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Cliff Harvey
Attended Worcester Polytechnic Institute
Lives in Connecticut
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This is an awesome result by the +LHCb Experiment, an apparently decisive observation of the first 'exotic' hadron consisting of at least four quarks. 

(All other known combinations of the color-charged quarks come in sets of either 2 (mesons) or 3 (baryons, such as protons). Lone color charges are banned by the strong interaction.)

Observation of the resonant character of the Z(4430)− state
http://arxiv.org/abs/1404.1903
The LHCb Collaboration has reported today an analysis of about 25 200 B0 → ψ’Kπ-, ψ’ → μ+μ+ decays observed in 3 /fb of pp-collision data collected at √s = 7 and 8 TeV. The LHCb data sample exceeds by an order of magnitude that of Belle and BaBar together. The significance of the Z(4430)- signal is overwhelming, at least 13.9σ, confirming the existence of this state. The Z(4430)- quantum numbers are determined to be JP = 1+ by ruling out 0-, 1-, 2+ and 2- assignments at more than 9.7σ, confirming the evidence from Belle. The LHCb analysis establishes the, so called, resonant nature of the observed structure in the data, and in this way proving unambiguously that the Z(4430) is really a particle.

They measure it to have:
Mass:  4475 ± 7 MeV
Width:  172 ± 13 MeV
Amplitude fraction: (5.9 ± 0.9) %

http://en.wikipedia.org/wiki/Exotic_hadron
 
LHCb confirms that the Z(4430) state observed by the Belle collaboration is a particle. It must be formed of at least four quarks.
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Do they know which four quarks are involved?
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Heres a nice little summary of a fantastically under-appreciated insight in theoretical physics, which can be summarized by the simple slogan: Gravity is Yang-Mills Squared.

This is a prime example, and a relatively easy one to explain at that, of the stark connections between the two big frameworks of fundamental physics, gravity on the one hand and Yang-Mills theory describing the remaining 3 forces on the other. These kinds of connections are what puts theoretical physics in such a fascinating and exciting position. Despite the fact that the master theory that would fully explain these connections remains out of the reach of laboratory science, its impossible to study these established frameworks in any depth without noticing some of these dramatic clues lying around. 

Explaining such "coincidences" should be a primary target of any putative master theory. String theory actually provides quite a bit of intuition and understanding to back these relations – roughly it corresponds to the fact that a closed string (associated with gravity) is essentially the same as two open strings (associated with Yang-Mills forces) joined into a loop. The relationship gets more complicated beyond the tree approximation, and it will certainly be more complicated in any configuration that could fully reproduce the richness of the world around us, but the point is that these ideas have helped to distill some of the essential connections between the two seemingly distinct kinds of forces. (Further reading: http://arxiv.org/abs/1312.1326 )

Explanatory power is the key benchmark for any prospective theory of physics, so if nature utilizes some completely different framework it should be possible to find it eventually, and derive equally good or better explanations for some of these features. However that may not be the case, and in the meantime it should surprise no one that the field continues to focus its energy on the ideas that produce such useful results and understanding.

I hope that further research will turn many more of today's "miracles" into tomorrows derived facts, and encouragingly, the list of miracles is still intimidatingly large.
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There are a few more striking ways in which string theory insights have led to advances in pure QFT. I am collecting pointers and links to such here: http://ncatlab.org/nlab/show/string+theory+results+applied+elsewhere 
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Theorist David Tong does on awesome 30-minute summary of what we know about early universe cosmology in Wonders of the Big Bang, his talk for +The Institute of Art and Ideas (IAI). He explains the basic method of using particle models to predict the spectrum of the CMB, and describes various phase transitions that occurred during the first moments of the universe. He does a good job delineating what is actually established by experiment, especially by the Planck satellite most recently, versus what is speculative. He also alludes to the important distinction between conservative speculation versus more dramatic and assumption-ridden speculation.

Whats especially promising and exciting about this whole field is how it directly connects to extreme regimes of the universe that are otherwise pretty infeasible to probe with particle experiments. The big bang clearly isn't repeatable by humans, so obviously there is a fundamental limit of science we're up against here, but speculative models that attempt to complete the account from the Standard Models perspective can still make predictions that will be tested by more detailed CMB measurements, at least up to a point.

