Planet Musings

September 08, 2008

Steinn SigurðssonNitaly?

Steinn SigurðssonNASA rumblings


NASAwatch has a series on interesting posts on Mike Griffin, the Shuttle, its successor and a recent leaked e-mail.
Read if you deeply care about NASA funding and medium term policies and funding issues.


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Steinn SigurðssonCarnival of Space #69

Mark Chu-CarrollDES Encryption Part 1: Encrypting the Blocks

As promised, now we're going to look at the first major block cipher: the DES. DES stands for "data encryption standard"; DES was the first encryption system standardized by the US government for official use. It's an excellent example of a strong encryption system; to this day, while there are several theoretical attacks, there's no feasible attack on a single DES-encrypted message that's better than brute force. The main problem with DES is the shortness of its key: only 56 bits, which makes it downright practical to implement brute-force attacks against it using today's hardware.

DES works with 64 bit blocks, and a 56 bit key. As an interesting aside, there are some serious questions about just why the standard key was 56 bits. Officially, the key length is 64 bits, but during the standardization process, the key was modified at the request of the NSA so that 8 of the bits were used as parity checks - that is, as extra bits that could be used for checking the validity of a key. 8 bits for parity checking on a 56 bit key is really overkill - in fact, putting parity checks into the key at all is really rather questionable. There's been a lot of speculation that either the NSA knew some kind of trick that could be used against a 56 bit key, or that 56 bits put the encryption within the range of what they could crack using a brute force attack. But no one has ever admitted to either solution, and as far as I know, no one knows of any way that a 56 bit key could have been feasibly cracked using brute force with the technology of the time.

Anyway - getting past the politics of it, it's still a really interesting system. It's a rather elegant combination of simplicity and complexity. It's got a simple repetitive structure based on lookup tables, which gives it its deceptive simplicity; but those lookup tables are actually an implementation of a very complex non-linear discrete mathematical system.

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Cosmic VarianceCalling a Crackpot a Crackpot

As John has already described, on Wednesday, the Large Hadron Collider will circulate protons for the first time, marking a critical milestone on the road to the hopefully imminent discovery of new physics. Physicists the world around are tingling with anticipation, looking forward to the discovery of the mechanism of electroweak symmetry breaking, and wondering if this will be revealed to be due to supersymmetry, extra dimensions, new gauge interactions, or something as yet unthought-of.

None of them are worried about the end of the world.

Not that you’d know this from the attention that a few crackpots have received in media the world around. The lawsuit filed by biochemist Otto Rössler, and the restraining orders sought by Walter L. Wagner and Luis Sancho have been covered by almost every major newspaper, and while they eventually get around to the views of people who actually know what they’re talking about, the pressure of trying to appear balanced often leaves one with the impression that there is a genuine debate on this topic (for a particularly empty example of this, take a look at this Guardian snippet).

Saturday’s London Times article by Joanna Sugden does do a little better though. It isn’t perfect; for example it contains the claim that Rössler

had deduced that it would be “quite plausible” to conclude that black holes resulting from the collider experiment “will grow exponentially and eat the planet from the inside” across a devastating four-year period of decay.

which seems misleading, since “deduce” means “arrive at (a fact or a conclusion) by reasoning; draw as a logical conclusion”, and hardly seems appropriate in this case. Nevertheless, I did enjoy the final couple of paragraphs, particularly the plainly stated and clear statement that

The saner voice of science is shining through, however, …

That’s right - these crackpots are insane! It feels good to say it plainly every now and again. And as an example of this saner side of science, the Times then goes on to quote Valerie Jamieson, friend of the blog and snowmobiler extraordinaire.

as Valerie Jamieson, deputy features editor of New Scientist, explains on her blog.

“Scale the cosmic ray sums up to cover the 100 billion stars in the Milky Way and the 100 billion galaxies in the visible Universe and you find that nature has already made the equivalent of 1,031 LHCs. Or if you like, 10 trillion LHCs are running every second. And we’re still here.”

