This Week’s Hype

This week’s string theory hype comes to us from USC physicists Clifford Johnson and Nick Warner, courtesy of the USC press office (see here and here). It’s garden variety hype of this kind, exactly the same claims about strings and extra dimensions that were being made thirty years ago. There’s no acknowledgement these haven’t gone anywhere, instead we’re “closer than ever to an answer”.

When the question of testability comes up, the multiverse is not invoked as an excuse. Instead, it seems that dark matter is going to provide the test:

Observations show that dark matter and energy constitute more than 95 percent of the universe. Scientists have established that they are new forms of matter and energy, but so far their precise nature is unknown. They may hold the key to confirming the veracity of string theory, Johnson said.

“It’s really kind of amazing — and humbling. There are forms of matter that seem to show up naturally in string theory that could well be good candidates to be dark matter,” he said. “People are hoping that this could be a key to making contact between theory and nature.”

Hard to know what Johnson has in mind for his “show up naturally in string theory” claim. Presumably he’s thinking of the ancient “we’ll test string theory by finding superpartners” claim, somehow neglecting to mention that this hasn’t worked out.

I’m especially impressed by the description of string theory’s power to explain dark matter as “amazing – and humbling”, deftly pairing outrageous over-the-top hype with an invocation of the selfless humility of the research scientist.

Posted in This Week's Hype | 22 Comments

2016 Breakthrough Prizes

The 2016 Breakthrough Prizes were announced last night, discussed a bit in the last posting. Today there are programs going on at Berkeley, livestreams available here.

One thing that strikes me about these things is that the situation with the physics prize has changed dramatically since the first three years, when they went mostly to string theorists. Having a heavily promoted much larger cash prize than the Nobel, given largely to theorists for ideas many of which haven’t worked out, raised obvious questions about the wisdom of the whole thing. The last two years have seen a 180 degree turn, with the prizes going to experimentalists for successful experimental results. Even better, there has been an unusual emphasis on making an award to entire experimental collaborations, not just a small number of “great men” identified as collaboration leaders or spokespersons. I don’t know of any other major prizes that do this. The lack of an experimental Nobel for the Higgs discovery is one reflection of that problem, it’s great that the Breakthrough Prize people are doing something about it.

This is now just the second year of the math prize, which has never been as problematic as the early physics prize. However, the institution of cash prizes of this size, promoted in a Hollywood style, is something I don’t think anyone in the math community ever asked for, and it’s not at all clear it’s a good thing, or in keeping with some of the best values of the math research community. This year I think Peter Scholze set a remarkable example by turning down a prize, a move which unfortunately has gotten little attention in the media. I hope his action causes people to take a closer look at this gift horse. Instead of just celebrating the shower of cash and attention, research mathematicians may want to consider whether, just as they changed direction with the physics prize, Milner and Zuckerberg perhaps should be encouraged to listen to Scholze and move in a different direction.

Update: I just watched some of the talks at the afternoon symposia. Arkani-Hamed made the case for a Great Collider, mostly quite sensibly in terms of the desirability of better understanding the Higgs: is it pointlike? how does it self-interact? The argument is that addressing these questions goes beyond what the LHC can do, can be done by a large new collider.

On the math side, David Nadler gave a beautiful talk about Langlands/geometric Langlands, ending with a prediction for the future that a central role will be played by Peter Scholze’s work, including recent ideas on what Nadler calls “Arithmetic conformal field theory”. He suggested that 50 years from now, Hartshorne and other graduate textbooks on algebraic geometry will be replaced with new ones based on Scholze’s perfectoid spaces. Maybe if they hadn’t offered Scholze money they could have gotten him to talk about this stuff…

Update: The New York Times Science section has an article today about the goal of the Breakthrough prizes, to turn scientists into celebrities. Yuri Milner is quoted:

“We are at the very beginning of this journey,” he said, noting that if you were to look at a list of the top 100 celebrities in American society, there would not be a single scientist on the list.

“The question is why?” he added.

The question this raises, which may have something to do with Peter Scholze’s refusal to participate, is “what if good scientists don’t want to be celebrities?” The impulse to do science and mathematics at the highest level and the impulse to be a celebrity may just be two very different, incompatible things.