A good description of the inflationary period seems to require use of a scalar potential – the inflaton – and so in broad terms this may be related to the Higgs mechanism which was just verified last July. While we can't say for sure if there is any useful relation to draw between them, its certainly possible that we will one day understand a common origin for these two pieces of information about Nature's scalar sector. (Michio Kaku was once rightly called out for sloppily conflating the Higgs with the Inflaton on TV, which is certainly wrong, but the potential connection is well worth pondering.)

Steven Weinberg's book The First Three Minutes deals with the same subject, and its supposed to be really good.

The bottom line is the universe's baby pictures have a lot to tell us about the behavior of this quantum vacuum at much higher energies, which is where the big mysteries lie.

#sciencesunday
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David is a great physicist and fantastic at explaining stuff. I am looking forward to watching the clip.

And yes, The First Three Minutes is a true classic. It's also got one of the great Weinberg downers of all time as an ending. You should read it!
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 +Matt Strassler has an awesome series of posts on the strong force, part of a series called Quantum field theory, string theory and predictions. It takes place at the intersection of two independently interesting questions in high energy physics: First, how to turn the abstract formulation of the strong force into actual predictions for particle experiments (the former is relatively simple to understand and state for any physicist, but the latter is extremely difficult and computer-intensive to obtain). Secondly, to what extent are the frameworks we use – QFT and its theorized extension, string theory – understood, well-defined and predictive?

Matt has just completed Part 6 of the series. If you only want to read about the details of the strong force calculations, you might concentrate on parts 4 and 5. Of course, I highly recommend beginning at part 1 and reading the full exposition on quantum field theory, string theory and predictions:

http://profmattstrassler.com/2013/09/23/quantum-field-theory-string-theory-and-predictions/ , or
http://profmattstrassler.com/2013/10/07/quantum-field-theory-string-theory-and-predictions-part-4/

[In the image, I included two of the graphs from Part 4 that are among the most important and interesting in strong force phenomenology. The first shows some experimental scattering data that currently cannot be predicted by the theory of the strong force, quantum chromodynamics or QCD. It's the fraction of proton-proton collisions that are elastic – producing no new particles – as a function of collision energy. The second chart shows something that can be calculated to great accuracy from theory: the masses of various hadrons. The horizontal lines are the measured values whereas the nearby colored dots correspond to different numerical implementations of the same simplified model, involving just the 3 lightest quarks and all 8 gluons. However, as described in the text, actually extracting these predictions from the theory is incredibly complicated and difficult.]

To get a proper sense of where we are today in our quest to understand nature, its just as important to understand the limits of our knowledge as it is to understand what we definitely know. If you only read about the incredible successes of the Standard Model – and they really are spectacular – you might be surprised by just how much of quantum field theory, and even the Standard Model in particular, remain shrouded in mystery. This doesn't tend to come through the pop-sci media prism nearly well enough. In particular, it has been most heavily confused by the people who want to dismiss string theory in the name of "science" and "skepticism" by denying that it predicts anything, while implicitly holding up modern quantum field theory as the pinnacle of predictivity. The problem with this caricature is that it distorts the truth in two different ways, it exaggerates the predictive challenges associated with string theory, and second it completely sweeps the analogous challenges in QFT under the rug. So it's quite refreshing to see a real scientist and expert on particle physics standing up, calling out the misleading rhetoric, and shedding light on the neglected facts.

One very direct parallel between the predictive challenges of QFT and string theory is the major role played by the standard approximation techniques, called perturbation theory. Most of what we know about both frameworks comes from this approximation method. At the same time, both frameworks have some really important aspects that are not captured by it, as well as some partial methods to go beyond it. The basic idea is straightforward enough; there is a quantity called the coupling constant that in a precise sense controls "how strongly interacting" the theory is. The theories are perfectly solvable at zero coupling, and as long as the coupling is small, the system can still be well-described in perturbation theory by including some of its infinite number of corrections. When the theory is weakly-coupled the corrections get progressively smaller in general, which is why the perturbative approximation works.