Ignoring the little issue with superscripts (1,031 isn’t a particularly impressive number, but 1031 gets your attention), it’s nice to see an article in which crackpots are called crackpots and that shows that the author reads the right kind of blog!

Chad Orzellinks for 2008-09-08

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Tommaso DorigoA picture from the CMS control room


Shown below, a picture from the CMS control room taken a minute ago, showing the event display while taking cosmics during a global run, with the solenoid turned on…

I am currently on the day shift, taking care of the CMS tracker. This just means looking at a graphical user interface (GUI) or two, and a few plots on four large monitors, checking that temperatures are stable, voltages remain within bounds, everything is on, etcetera. Most of all, one needs to verify that nothing turns orange or red. If it does, a little Albert Einstein icon can be clicked on the GUI, bringing up a window which guides the user through the checks and actions required to fix the problem. Quite a no-brainer. That is a very welcome feature of the system, since this is my first day of shift, and I have not received a proper training yet.

All in all, things still look a bit obscure to me - the control system is new and today is the first time I see it.  But event displays such as the one above… No explanation necessary: they make a lot of sense to me!

Ars MathematicaTremellius and Naibod

God Plays Dice has a post that answers a question I’ve long had about the Mathematics Geneology Project: just how far back can you go? The answer is 1572, when Immanuel Tremellius and Valentine Naibod advised Rudolph Snellius. Snellius was the father of Willebrord Snellius, who discovered Snell’s law.

Tremellius was a Bible translator who was briefly jailed for being a Calvinist. It sounds like he was forced to move frequently as the prevailing winds for Protestants changed. (This was the early Reformation.) Naibod was an astrologer who had a book banned by the Catholic Church. An astrological prediction told him that his life was in danger, so he tried holing up in his house until the danger passed. Since the house showed no external signs of life, thieves thought the house was abandoned and broke in. Discovering Naibod, they murdered him. Apparently astrology works after all.

The Geneology Project has a page dedicated to what it calls extrema. I would support a campaign to rename the Guinness Book of World Records the Guinness Book of Extrema.

Cosmic VarianceGuest Post: David E. Kaplan on the LHC on the History Channel

You may have heard that there’s some sort of big science machine scheduled to turn on in Europe. Very soon, in fact: first (official) beam at the Large Hadron Collider is supposed to occur around 9:30 Central European Summer Time (3:30 a.m. Eastern, if I have done the math correctly) on Wednesday. Call it Tuesday night, for us West Coasters.

The folks at the History Channel recognize the importance of the event, and they’ve recruited Friend of CV David E. Kaplan, a particle theorist at Johns Hopkins, to host a special show entitled the Next Big Bang. And we, of course, have recruited David to tell you a little about the show. (In the picture, David is the one wearing glasses.)

(p.s. This LHC game is surprisingly educational. Via DILigence.)

—————————————————-

Hello All. This post represents shameless advertising for a television program which I am hosting on the History Channel this week. The show is a one-hour program about the Large Hadron Collider (LHC) experiment outside of Geneva and will air the day before the first proton bunch circulates the entire 27 km ring (September 9th, 8pm/midnight EDT/PDT, 7pm/11pm CDT, 6pm/10pm MDT). The show will visually describe the complexity and scale of the experiment and some of the potential discoveries we hope to make (the Higgs particle, supersymmetry, dark matter, extra dimensions).

For many reasons this is an amazing moment in the history of science (many which have probably been repeated on this blog before). [Indeed -- ed.] There are roughly 75 countries with at least one institution (university or lab) which has contributed to the construction of this machine. The list includes strange bedfellows: India and Pakistan, Israel and Iran and the United States, Greece and Turkey, Russia and Georgia, all of western Europe, most of eastern Europe, some of northern Africa and south America, Japan, China, S. Korea, etc. This unlikely team has constructed the biggest single machine in the history of the planet after over 20 years since the first plans were laid. At 10,000 scientists, this project represents the modern day pyramids.