The New York Times article doesn’t mention the Scholze story, but it does discuss the young student, Ryan Chester, who was given a $400,000 award for making a film about special relativity. It turns out that doing a great job of making such a film has a lot more to do with interest in being a filmmaker than interest in being a scientist:

Mr. Chester, however, said in an interview that he was not planning to study science in college, but instead will probably study film, hopefully at a school like the University of Southern California or New York University.

Update: Videos from the symposia and panel discussions at Berkeley are available here.

: In other large-check news of the day, the IAS has announced a $20 million donation from Robert Rubenstein, CEO of the Carlyle Group, a top private equity firm. This completes a $212 million capital fundraising campaign.

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Various News

Later tonight will be the 2016 Breakthrough Prize ceremony, broadcast live on the National Geographic channel. While mathematicians and physicists are getting their popcorn ready, waiting to find out which of their colleagues will be $3 million richer, they might want to check out Mathematics Without Apologies, where Michael Harris is writing about his experience on the red carpet at last year’s ceremony. In other news:

  • A few miles down the road from the event tonight at the NASA Ames Center, the Stanford Institute for Theoretical Physics has a new website. They have various videos you can watch, as well as this account of the history of the SITP:

    The gauge hierarchy problem was first addressed in the earliest days of SITP by Susskind and Dimopoulos, whose ideas eventually led to the introduction of supersymmetry into particle physics. The gauge hierarchy problem and the discovery experimental discovery of supersymmetry were principle reasons for the building of the Large Hadron Collider, but the puzzle remains. To this day Dimopoulos and his band of young postdocs and students have offered the most exciting proposals for discovering new physics in this area.

    Personally, I thought the Higgs was the principal reason for the LHC, but perhaps I was misinformed.

  • Several people wrote to tell me about a USA Today article reporting Study may have found evidence of alternate, parallel universes, noting that this needed a new installment of This Week’s Hype. I’m very pleased to see that the excellent science journalist Jennifer Ouellette has been on the case, debunking this much better than I ever could. The blame for this kind of thing is jointly shared by physicists and journalists, glad to see that at least some journalists are taking action to deal with the problem.
  • There have also been several suggestions that I write about Leo Kadanoff, the great theoretical physicist who passed away a little while ago at the age of 78. Unfortunately I never met him, and only had a general acquaintance with his work. A very good obituary by Kenneth Chang did appear in the New York Times.
  • I’ve also heard from lots of people with more stories about the Khrzhanovsky film about Landau described here. It seems that I’m the only one who didn’t know about this. In other performing arts/physics news, Lee Smolin discusses here a project he has been involved in.
  • The LHC has finished its 2015 run colliding protons at 13 TeV, will now turn to heavy ion physics. Integrated luminosity recorded by ATLAS and CMS is about 4 inverse femtobarns. Results of the analysis of this data may start to be available publicly around the time of Moriond in March. Consulting Jester to see what to expect, it looks like better limits on or evidence for stops, Z-primes and gluinos should be available. In particular, we’ll finally see a conclusive test of string theory (Gordon Kane argues that string theory predicts a 1.5 TeV gluino, see here).
  • In other news from the LHC, it seems that humanity narrowly missed a major problem back in August, when Simon Parkes, a Labour town councillor for Whitby in North Yorkshire, foiled a sinister plot by the Illuminati to “use the LHC to open an evil portal that would allow them to become more powerful.”

Update: Awards ceremony hasn’t started, but names are out: Ian Agol for mathematics, 5 teams of 1300 people for neutrino oscillations (with 7 specifically identified, including the 2 winners of this year’s physics Nobel).

Junior recipients in math are Larry Guth and Andre Neves, in physics Bogdan Bernevig, Liang Fu, Xiao-Liang Qi, Raphael Flauger, Leonardo Senatore, and Yuji Tachikawa.

Update: The big news, via Michael Harris, is that Peter Scholze (to my mind a better mathematician than any of those who got prizes) turned down a $100,000 prize. Good for him.

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The Elephants in the Room – What every physicist should know about string theory

The string wars seem to still be going on, with the latest salvos coming from Ashtekar and Witten. In a very interesting recent interview, at the end Ashtekar has some comments about string theory and how it is being pursued. About claims that string theory is the only possible way to get quantum gravity he says:

I don’t know why science needs such statements; indeed, scientists should not make such statements. Let the evidence prove that it’s the only theory. Let the evidence prove that it is better than other theories or let its predictions be reproduced more than those of others. Science should not become theology. And, somehow such statements have a strong smell of theology, which I don’t like.