The value of the coupling constant also effectively depends on the distance scale. The electroweak forces are, as the name implies, weakly coupled. This is why the electroweak theory has had such incredible success making verified predictions using perturbation theory, culminating with the Higgs boson last July. It's also very important that the electroweak forces become more weak at longer distances. So the breakdown of this perturbative description lies somewhere in the very high-energy / short-distance regime. But the strong force is a whole different animal, and in this case that perturbative success story I just told you is turned on its head. The strong force becomes more weakly coupled at short distances. So we can make very precise predictions for very high-energy scattering experiments, but at longer distances and lower energies we loose control of it completely. This de-facto means that we can't really make meaningful predictions for a whole range of situations that actually matter in practice. In string theory we have the same basic challenge: the theory can be weakly or strongly coupled, and most of the direct knowledge comes from the weakly couple regimes.

There is another major aspect to the comparison with string theory that Matt touches on a little bit, but could use some elaboration. Namely there is a crucial difference between a framework and a model. A framework is the broad mathematical structure that describes the real world, but is also general enough to describe other worlds like ours, with the the same basic principles, but different precise properties. In order to make any predictions, we need a framework but we also need a model, which amounts to making some choices, and then at this point we get to actually making predictions. Overall, the whole backlash against string theory you see these days is based on comparing string theory to the standard model. But thats the wrong comparison; the correct comparison is between string theory and quantum field theory. Both of these frameworks accommodate such a wide range of phenomena that its difficult to come up with any completely general prediction. But thats only if you refuse to specify a model. When the Standard Model was written down, a specific kind of guess was made about what kinds of matter exists, and how it interacts. This model comes from a framework that could be branded "not even wrong" by today's commentators, since there are an infinite number of quantum field theories, and in complete generality they predict essentially nothing. But in neither case is that any barrier to making predictions. (This is the main message of Part 2.)

This confusion between models and frameworks actually stems from the uniqueness of string theory, but this uniqueness isn't a negative if your goal is to learn something about nature. Just like quantum field theory needs a specific model to make any predictions, the same is true for string theory. But unlike QFT, there is only one string theory, so your choice of model is in reality a choice of configuration, (or 'vacua', or 'regions of moduli space'). Some configurations are difficult to analyze, just like some regions of QFT, but a great many are very well-understood and can and do make many predictions for particle physics. This framework / model distinction is also crucial for framing the very problem string theory exists to solve. Namely that the short-distance breakdown of quantum general relativity is the main problem today that cannot be solved within the framework of quantum field theory. This is fundamentally different from the many shortcomings of the SM that are expected to be solved by new models, without the need for a whole new framework, like for example neutrino masses, dark matter, or the cosmological matter/antimatter asymmetry. But generalizing to a whole new framework is a totally different matter. The scale of these problems is wildly different, and so are the associated challenges. It's no wonder people get bent out of shape about theoretical physics if they haven't understood this difference. That is also, in a nutshell, the reason for the interest in string theory: its the framework that can produce realistic models and is powerful enough to fully overcome this main hurdle.

For more in-depth discussion about the framework / model distinction in light of history and string theory, I highly recommend this great writeup by +Urs Schreiber

http://ncatlab.org/nlab/show/string+theory+FAQ

Overall, these kinds of issues have come up before in science. There is no doubt that the challenges are daunting, but thats just life. Nobody ever claimed solving these problems was supposed to be easy. If its hard to make a prediction, thats a reason to work harder, not run around yelling about a "crisis in physics". And moreover many of these challenges are directly related to why these frameworks are so interesting and so effective. Much of the beauty of QFT lies in how diverse its actual implementations are, even just in the ones Nature actually uses! By the same token, most of the criticism of string theory has to do with this same richness and variety, but it is still a completely rigid framework that can be very predictive in practice. Overall you can't help but get the impression that people want something that is simpler and easier to understand, but the frameworks that are robust enough to describe Nature tend to be a bit more complex and a bit more interesting. As Matt expertly demonstrates, that certainly holds true for quantum field theory.

#sciencesunday
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Yeah, as I said, there are correction terms for the non-supersymmetric case that have been computed. I'll list some references later.
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Cliff Harvey

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Frank Wilczek — Multiversality
If you haven't seen it yet, I recommend this great article by the Nobel-winning theorist reviewing some of the various notions of a "multiverse", how they're suggested by the features of the physical world as we see it, and possible implications for fundamental physics research going forward. Its pretty easy, non-technical reading for the most part, except partially the last section.