What gets me though is that high-energy physics have not really seen a discovery that has directly shaken the standard model of particle physics for thirty years. The discovery of neutrino masses were a surprise, but fit nicely in the standard model if there is new physics at (unreachably) high energies. Dark matter was certainly a surprise, but could potentially only couple to us gravitationally, and again not uproot the standard model. The same can be said about dark energy to an even greater extreme. However, an unexpected particle has not been discovered since the seventies. The seventies were the time that not only the standard model was discovered experimentally, but its underpinnings, quantum field theory, was confirmed as the correct underlying description of all matter interactions (other than gravitational). The (perhaps, not so) amazing thing is, the surprising discoveries stopped by the end of the seventies, and we have been confirming the standard model even since.

The implication is that almost the entire particle physics community, both theorists and experimentalists, who are actively working on LHC physics have never been involved in a surprising discovery. This large community of scientists have been building up to this moment for their entire careers. The scale of these experiments are such that one can really only expect one discovery per generation, and this one is ours.

The show is not perfect, but there are some stunning analogies. I did not write the show, but I fact-checked most of it. There is no attempt to scare the viewer with ‘disaster scenarios’, but simply an attempt to cover what the physicists are constructing and what they expecting or hoping to discover. There is also a bit of history of particle physics.

Enjoy the show. I’ll stay connected so I can answer any questions that come up.

photo by Maxmillion Price, copyright CERN

Insertion of the tracker into the CMS detector. Photo by Maxmillion Price, copyright CERN. Click for full size.

n-Category Café 8

Next Saturday I’m going to the University of Glasgow to give talks about some of my favorite numbers: 5, 8 and 24. Different numbers have different personalities, as I try to explain here:

If you can’t attend, you can still pretend. So far I’m only satisfied with my talk on the number 8 — click on the title below to see the transparencies…

8

Abstract: The number 8 plays a special role in mathematics due to the “octonions”, an 8-dimensional number system where one can add, multiply, subtract and divide, but where the commutative and associative laws for multiplication — ab=ba and (ab)c=a(bc) — fail to hold. The octonions were discovered by Hamilton’s friend John Graves in 1843 after Hamilton told him about the “quaternions”. While much neglected, they stand at the crossroads of many interesting branches of mathematics and physics. For example, superstring theory works in 10 dimensions because 10 =8 +2 : the 2-dimensional worldsheet of a string has 8 extra dimensions in which to wiggle around, and the theory crucially uses the fact that these 8 dimensions can be identified with the octonions. Or: the densest known packing of spheres in 8 dimensions arises when the spheres are centered at certain “integer octonions”, which form the root lattice of the exceptional Lie group E 8 . The octonions also explain the curious way in which topology in dimension n resembles topology in dimension n+8 .

If you can attend, I hope you do! I think Eugenia Cheng, Simon Willerton and Danny Stevenson may be there… and surely Tom Leinster will, since he’s organizing the show. Details on the schedule can be found here.

By the way, I don’t like how the newspaper suggests I said schoolchildren have a “limited” understanding of mathematics. Did I really say that? Of course it’s true in some sense, but it misses the point in a mean-spirited way. It’s a bit like calling a baby “a short, weak kid who cries a lot and never talks”.

September 07, 2008

Scott AaronsonOn mathematicians and mountains

Luca and Terry Tao have already reported the tragic loss of the brilliant probabilist Oded Schramm in a hiking accident.  I didn’t know Oded, but I knew some of his great results and was deeply saddened by the news.  My heartfelt condolences go out to his friends and family.

It was two years ago that we lost Misha Alekhnovich, who I did know, in a whitewater rafting accident.  Other mathematicians and scientists lost in similar ways have included Heinz Pagels, Jacques Herbrand, Raymond Paley, Krzysztof Galicki, and Erik Rauch.  The teenage Einstein very nearly died while hiking on a mountain near Zurich.  I have more than one irreplaceable colleague who’s repeatedly courted death on the ski slopes.