About AdS/CFT and the current state of its relation to quantum gravity:

We seem to be using these gravity ideas in other domains of physics rather than solving quantum gravity problems. I don’t think that the quantum gravity problems have been solved. And I have said this explicitly in conferences with panels – in which Joe Polchinski, Juan Maldacena and I were panellists – that, in my view, this is very powerful and these are good things. However, the AdS/CFT conjecture is the only definition of non-perturbative string theory one has – and it’s a definition, it’s not a proof of anything. It talks about duality, but there’s no proof of duality. To have a duality, A should be well defined, B should be well defined and then you say that A is dual to B. Since we don’t have another definition of string theory, we cannot hope to prove that string theory is dual to its conformal field theory. You can define string theory to be the conformal field theory. You have to construct a dictionary relating string theory in the bulk and conformal field theory on the boundary. That dictionary has not been constructed in complete detail.
Again, nobody is taking anything away from the successes that the AdS/CFT duality has had; but there is a big gap between the successes and the rhetoric. The rhetoric is at a much higher level than the successes. So, for example, in this conjecture, first of all the space-time is 10 dimensional. The physical space-time is supposed to be asymptotically anti-de Sitter, which has a negative cosmological constant. But we look around us, and we find a positive cosmological constant. Secondly, the internal dimensions in the conjecture, or this definition, are macroscopic. The Kaluza-Klein idea is that there are higher dimensions but because they are all wrapped up and microscopic, say, at Planck scale, we don’t see them. That’s plausible. But here, in AdS/CFT duality, they need the radius of the internal dimensions to be the same as the cosmological radius. If so, if I try to look up I should see these ten dimensions; I don’t. So, it can’t have much to do with the real world that we actually live in. These are elephants in the room which are not being addressed.
… there are these obvious issues and practitioners just pretend that they don’t exist. And that to me is unconscionable; I feel that that’s not good science. I don’t mean to say string theory is not good science, but publicizing it the way it’s done is not good science. I think one should say what it has done, rather than this hyperbole.

A good example of the problems Ashtekar is concerned about is provided by an article in the latest Physics Today by Witten with the title What Every Physicist Should Know about String theory. It’s devoted to a simple argument that string theory doesn’t have the UV problems of quantum field theory, one that I’ve seen made by Witten and others in talks and expository articles many times over the last 30 years. This latest version takes ignoring the elephants in the room to an extreme, saying absolutely nothing about the problems with the idea of getting physics this way, even going so far as to not mention the first and most obvious problem, that of the necessity of ten dimensions.

The title of the article is the most disturbing thing about it. Why should every physicist know a heuristic argument for a very speculative idea about unification and quantum gravity, without at the same time knowing what the problems with it are and why it hasn’t worked out? This seems to me to carry the “strong smell of theology” that Ashtekar notices in the way the subject is being pursued.

Witten is a great physicist and a very lucid expositor, and the technical story he explains in the article is a very interesting one, with the idea that most physicists might want to hear about it a reasonable one. But the problems with the story also need to be acknowledged and explained, otherwise the whole thing is highly misleading.
Besides the obvious problems of the ten dimensions, supersymmetry, compactifications, the string landscape, etc. that afflict attempts to connect this story to actual physics, there are a couple basic problems with the story itself. The first is that what Witten is explaining as a problematic framework to be generalized by string theory is not quantum field theory, but a first-quantized particle theory, with interactions put in by hand. This can be used to produce the perturbation series of a scalar field theory, but this is something very different than the SM quantum field theory, which has as fundamental objects fields, not particles, with interactions largely fixed by gauge symmetry, not put in by hand. For such QFTs, there is no necessary problem in the UV: QCD provides an example of such a theory with no ultraviolet problem at all, due to its property of asymptotic freedom.

