energy theorist who wants to know Sugra. The first nine chapters also make a great source for classical field theory and can be used as a complement for PhD students learning QFT and GR.
    A wonderful work!

Update: A few more recent and upcoming string theory textbooks are:

Posted in Uncategorized | 26 Comments

LEP3

For many years now discussion in the HEP community of what might be the appropriate next machine to try and finance and build after the LHC has centered around the idea of a linear electron-positron collider. The logic has been that an electron-positron machine would provide a much better environment that the LHC for detailed studies of physics at the TeV scale. At these energies, synchrotron radiation losses when accelerating electrons are so high in a circular geometry that such a machine would have to be a linear collider to keep the power needed something plausible. The two main proposals under study have been the ILC (250 GeV + 250 GeV, later upgradeable to 500 GeV + 500 GeV) and, a less mature technology, CLIC (1.5 TeV + 1.5 TeV). These would be very expensive machines to build and operate ($10 billion and up?), requiring completely new technology, tunnels and detectors.

The operating assumption has been that initial results from the LHC would show the existence of new supersymmetric or other particle states in the region of multiple hundreds of GeV to small numbers of TeV, and the linear collider designs could then be chosen and optimized to study this new physics. The other main goal of such a collider would be detailed study of the Higgs, and knowing the mass of the Higgs is also highly relevant to what kind of linear collider to build.

The initial LHC results are now in (125 GeV Higgs, nothing new at the TeV scale) and they are rather discouraging for the linear collider idea, providing no strong motivation for studying electron-positron collisions around 1 TeV. A “Higgs Factory” capable of producing and studying large numbers of Higgs particles is an attractive idea, but the production cross-section for a 125 GeV Higgs is dominated by the process e+ + e -> Z + H, which starts to get large around 220 GeV and reaches a maximum value around 255 GeV. So, for most Higgs studies, the right energy for an electron-positron machine is around 250 GeV, not 1 TeV.

This realization is driving a new proposal that is getting a lot of attention: the idea of going back to circular electron-positron colliders, building a new machine in the LHC tunnel, optimized as a Higgs factory, and designed to operate at 120 GeV + 120 GeV. This is being called “LEP3″, since it would be in many ways similar to LEP2, the predecessor machine to the LHC, which operated in the same tunnel, reaching an energy of 209 GeV. There would be huge cost advantages to building such a machine over the ILC or CLIC, since it can use the LHC tunnel, infrastructure, and, crucially, the CMS and ATLAS detectors (the detectors are a large part of the cost of a new accelerator).

Space was left in the LHC tunnel to allow another ring, so there are various possibilities for having a LEP3 and the LHC cohabitate. Until now, the assumption has been that the LHC would be upgraded to the”HL-LHC”, operating at higher luminosity throughout the 2020s, then perhaps an “HE-LHC”, operating at higher energies during the 2030s. This plan is being challenged by the LEP3 proposal, with the argument that it might turn out that Higgs physics is where the only action will be, and a long period of LHC operation at higher luminosities and modestly higher energies might be less worthwhile than building a LEP3 Higgs factory.

There’s a very good article about this at PhysicsWorld. For more detail about LEP3, see here, here and here. John Ellis is one of the co-authors of the latest document proposing study of the LEP3 possibility, and the Physics World article has him arguing that, after waiting to see if LHC14 turns up anything:

LEP3 could be a more secure option than the ILC if only a Higgs is discovered…If the LHC does not discover anything beyond the Higgs, then would you keep running it for years?

Lyn Evans, who led construction of the LHC and is now director of the linear-collider project argues against the LEP3 concept:

The first job is to fully exploit the LHC and all its upgrades, This is at least a 20 year programme of work, so I think that it is very unlikely that the LHC will be ripped out and replaced by a very modest machine with little scope apart from studying the Higgs.

The problem is, what if, as seems increasingly likely, “studying the Higgs” is the only new physics accessible in these energy ranges? Dreams of superpartners and extra dimensions may die hard.

Posted in Experimental HEP News | 30 Comments