I’d like to issue a plea to any mathematicians and scientists who might be reading: please go easier on the extreme outdoor activities.  Let those who live for such things demonstrate their daring by gambling their lives; those who live for the ages can find safer recreations.  The world needs more nerds, not fewer.

BackreactionInterna II

While my wife is busy with all kinds of last-minute preparations for the conference tomorrow, I've spent the weekend unpacking the last bunch of boxes. Normal life hopefully will resume soon, including an occasional contribution to our blog...

In the meantime, just days before the first beam is supposed to go around in the LHC, I've come across a portrait of physicist Peter Higgs very worth reading in this week's edition of the German newspaper Die Zeit, "Das Teilchen Higgs".

As most of you don't read German, never mind, it's Higgs time in British newspapers anyway: I can refer you instead to the portraits Father of the 'God Particle' by James Randerson in The Guardian of June 30, 2008 , Prof Peter Higgs interview: Smashing atoms at CERN and the hunt for the 'God' particle by Roger Highfield in the Telegraph of August 4, 2008, or The man with the answer to life, the universe and (nearly) everything by Jonathan Leake from The Sunday Times of August 17, 2008.

For a bit more technical background on the prehistory of the "Higgs boson", and the role of many other physicists played in it, check out Peter Higgs: the man behind the boson by Peter Rodgers in Physics World from July 10, 2004, which includes links to all the relevant original papers, or listen to Peter Higgs himself telling the story of My Life as a Boson (recorded on May 21, 2001 at the Michigan Center for Theoretical Physics).

And, of course, Peter Higgs is also on YouTube.





Tag:

n-Category Café Military Research

I just got an email from the U. C. Riverside grants office informing me of opportunities to apply for funding from the Multidisciplinary University Research Initiative. That sounds pretty bland… but the list of topics they’re funding is anything but! You see, this initiative is run by Office of Naval Research — a U.S. government agency that funds military research.

It’s interesting (and a bit creepy) to see what the U.S. military are excited about these days, so I thought I’d show you.

Will we see this stuff put to use in the next war?

Here’s the email:

The Office of Naval Research has released the DOD MURI solicitation for 2009, ONR-BAA-08-019. The program will make awards to interdisciplinary teams in the following 32 topic areas:

NAVY TOPICS

(1) Cellular, Molecular, Genetic and Biochemical Correlates of Training

(2) Removing the Botnet Threat

(3) Machine Intelligence and Adaptive Classification for Autonomous Systems

(4) Highly Decentralized Autonomous Systems for Force Protection and Damage Control

(5) Bio-inspired Autonomous Agile Sensing and Exploitation of Regions of Interest within Wide Complex Scenes

(6) Computational Intelligence for Decentralized Teams of Autonomous Agents

(7) Dynamic Biological Adaptations to the Undersea Light Field

(8) Grounding Language Understanding in Cognitive Architecture

(9) Tailoring Electronic Bandgap of Nanostructured Graphene

AIR FORCE TOPICS

(10) Neurological System-Inspired Multifunctional Materials Design for Autonomous State Awareness against Exogenous Threats

(11) Chemical Energy Enhancement by Nonequilibrium Plasma Species

(12) Ultracold Molecules

(13) Search for New Superconductors for Energy and Power Applications

(14) Complex Nonperiodic Nanophotonics

(15) Multi-Scale Fusion of Information for Uncertainty Quantification and Management in Large-Scale Simulations

(16) Learning Decision Architectures for Intelligent Cooperative Control of Autonomous Systems

(17) Information Dynamics In Networks

(18) Synthesis, Analysis, and Prognosis of Hybrid-Material Flight Structures

(19) Biophotonics: Optical Effects through Nature’s Photonic Control

(20) Fundamental Graphene Material Studies and Device Concepts

(21) Application Software and Data Protection for Untrusted Platforms

ARMY TOPICS

(22) Disruptive Fibers for Flexible Armor

(23) Network-based Hard/Soft Information Fusion

(24) Tailored Stress-Wave Mitigation

(25) Integrated Quantum Circuits

(26) Adaptive Structural Materials

(27) Transformational Optics

(28) Emergent Phenomena at Complex Oxide Interfaces

(29) Application of Systems Biology to Regenerative Medicine

(30) Mechanisms of Bacterial Spore Germination

(31) Opportunistic Sensing

(32) Cyber Situation Awareness

Proposals may be submitted only by univerisites. National labs, industry, and foreign institutions may collaborate, but they may not receive any MURI funds.