This strikes me as a particularly timely review, given the widespread interest in the ideas, and the frequent confusion caused by different incarnations of multiversality going under the same name. Also because we seem to be reaching the point when many physical questions may inevitably have environmental answers; i.e. not understandable from deeper principles but from happenstance and from the requirement of supporting intelligent life. It therefore becomes increasingly important to ask what other kinds of environments may possibly be supported within the same physical arena. That may help us figure out which questions admit such an anthropic explanation, and by extension, which have any hope of being answering meaningfully at all.

Here I'm grateful to Wilczek for articulating the appropriately nuanced response to this dilemma that has long seemed necessary to me: You have to be prepared to accept that some questions may be anthropic in nature, but on the other hand you also can't be too quick to invoke anthropics and choke off other possible explanations while they are still viable too. Its a fine balance that may never be completely settled and agreed upon.

What is frustrating to me about this situation from a cultural perspective is how its exploited as ammunition by some voices who want to tear down theoretical physics as a whole, as if everyone involved is giddy at the fact that distinguishing (and falsifying) different models is becoming increasingly hard. There is simply no avoiding these difficulties now that it takes a $10 billion experiment to advance the energy frontier. Don't like it, and you may have to move to another universe. This difficulty does not at all diminish the theoretical knowledge we've gained about physical frameworks: conditional "A implies B" statements that define a map of consistent physical ideas, and possible extensions of the experimentally established theories, while ruling out enormous swaths of "word-level ideas" as senseless or otherwise unviable. The ideas theorists like to play with these days, like supersymmetry and string theory, would not attract anywhere near the interest they do if we didn't understand in such detail how horrendously constrained the problem actually is. Thats why the growing cottage industry, lead by people like Peter Woit, dedicated to tearing down such ideas are not, as they claim, advancing skepticism and scientific ideals. On the contrary, by trying to obscure the reasons those particular speculative extensions are interesting, they also undermine the knowledge that forms the foundation for the most established and wildly successful scientific principles and theories. They are therefore, in my view, just another part of the anti-scientific sentiment these days. Everyone agrees experiment has the final word, but until something is falsified, it just doesn't make sense to abandon the frameworks that are by far the most coherent with everything we know.

Anyway, the anthropic principle and the related different kinds of multiverse suggested by some physical mysteries will definitely be playing a huge role in theoretical physics over the next century. Overall, that may mean diminishing returns, and likely disappointment for those hoping for another really disruptive revolution. But at the end of the day, we can only ever see some fraction of the physical reality that exists out there. That's the essence of multiversality, and while its a slightly sad thought, I'm nothing but excited to see how much we can actually learn.

Abstract: Valid ideas that physical reality is vastly larger than human perception of it, and that the perceived part may not be representative of the whole, exist on many levels and have a long history. After a brief general inventory of those ideas and their implications, I consider the cosmological "multiverse" much discussed in recent scientific literature. I review its theoretical and (broadly) empirical motivations, and its disruptive implications for the traditional program of fundamental physics. I discuss the inflationary axion cosmology, which provides an example where firmly rooted, plausible ideas from microphysics lead to a well-characterized "mini-multiverse" scenario, with testable phenomenological consequences.
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Hey Cliff, seems there is a typo right in the first line (the headline in boldface): you have "Universality" where you crucially mean "Multiversality". Unless I am missing some subtlety, that is...
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+Lawrence Lessig on organizing against institutional corruption
Its frustrating that for all the energy we see invested in political issues in the US, so far only a tiny fraction has been effectively focused on the central problem underlying essentially all of them: namely the system of private funding for public political campaigns. This would-be democratic republic is dominated by a transactional model of politics; a politics-by-auction. Numerical and anecdotal evidence of this situation is overwhelming, for example by the 93% correlation rate between winning the “money primary” and winning a House Congressional race. [1]

But this frustration is also what strikes me as precisely a cause for optimism, because it seems as though only a comparatively small fraction of the political energy that exists in the country would need to be refocused in order to actually make headway on the issue. The awareness seems much higher now. The signs of the problem are much more jarring and unavoidable. The understanding that campaign finance is a prerequisite for any other sane policies is increasingly obvious.