Another huge elephant in the room ignored by Witten’s story motivating string theory as a natural two-dimensional generalization of one-dimensional theories is that the one-dimensional theories he discusses are known to be a bad starting point, for reasons that go far beyond UV problems. A much better starting point is provided by quantized gauge fields and spinor fields coupled to them, which have a very different fundamental structure than that of the terms of a perturbation series of a scalar field theory. A virtue of Witten’s story is that it makes very clear (while not mentioning it) what the problem is with this motivation for string theory. All one gets out of it is an analog of something that is the wrong thing in the simpler one-dimensional case. The fundamental issue since the earliest days of string theory has always been “what is non-perturbative string theory?”, meaning “what is the theory that has the same relation to strings that QFT has to Witten’s one-dimensional story?” After 30 years of intense effort, there is still no known answer to this question. Given the thirty years of heavily oversold publicity for string theory, it is this and the other elephants in the room that every physicist should know about.

Update: For another take on string theory that I meant to point out, there’s an article quoting Michael Turner:

Turner described string theory as an “empty vessel,” and added: “the great thing about an empty vessel is that we can put our hopes and dreams in it.”

The problem is that the empty vessel is of a rather specific shape, so only certain people’s hopes and dreams will fit…

Update: Many commenters have written in to point out this article, but I don’t think it has anything at all to do with the topic of this posting. There are lots of highly speculative ideas about quantum gravity out there, most of which I don’t have the time or interest to learn more about and discuss sensibly here.

Update: It is interesting to contrast the current Witten Physics Today article with a very similar one that appeared by him in the same publication nearly 20 years ago, entitled Reflections on the Fate of Spacetime. This makes almost the same argument as the new one, but does also explain one of the elephants in the room (lack of a non-perturbative string theory). It also includes an explanation of the T-duality idea that there is a “minimal length” in string, an explanation I was referring to in the comment section when describing what I don’t understand about his current argument.

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Russian Math-Physics Film News

I’m pressed for time, heading out tomorrow for a short vacation in San Francisco, but I did want to write a little bit here before leaving. Last year around now, a theme was Hollywood blockbuster films with physics/math themes, this year there seem to be none of those, instead I’m hearing about some Russian films with such themes.

This evening here at Columbia there was a showing of Ekaterina Eremenko’s Colors of Math, an exploration of the sensual nature of mathematics, pairing research mathematicians with the five senses. Part of it is available on Youtube. Eremenko went to graduate school in mathematics in Moscow, then later on to a career in modeling and TV, and in recent years has been making films (see here). Her current project is called The Discrete Charm of Geometry, trailer is here.

Somehow I’d missed until today hearing about a truly fantastic Russian film project which has been going on for years, showing no signs yet of reaching an endpoint. The topic is the life of the great Russian theoretical physicist Lev Landau, and the London Review of Books has a column by James Meek about the film here. It seems that the director, Ilya Khrzhanovsky, has been working on this for a decade, creating a huge set in Kharkov, where Landau worked during the 1930s, and doing his best to recreate the time as accurately as possible. Meek describes the shooting as follows:

For more than two years, between 2009 and 2011, hundreds of volunteers, few of them professional actors, were filmed living, sleeping, eating, gossiping, working, loving, betraying each other and being punished in character, in costume, with nothing by way of a script, on the Kharkiv set, their clothes and possessions altered, fake decade by fake decade, to represent the privileged, cloistered life of the Soviet scientific elite between 1938 and 1968.

Among those brought in to participate in all of this were well-known physicists and mathematicians Dmitry Kaledin, Nikita Nekrasov, Andrey Losev, Carlo Rovelli, David Gross, Shing-Tung Yau and Alexander Midgal.

Post-production is now going on in London, in a huge five-story building in Mayfair, financed by someone who doesn’t want to be identified. It’s unclear what will emerge from the seven hundred hours of film shot in Kharkiv, perhaps “a dozen or more movies, a TV series, and a user-directed internet narrative system.” Whatever it is, I’m very curious to see the result.

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The Latest Information on Information

The field of hep-th has always been quite faddish, with many of the fads easily recognizable just from looking at the buzzwords appearing in paper titles. In recent years “entanglement” is a buzzword that has been all the rage, and John Preskill has some data here (slide 3) on how many hep-th papers have it in their title. Extrapolating from 62 in 2011, 119 in 2013 and a projected 220 this year, long before we see a new accelerator, all hep-th papers will have “entanglement” in their titles. Another very visible trend is that an increasingly large fraction of these and other papers in hep-th (which used to mean high-energy particle physics) are now about low-energy non-particle physics topics.