White papers (4pp) are strongly encouraged and are due October 31. Full proposals are due January 9, 2009.

It is common for MURI proposals to involve multiple institutions. Considering that the full proposal deadline is so soon after New Year’s, it would be best to nail down your team and your budgets well before the holidays

The solicitation should be available at https://www.onr.navy.mil/sci_tech/3t/corporate/muri.asp

Amusingly, when I clicked on the above link, my web browser warned me against going there, saying the certificate of this site was unauthenticated (or something like that). Visit at your own risk! I have no reason to be especially suspicious, but it made me wonder. Are there known cases of ‘military phishing’ — like a North Korean agency posing as the Office of Naval Research and inviting grant proposals?

I understand some of the topics listed above, but not all.

Graphene is mentioned twice.

I wrote about this substance in week262 after visiting the nanotech labs in Singapore. Some people think it could be used to build transistors that operate 1000 times faster than current ones.

Topic 6, “Computational Intelligence for Decentralized Teams of Autonomous Agents”, reminds me of this article from New Scientist:

Military robots to get swarm intelligence

25 April 2003

Will Knight

A battalion of 120 military robots is to be fitted with swarm intelligence software to enable them to mimic the organised behaviour of insects.

The project, which received funding this week from the US Defense Advanced Research Projects Agency (DARPA), is aimed at developing ways to perform missions such as minesweeping and search and rescue with minimum intervention from human operators.

The project is run by US software company Icosystems, which specialises in creating programs that mimic behaviours found in nature. Their software will use simple rules to co-ordinate complex behaviour among the robots.

“We will be addressing some fundamental questions about control strategies for robotic swarms,” says Paolo Gaudiano, vice president of technology for Icosystems.

The robots’ behaviour has been modelled in a computer environment by Icosystems but the company will now be able to test different approaches in the real world. The 120 robots were built for the US military by I-Robot, a company co-founded by robotics pioneer Rodney Brooks.

I was also reminded of a conversation I had yesterday. I was speaking with some students of a top expert on mathematical physics — classical mechanics, in particular. And, I found out that he’s working with engineers on problems of control theory involving swarms of autonomous agents: like, getting a bunch of robot-controlled vehicles to navigate terrain without human help. As above, the stated applications were very noble, like distributing relief aid.

I’m sure glad they’re not planning anything nasty.

Dave BaconWeather Politics

The lore I heard when I lived in New Mexico was that the reason Gore won the state in 2000 was that there was a snowstorm in the southern part of the state (which is more conservative.) In 2004 there was no snowstorm in the state, and the state went to Bush. If you could control the weather by fixing particular weather in different locations (weather that was not too far beyond the typical weather for the area), I wonder how many electoral votes could you swing?

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Doug NatelsonPackard highlights

Some things I learned at my final Packard meeting:
  • The density of stars in a globular cluster is just absurd - something like 104-106 stars in a volume 10 ly on a side. Wow.
  • The joint between the stem and base of a wine glass is a perfect lens for demonstrating the types of Einstein rings that one sees in gravitational lensing.
  • In the protoplanetary disk phase of solar system formation, elements get mixed on very rapid timescales (like around 1000 years).
  • Bacteria are much better at using 40Ca in their metabolism than 44Ca, and it's not at all clear how this works kinetically.
  • 3-5 million years ago, in the early Pliocene, the global climate is a good test case for comparison with global warming models. Bad news for me: if the trends can really be mapped onto today, the hurricane rate is likely to increase by a factor of two.
  • Using isotopic analysis (!), it is possible to put an error bound on how many people the lions in the Fields Museum actually ate: 41 +- 11. Anecdotal evidence had put the number between 15 and 135.
  • We're all going to be able to get our genomes sequenced very soon, since the rate at which DNA can be sequenced (base pairs per day, for example) has gone up by five orders of magnitude in the last five years.
More later....