So I don’t think it is at all fantastical to talk about actually addressing this problem anymore. Some kind of public financing system would be the most direct solution, involving either small dollar donations amplified by public funds, or based on publicly funded “democracy vouchers” that citizens could give to candidates as they see fit. These kinds of reforms can be legislated, and they are the focus of Lessig and the RootStrikers, among other groups. Another class of approaches is the kind pursued by Wolf-PAC which is to press for Article V resolutions at the state level to amend the Constitution. This may be an important option to keep available, particularly given that the Supreme Court’s warped view of the first Amendment could lead them to strike down any public financing legislation as “unconstitutional limits on free speech”. (Sounds like something out of The Onion, I know, but it is exactly what the USSC did to Arizona’s public finance system in 2011.[2])

I don’t know which strategy will eventually be able to get the job done, but I do know that a large number of concerted efforts like these can build on each other. I know that collectively asserting awareness and determination is the first step towards attaining any such ambitious goals. And I now that failure would mean surrendering to an unacceptably bleak future.

So I strongly encourage following some of these organisations and getting involved in some way.

http://www.rootstrikers.org/
http://www.wolf-pac.com/
http://unitedrepublic.org/
https://represent.us/
http://unlimitedcorruption.com/

[1] https://www.opensecrets.org/news/2012/01/big-spender-always-wins.html
[2] http://en.wikipedia.org/wiki/McComish_v._Bennett
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+Cliff Harvey , have you seen any data that describes money in politics, but corrects for incumbency? Like, breaks things down into 'incumbent with more / less money' and 'challenger with more / less money' It seems like it could be a pretty significant data point. Like maybe we're looking at correlated facts that aren't causal.
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Press conference on BICEP2, and other links
Heres the video of the press conference given this monday on the apparent detection of primordial gravitational waves by the BICEP2 experiment. As press conferences go its pretty solidly informative, with lots of details about the experiment but not so many that you get bogged down. It also has some interesting discussion about the theoretical aspects of inflation and with both major co-founders Alan Guth and Andrei Linde participating.

Needless to say, if its confirmed this an enormously important event, and I can't resist commenting on what seem to me like the most exciting implications. First its incredible to have what is really the first direct evidence of a quantum-gravitational process, and in particular a process driven by the mechanism of Hawking radiation. Both of these are things that seem nearly inevitable for any sensible theory of physics based on what we know today, but its still awesome to see them begin to move from the realm of well-grounded theoretical extrapolations into the realm of experimental science.

Even more exciting to me though are the hints by this measurement at grand unification, the possibility that the 3 non-gravitational forces may unify into one. It so happens that the just-measured energy scale of inflation corresponds to exactly the energy scale where the strengths of the 3 forces become about the same, at some 10^16 GeV, if you extrapolate them far beyond the energies that accelerators probe. This kind of of possibility has been the wet dream of particle theorists for many years. The hints towards such a scenario are indirect, but the fact that there is now one more indirect hint towards exactly the same energy scale is extremely tantalizing, and I feel more confident saying this now that some well respected theorists have concurred on this point. In the coming years, better measurements of the primordial B-modes will surely have something useful to say for building models of inflation, and I'd especially be on the lookout for models that can parsimoniously explain the dynamics of inflation together with some aspect of grand unification.

Now if anyone reading this still needs to get up to speed on the very basics of what's going on here, I think +Matt Strassler's articles are perhaps some of the best if you're starting from very basic knowledge:

http://profmattstrassler.com/2014/03/17/a-primer-on-todays-events/
http://profmattstrassler.com/2014/03/18/if-its-holds-up-what-might-bicep2s-discovery-mean/

If you have a bit more of a head start on the basics, there is an awesome article by Liam McAllister on +Luboš Motl's blog that very efficiently covers this measurement and its implications. In particular explaining what is the most interesting model-building constraint thrust on us by this data; the fact that the inflaton field has to be able to move by trans-Planckian amounts:

http://motls.blogspot.se/2014/03/bicep2-primordial-gravitational-waves.html

And here are a couple technical review articles I've read in preparation for this announcement. I'd welcome any other good suggestions:

http://arxiv.org/abs/1402.0526Inflationary Cosmology after Planck 2013
http://arxiv.org/abs/0907.5424TASI Lectures on Inflation