I make periodic attempts to listen to talks or read papers explaining the hot topics at issue, but have to confess that I tend to lose interest, not seeing anything relevant to the standard model or unification, or to the kind of deep mathematics that in the past has provided insights into those topics. Suggestions of what to read to follow these latest fads are welcome, when I have more free time I’ll look into them. In the meantime, I’m just reporting a trend, will leave it to others to decide what it all means.

This brave new world of hep-th is generating a lot of activity. The week before last saw a big “The Information Universe” conference in the Netherlands, that addressed questions such as

– Is the universe one big information processing machine?
– Is there a deeper layer in quantum mechanics?
– Is the universe a hologram?
– Is there a deeper physical description of the world based on information?

Last week was the kick-off meeting of the It from Qubit collaboration, which is supposed to bring together quantum information theory and fundamental physics. This is an extremely large effort, very well-funded by the Simons Foundation. They just announced that they’re planning on hiring a dozen or so postdocs this year. If you get one of those jobs, there’s a warning that you’ll have a “significant burden” of having to travel to collaboration meetings in places like Bariloche, but at least on long flights you’ll be flying business class.

For a detailed explanation of the plans of It from Qubit, see here.

After the Simons-funded meeting a few days ago at Stanford, this weekend there’s yet another quantum information/entanglement/HEP meeting at Stanford, this one funded by the Templeton Foundation. The program for the Templeton Program meeting is here.

Update: It seems that this page has been edited this weekend to remove reference to the It from Qubit collaboration travel policy, however you can still find it here.

Update: For popular expositions of these ideas, there’s a new article in Science News, and a book coming out by George Musser, reviewed today by Sabine Hossenfelder. I haven’t seen the book, but the Science News article doesn’t help me understand much: all I get out of it and the papers its links to are some very vague conjectures about understanding quantum gravity via AdS/CFT. Standard facts about quantum mechanics on the CFT side become more exciting sounding conjectures about gravity on the AdS side, but it remains unclear to me exactly how any of this is supposed to really work. For one thing, we don’t live in AdS space.

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Prizes and Other Stuff

  • There will be an awards ceremony November 8 for the 2016 Breakthrough Prizes, hosted by Seth MacFarlane, and airing live on the National Geographic Channel, later to run on FOX. The next day at Berkeley there will be a Breakthrough Prize Symposium, featuring talks by the winners and others.

    In physics the prizes to be awarded include the big $3 million prize and up to three $100,000 prizes for young researchers. The symposium physics schedule lists as speakers “2016 Breakthrough Prize Laureates”, with the plural perhaps a hint that more than one person will be sharing the $3 million. The first three rounds of these mostly went to string theorists but there seems to have been some sort of policy change last year (the award went to Supernova observations indicating an accelerating cosmology). I have no idea at all who they’ll choose this year. The theorist speakers discussing the future of the subject at the symposium are Arkani-Hamed, Hall and Bousso, a clean sweep for multiverse mania.

    On the mathematics side, there’s also a $3 million prize and up to three $100,000 prizes. The symposium schedule lists “2016 Breakthrough Prize Laureate”, so maybe a hint there’s just one in math.

  • In other news on the prize front, the APS will now be awarding a Medal for Exceptional Achievement in Research, with the first one going to Edward Witten.
  • The Wall Street Journal has published a response to the Gross/Witten piece advocating a Chinese “Great Collider”. Physicist Jonathan Katz describes particle physics as a “dying”, “moribund” subject. He argues that research funding should go to “tabletop experiments”, like for instance the ones he does.
  • The new AMS Notices is out, with a piece by Loring Tu on the origin of the theorem due to Atiyah-Bott often known as the Woods Hole Fixed Point Theorem. Tu does a great job of explaining this beautiful mathematics, as well as the details of the controversy over Shimura’s role in sparking this by a conjecture. He doesn’t much discuss Shimura’s memoir, which I wrote about here, which includes the claim that Serre attacked him out of jealousy about Shimura’s conjecture. I’ve never really understood Shimura’s point of view on this, since usually mathematicians value theorems over conjectures, and it is clearly Atiyah-Bott who had the theorem here.
  • From David Mumford’s blog I learned about an experimental neurobiology paper co-authored by Atiyah. It is quite interesting, but even more interesting is the blog entry by Mumford that it inspired. Mumford is one of the greats of algebraic geometry, and he gives a fascinating characterization of the different sorts of ways in which mathematicians pursue research. Mathematics done at the highest level involves strikingly different personalities and research strategies, which Mumford characterizes as four different tribes: “explorers”, “alchemists”, “wrestlers” and “detectives”. If you’re at all interested in how mathematics research is done, this is highly recommended reading.
  • Also recommended, if you’re interested in the overlap of physics and philosophy, is a new piece by Massimo Pigliucci on String Theory vs. the Popperazi.
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This and That