Marco FrascaGluon propagator


Notwithstanding a lot of work on lattice computations, the question of the behavior of the gluon propagator at lower momenta does not seem to be settled yet. The reason for this is that there exists a lot of theoretical work, done by very good physicists, that seems blatantly in contradiction with lattice evidence. One of the pioneers of this work has been Daniel Zwanziger . He is a very smart physicist and he has done a lot of very good work on gauge theories. Just yesterday I was reading a recent paper by him on PRD. This is a beatiful paper and there is proof of the fact the the gluon propagator should have D(0)=0 to grant confinement. The argument given by Zwanziger is the following (I copy from the paper):

“We must select the solution to these equations that corresponds
to a probability distribution Q(A^{tr}) that vanishes outside
the Gribov horizon. To do so, it is sufficient to impose
any property that holds for this distribution, provided only
that it determines a unique solution of the SD equations.
Besides positivity, which will be discussed in the concluding
section, there are two exact properties that hold for a probability
distribution P(A^{tr}) that vanishes outside the Gribov
horizon: (i) the horizon condition and (ii) the vanishing of
the gluon propagator at k=0.”

On a similar ground it is obtained that the ghost propagator is infrared singularly enhanced, that is, it goes to infinity faster than the free particle propagator. We see that all the conclusions in this paper rely on Gribov copies and on the fact that fixing the gauge should not be enough for a Yang-Mills field to be completely determined. Gribov’s work has been a reference point for a lot of years working in gauge theories and so it is perfectly acceptable to derive other conclusions from it.

Of course, any acceptable theoretical work must compare with experiment and agree with it. Otherwise is not physics but something else and we, as physicists, can forget it. But in nature a pure Yang-Mills theory does not exists. Gluons interact with quarks and things are not that simple to be understood and compared with theoretical work. So, another approach has been devised using large scale computations on powerful computers. People computed both the spectrum and the propagators in this way. The propagators have been obtained on very large lattices (see here). We have often commented about them and we can give a summary here

  • For the gluon propagator D(0)\neq 0.
  • The ghost propagator is that of a free particle.

We give here the result on the largest lattice (27fm)^4 due to Cucchieri and Mendes

A. Cucchieri, T. Mendes - (27fm)^4

A. Cucchieri, T. Mendes - (27fm)^4

where it is seen immediately that the gluon propagator does not go to zero at lower momenta. But one can think that there could be something wrong on these computations even if we know that have been obtained by three different groups independently. There could be something that was not accounted for. But quite recently Axel Maas proved that things went right without really wanting this. How did he do that? He considered Yang-Mills theory in D=1+1 and showed the for this case D(0)=0 and the ghost propagator is more singular than the free particle case (see here and here). We know as well from ‘t Hooft’s paper that this case is absolutely trivial (see here). Trivial in this case means that there is no dynamics in D=1+1! So, we recognize that a scenario where the gluon propagator goes to zero only happens when no dynamics exists. We can understand here the reasons of the failure of this scenario: People that derived this case have simply removed any dynamics from Yang-Mills theory.

Now, we can come to the question of Gribov copies. They appear to be essentially irrelevant and useless for the understanding of the behavior of a Yang-Mills theory and have induced a lot of fine people to obtain wrong conclusions. It is the very first time that I see such a situation in physics and I hope it will not end proving to be an example of something bigger going to happen.

US/LHC BlogWednesday Expectations

First beam is quickly approaching. For ATLAS. Actually several other experiments have already seen beam (it is hinted that CMS will see something today). But as ATLAS is the last experiment on the ring, it means that we have to wait until the 10th. It is annoying being the last on the ring sometimes.