Finally, the last big message that I take away from this event is that nature doesn't give a damn if it's taxing on our intuition. Many commenters in recent years have expressed fervent opposition to inflation and other ideas because they don't like that it tends to produce other universes, and similarly misguided reasons. Many of these voices have failed to distinguish a proper scientific skepticism, which is to listen to nature and be weary of ideas that fly in the face of established physical principles, from a "skepticism" that is merely a general resistance to ideas that sound outlandish from a human's intuition. Its certainly not a bad thing to propose a model that turns out to be wrong, but some of the models of the early universe that have just been falsified were motivated by exactly these sorts of feelings. With respect to those cases, this finding seems like one more indication from the universe that these attitudes may not be a useful guide to understanding how things work fundamentally.

To quote Liam McAllister, we learned this week that "the tensor fluctuations write quantum gravity on the sky," and that is definitely something worth celebrating.
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Cliff Harvey

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I'm really excited about the possibilities for scientific computing in Haskell. Heres one inspiring example by +Gabriel Gonzalez, an all-atom protein search engine.

I've finally gotten around to learning the language, and its just fantastic. It really couldn't integrate any better with a mathematical approach to problem solving. Programs are just functions (and functors) so its only natural to want to reason about them and define them that way. Haskell seems like the most direct, elegant and useful way I can imagine to do that, at least for what I want to do.

This was explained really well by +Mark LentcznerHaskell Amuse-Bouche

I'd love to see any other cool applications, or generally any instructive Haskell examples, especially with a math or physics bent.
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Interesting to hear that you are into Haskell. Just in case you are not aware of it, I'll point out the following: there is a kind of refinement of Haskell-type languages, namely "dependently typed" functional programming languages (whereas Haskell is "non-dependently typed") such as "Coq" and "Agda" (http://ncatlab.org/nlab/show/Coq). That little extra of generality turns out to have a dramatic effect: these dependently typed functional programming languages secretly (as was realized just a few years back) "run homotopy type theory". You will have heard me mention this elsewhere a few times (http://ncatlab.org/nlab/show/Homotopy+Type+Theory+--+Univalent+Foundations+of+Mathematics). This is the "brave new foundations" of mathematics that is all based on the "gauge principle", in a precise sense, and which naturally interprets at least a good chunk of modern physics (http://arxiv.org/abs/1311.1172).

I am just saying: if you are into Haskell, you are just one step away from entering into some really deep fascinating territory.
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Videos: lectures, interviews, panels  - 
 
Ed Witten igniting the second superstring revolution, 1995

This is fantastic bit of history pointed out to me by +Dylan Allegretti on my stream. Witten gives an overview of the arguments connecting various superstring theories with each other and with 11-dimensional supergravity using the BPS property and dimensional reduction.

Quite a gem, and its breathtaking to watch, even all these years later.
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I had the same question. While I never got first-hand information, it
seems clear from the video itself that the talk was given not long
after the famous article "String theory dynamics in various
dimensions" (http://ncatlab.org/nlab/show/M-theory#References)
appeared, because that's what Witten is talking about in the video,
and clearly (as the discussion half-way through the video shows) the
audience is both expert and at the same time apparently hears all this
for the first time. So I suppose the video is from 1995.

Why it was suddenly uploaded a few weeks back, I have no idea, but
maybe somebody else here has.
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Mathematics  - 
 
Supersymmetry in the foundations of mathematics.

+Urs Schreiber is partly responsible for the massive overflow of my reading list.

See also: https://plus.google.com/u/0/108081058828040288656/posts/KRbZ4znef7a
 
Supersymmetry in the foundations

As we see amplified these days, homotopy theory,  instead of being the complicated edifice as which it was historically obtained, is actually simple in that it is foundational. That's the point of the new "univalent foundations" (http://ncatlab.org/nlab/show/Homotopy+Type+Theory+--+Univalent+Foundations+of+Mathematics):

homotopy theory follows from formal logic the moment you stop insisting that you can decide if two things are actually equal and admit that you can only provide an explicit equivalence that exhibits the equal-ness. (What physicists call a gauge equivalence.. )

Algebra in homotopy theory is homotopical algebra, and in a way the most fundamental object here is the sphere spectrum, the free commutative infinity-ring on a single element. The sphere spectrum is in homotopy foundations what the integers is in traditional foundations.