  • The Perimeter Institute’s public lecture series tonight will feature Neil Turok on The Astonishing Simplicity of Everything. I think Turok is one of the few theorists speaking to the general public who has got the story of the current situation right: the LHC and CMB results point to the Standard Model + simple model of cosmology, ruling out many of the complicated models that have enthralled theorists for decades. By all rights, this should change the behavior and attitudes of theorists, I hope talks like his will have an effect. In any case, it should be vastly better than the last one of these, devoted to a misleading sales job for a failed theory.
  • Nature magazine has a very good piece by Davide Castelvecchi on Shinichi Mochizuki and his impenetrable proof. It gives an accurate picture of the current situation: still virtually no experts have been able to understand Mochizuki’s claims well enough to evaluate whether he has a valid proof. One counter-example is Ivan Fesenko, who is organizing a December workshop that may clarify the situation.
  • The big news this week is the physics Nobel for the discovery of neutrino masses. I haven’t written about this partly because I’m pretty ignorant about the history of the experiments awarded the prize (or, more accurately should have gotten the prize, not just a single person from the experiment), and the web is full of well-written coverage of this. The issue of the theory of neutrino masses is a fascinating, but quite intricate one, and some day I hope to write a bit about it, but lack the time right now.
  • Tommaso Dorigo has a posting here about the great Italian theorist Guido Altarelli, who passed away last week.
  • At some point I came across a list of the top donors to US political campaigns and was a little bit surprised to see that Jim Simons was on it, at number 7. I also noticed that someone else at his hedge fund spends even more on politicians than Simons does: Robert Mercer, a computer science Ph.D., is at number 4 (better informed people have pointed out to me that these numbers only include some publicly reported categories of donations). The Washington Post has a profile on Mercer today, which explains that he’s one of the people we have to thank for Ted Cruz (Mercer is the top donor in the US to 2016 presidential campaigns, according to this).

    In terms of funding politicians and science, increasingly it’s the hedge fund guy’s world, we just live in it. I’m a big fan of much of what the Simons Foundation does, less so of Mercer’s science funding, which goes to the Oregon Institute of Science and Medicine. The people there seem to be interested in climate denialism, surviving nuclear attack, and getting ahold of your urine.

    Physicists and mathematicians don’t always have huge success in the hedge fund business. Robert Stock, a physics Ph.D from Carnegie-Mellon, seems to have gone from trying to blow up missiles with lasers to instead having more success blowing up a hedge fund, Spruce Alpha.

Update: According to today’s New York Times, for the 2016 presidential election cycle, Mercer is the number two donor in the US, at 11.3 million. Simons is way, way down the list at 550,000. Their list of donors is heavily dominated by the financial industry (64 individuals or families), with the next largest number from the oil and gas industry (17 individuals or families).

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A few odd things that I’ve run into recently:

  • The IAS has a weekly meeting to discuss current topics in HEP theory. From their events calendar, next week’s meeting will be devoted to “The Cosmological Constant and the String Landscape”, with suggested readings the 28 year old papers by Weinberg on anthropics and the CC, as well as the KKLT paper (I’m a fan, see here) and its Bousso/Polchinski predecessor from about 15 years ago. I would have thought this was a very well-worn topic. The one recent reference is a defense by Polchinski of KKLT against some technical challenges, but if the intent is to discuss those, it’s unclear why they’re not in the references (and they have nothing to do with Weinberg/CC/anthropics).
  • Mochizuki has two new things on his website. One is a long discussion of the use of the words “anabelioid” and “Frobenioid”, the other is an animated video of a diagram explaining a theorem (see near bottom of here).
  • A couple years ago there was a controversy over the proof of the so-called “Yau-Tian-Donaldson” conjecture (see here), with Donaldson and his collaborators publicly complaining about Tian’s paper claiming credit for proof of this conjecture. The Tian paper was submitted to the Courant journal Communications on Pure and Applied Mathematics in February 2013, was published there in the July 2015 issue (a technical corrigendum appeared a couple weeks ago). More expertise than I have would be needed to see if the published version addresses the Donaldson et al. concerns, a quick look doesn’t indicate evidence of that.