For the 10th, the beam is only a single beam, so there will be no collisions. But it is still exciting all the same. And what can we expect to see in the detector with single beam? Two things.

One is ‘beam halo’ events. These are muons which have left the beam core and are moving along side the beam. The other is ‘beam gas interactions’ which are when one of the protons in the beam collides with some other particle in the beam pipe (the beam pipe is under vacuum but no vacuum is perfect). Even with these two types of events, we don’t expect to see a lot of hits in the detector. But even a few hits tells us a lot. Single beam is also very useful to help us establish our timing. This means determining when to read-out our electronics relative to when the beam bunch enters the detector. In other words, we won’t be sitting around, bored come Wednesday.

Someone once asked me what ATLAS planned to celebrate with. And the answer is… Champagne, of course. We even have it prepped and ready to go in control room (as seen here). The label reads ‘Break in case of collisions’. Not a problem.

Atlas celebrate

Tommaso DorigoNo Z’ below 1 TeV


New heavy bosons are predicted by several models of physics beyond the standard model. In particular, heavy versions of the Z° boson, called generically Z’ but sometimes distinguished by greek subscripts (Z_\eta, Z_\chi, Z_\psi etc.), might constitute the quickest route to a discovery of superstring-inspired E6 models; and also Kaluza-Klein spin-2 gravitons may appear as a Z’. I won’t describe what those models are about (and besides, I am not the best person to do that), but just mention that many of my colleagues pin their hopes of finding new physics on just such a signature: the production of a new Z’ boson, with its decay to a pair of charged leptons. A pair of muons of several hundred GeV, for instance, is a great discovery channel, because muons cannot easily be mistaken with other final state particles -all collider detectors have an outer shell of drift chambers specifically designed to detect muons, in fact, exploiting the high penetrating power of these particles.

With only a few days separating us from the official start of LHC operations, it is now as good a time as any to take stock with respect to the experimental situation with the search for Z’ bosons. A recent result by CDF, based on 2.3 inverse femtobarns of proton-antiproton collisions produced by the Tevatron accelerator, has pushed the lower limit for the mass of these particles above the TeV. Interestingly, one TeV was a reference point good enough for CMS and ATLAS to produce expectation plots in their technical design reports. Take CMS, for instance: the expected dimuon mass spectrum after just 100 inverse picobarns (about ten times the data that LHC will collect this fall) would present a very narrow, distinctive peak of about 18 events, as shown by the empty histogram over the sharply falling background (shown by the green histogram).

The graph above would be a unmistakable evidence for the production of a new massive neutral particle. Unfortunately, we now know it’s just not going to happen. The CDF result excludes a Z’ boson with mass below 1030 GeV. The analysis is straightforward: having noticed that the mass is measured with the momenta of the two muons, which are obtained from their curvature in the 1.4 Tesla magnetic field, one finds that the mass resolution degrades significantly with dimuon mass, but if one plots the inverse of the mass, this has a fixed relative resolution, making it much easier to search for a signal of unknown mass in a wide range. The data (blue points) is shown in the plot below.

From the very good agreement of all data points with the expectation -which is due to the sum of electroweak production of muon pairs through the so-called Drell-Yan mechanism (yes, that includes the regular Z° boson decay) and background processes due to QCD- it is not too hard to extract direct lower limits on the cross-section times branching-ratio of Z' \to \mu \mu. These are shown below (the red curve) as a function of the hypothetical Z’ mass.

The plot is busy as much as it is colorful. First off, ignore the stretched Brazil flag, and only look at the red curve. That is the upper limit on the cross section, at 95% Confidence Level. That is the result of trying to fit a signal in the histogram of inverse masses, which does not seem to contain any. At 1 TeV, the limit is set at 3.5 femtobarns. Since a SM-like Z’ would have a 4.5 femtobarn cross section, such a particle is excluded. All mass values above 1030 GeV are instead still possible.

The “brazil flag” is then just a prediction of the cross-section limit that CDF could set, a priori computed using the analysis methodology, before looking at the data. The red line wiggles around but stays within the 1-sigma band (yellow).