Recently Kapranov (based on some pre-history of thoughts that are hard for me to track down precisely) amplifies a simple but striking observation (http://ncatlab.org/nlab/show/super+2-algebra#References):

grading over the sphere spectrum is supersymmetry.

More in detail: a commutative oo-ring whose oo-group of units is graded over the sphere spectrum is a homotoy-analog/refinement of a superalgebra (http://ncatlab.org/nlab/show/super+algebra#AbstractIdea)

Hm, you think, so which commutative infinity-rings are graded in this way over the sphere spectrum?

Just about a year ago Sagave gives a striking reply to this: every single one is, and canonically so (http://ncatlab.org/nlab/show/infinity-group+of+units#AugmentedDefinition).

In summary, there is a remarkable piece of magic that is happening here, magic in the sense that it opens our eyes to a truth that has been there all along without us noticing it: supersymmetry is right there in the new foundations. It's inevitable.

Hints of this have been seen all along of course. It is standard among mathematicians to praise the role that the idea of supersymmetry has played in pure mathematics, quite independently of its role in physics. Notably index theorems tend to have their most natural formulaton in superalgebra.

Hm, index theorems? What is an index theorem? An index theorem is the characterization of a push-forward in a cohomology theory. A cohomology theory, in turn, is just the theory of maps into a commutative infinity-ring. And there the circle closes.

For instance start with the abelian 2-group B U(1) of ordinary line bundles. Its group ring (meaning: infinity-group infinity ring over the sphere spectrum) contains an element called the Bott element, quotienting that out yields the commutative infinity-ring known as KU, the one that gives the cohomology theory known as ordinary complex K-theory .

KU = S[BU(1)][Bott^-1]

(This is Snaith's theorem http://ncatlab.org/nlab/show/Snaith+theorem ).

Now what is the infinity-group of units of KU? That's the 2-group of super line 2-bundles.

http://ncatlab.org/nlab/show/super+line+2-bundle

In some disguise (see the references at this link) this has been known for ages. This is why supergeometry is such a powerful tool in K-theory and index theory. But here we see that this nice "technical trick" as it may seem is but a shadow of something very deep, with "very deep" in the technical sense: just a handful of lines of code above the very univalent foundations of mathematics.

Kapranov combined with Sagave shows us that commutative algebra in homotopy theory is automatically and necessarily, in a "god given" way: superalgebra.

And if you have read this far, maybe check out if you can lend a hand here: http://nforum.mathforge.org/discussion/5027/super-2lines-and-sphereaugmented-units-of-mu/#Item_1
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Education
  • Worcester Polytechnic Institute
    Physics
Basic Information
Gender
Male
Story
Tagline
I love high energy physics, computer science and giant robots
Introduction
Above all, Im passionate about physics. More generally Im interested in furthering understanding of this world at all levels, from particle physics to economics to galactic superclusters and everything in between. I have an artistic side I once cultivated aggressively but has somewhat fallen by the wayside. My inner artist/musician is howling to get let out soon.

As a physics major at WPI, I did a couple major research projects on quantum information theory, specifically on proofs of Bell's theorem involving 4 and 5 qubits. Those projects heavily shaped the way I view physics in general, and its deep foundational issues in particular. Despite the difficulty of the subject, I am convinced there is much more confusion than is necessary, as sloppy reasoning and explanations persist.

At the moment Im mostly spending my time learning quantum field theory and string theory. I am consistently amazed by the unity of physical and mathematical logic, and as I've studied the structure of this logic I've inexorably gravitated to the stringy school of thought. Despite the challenges, it seems to me an essentially indispensable set of puzzle pieces that allow the whole structure to make sense. It appears so deeply enmeshed that extrication just does not seem very likely. But, as a scientist, I of course try to challenge any presumptions of mine aggressively.

Ill forever be a theorist at heart, but I also want to find a rewarding way to use my skills for something more down to earth. I think becoming a better computer scientists may be one of the better ways for this to happen.

And I believe that those of us awake to the challenges facing the human race – especially intellectuals, anyone who analyzes things systematically – has a certain obligation to actively stand for the truth and what is right. As a US citizen Im especially focused on the issue of campaign finance as fundamental to all other political problems in the US. 

"There are a thousand hacking at the branches of evil to one who is striking at the root."

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