    At the time I wrote:

    On a more positive note, perhaps this controversy will not interfere much with future progress in this area, as Donaldson and Tian are jointly organizing a Spring 2016 workshop on this topic at MSRI.

    The MSRI directory for this year though lists Tian as visiting, but not Donaldson.

  • Among the many oddities associated with string theory is the decision of a group in Philadelphia to name a group of charter schools there the String Theory Schools. I don’t think they teach string theory, just liked the name. The financing of these schools is now attracting controversy. It seems they are running into some financial trouble, involving huge real estate deals and tax-exempt bond financing. For the details of the story, see here. For some analysis, see a Naked Capitalism piece: Private Equity Asset-Stripping Strategy Meets Charter Schools to Produce Even Better Looting.
  • Presidential candidate Ben Carson has been widely (and quite appropriately…) criticized for some of his odd and non-sensical views about science. In USA Today’s factcheck piece about this, we’re told

    Carson went on to claim that the presence of stars and planets is related to the existence of multiple Big Bangs that eventually might produce an ordered universe:

    Carson: And then they go to the probability theory, and they say “but if there’s enough big bangs over a long enough period of time, one of them will be the perfect big bang and everything will be perfectly organized.” And I said, so you’re telling me if I blow a hurricane through a junkyard enough times over a long enough period of time after one of them there will be a 747 fully formed and ready to fly?

    That is not an accurate reflection of the Big Bang theory. Though some theories of the origin of the universe suggest that the Big Bang was only one of many such explosions, these theories do not state that the currently ordered existence is a spontaneous result of one of these repeated Big Bangs.

    He’s getting it somewhat wrong, but this does sound a lot like Carson has been reading about the string theory multiverse…

Update: Please do not use the reference to Carson as an excuse to post your thoughts on US politics and the ongoing political campaign. I think everyone would appreciate not having to be subjected to that topic here.

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The Free Particle

Following on my notes about Euler’s formula, I’ve finally finished some work on another piece of elementary exposition, a discussion of the free quantum particle, which can be found as chapters 10, 11 and 12 of the book I’m working on.

These chapters are a complete rewrite and major expansion of what used to be there, a rather slap-dash single chapter on the subject. The excuse for this in my mind had been that it’s a topic treated in detail in every quantum mechanics textbook, so best if I passed over it quickly and moved on to things that weren’t so well treated elsewhere. Another reason for this was that my understanding of analysis has never been what it should be, and it seemed best if I not make that too obvious by how I handled the mathematics of this subject.

This summer I started rewriting the book from the beginning, and once I hit the chapter on the free particle it became very clear that it needed improvement, both for its own sake and for how the material was needed in later chapters. I spent some time doing some remedial study in analysis, and after a while got to a point such that I felt capable of writing something that captured more of the relevant mathematics. Finally, today I got to the point where these three chapters are in decent shape, and soon I’ll move on to later ones.

One thing that I’d never thought much about before, but that struck me while rewriting these chapters, is the quite peculiar nature of a position eigenstate in quantum mechanics. Normally one only thinks about this in relativistic quantum field theory, where the problems associated with localizing a relativistic particle motivate the move to a quantum field theory. Of course a position eigenstate is just a delta-function, but what is peculiar is the dynamics, what happens if you take that as an initial condition. See the end of chapter 12 for what I’m talking about (be sure you have the latest version, today’s date on the front), I won’t try and reproduce that here. Part of this story is the tricky nature of the free-particle propagator in real time, as opposed to its much better behavior in imaginary time. The issue of analytic continuation in time continues to fascinate me, including the quite non-trivial nature of what happens even for the supposedly trivial case of a free particle in one spatial dimension.

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