The phase space of new physics continues to shrink, without any real hint from collider data of the SM becoming inadequate…

Chad OrzelExpress an Opinion, Win a Prize

Sunday's a travel day for me, as I take a tiny little prop plane to the exotic land of Canada, for the Science in the 21st Century workshop. After an hour and a half bent double in a goddamn Cessna, I'll probably be too sore to type, so don't expect much blogging from me.

If you're looking for something to fill the blog-shaped hole in your day, though, you could enter the Millionth Comment Contest ScienceBlogs is running. The lucky winner will get an all-expenses-paid trip to New York to do see cool science-y stuff, and have dinner with a blogger of their choice.

All you need to do is give them an email address, and make a comment. Friday's poll post would be an excellent place for the comment, if you haven't already responded.

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n-Category Café Equivariant deRham Cohomology and Action Lie Algebroids

The trimester program Geometry and Physics at the Hausdorff Institute in Bonnn is over. After a concentration of official activity around July it was getting a bit more relaxed again in August and we could pick up again our “internal seminar” among the program participants. Maybe a bit too relaxed: in the last weeks this internal seminar was attended just by Alejandro Cabrera and myself. But a 2-body seminar can be very useful.

I had mentioned a seminar talk by Alejandro on BV Poisson reduction recently here. Now in the internal seminar Alejandro was looking into the general mechanism of localization of integrals over graded spaces following

Richard Szabo
Equivariant Localization of Path Integrals
arXiv:hep-th/9608068

We talked about the relation of this to BV-BRST quantization. Maybe some of the things we discussed there are too top secret to be shared here for the moment, but I can share the following useful literature that Alejandro tracked down, on the relation between equivariant deRham cohomology and action Lie algebroids, and an interpretation of this in the context of rational approximations to universal -bundles in the sense of L -connections (blog, arXiv).

Given the action of a compact connected Lie group G on a manifold X, there are several closely related but different differential algebra models for the G-equivariant deRham cohomology of X: notably there is the ancient Cartan-Weil model and then more recently there is what is called the BRST model.

It was shown in

V. Mathai, D. Quillen
Superconnections, Thom classes, and equivariant differential forms
Topology, 25(1):85-110, 1986

that the underlying complexes of these two models are isomorphic. Now, both these complexes are obtained as sub-complexes of bigger complexes. In

J. Kallkman
BRST model for equivariant cohomology and representatives for the equivariant Thom class
Comm. Math. Phys., 153(3):447-463, 1993

it is shown that also these bigger complexes are isomorphic.

When Alejandro showed me this bigger complex I said: “hey, this looks like the Weil algebra of the action Lie algebroid of the action of G on X”.

Alejandro quickly demonstrated that this is indeed the case and shortly afterwards also came up with a reference where, up to some inessential difference in language, precisely this statement is demonstrated:

Rajan Mehta
Q-Algebroids and their cohomology
arXiv:math/0703234

Recall what this statement about the Weil algebra of the action Lie algebroid means (I am following the notation and terminology from L -connections :

an L -algebroid with space of objects the smooth space X is a non-positively graded cochain complex g of (A:=C (X))-modules equipped with a degree +1 derivation d g: A g * A g * covering the differential on g * and squaring to zero.

The “quasi free” (namely free just as a graded commutative algebra over A) differential graded commutative algebra CE A(g):=( A g *,d g) is the Chevalley-Eilenberg algebra of the L -algebroid (A,g).

The Weil algebra of the L -algebroid, obtained by throwing in another but shifted copy of g as well as the “locally shifted copy” Γ(TX)[1 ] of C (X) is W(g):=( (Γ(TX) *g *g *[1 ]),d W(g)=(d g 0 σ σd gσ)), where the matrix on the right is supposed to indicate how the differential d W(g) acts on the original generators in C (X)g *[1 ] and their shifted copies Γ(TX) *g *[2 ]. Here σ denotes the degree +1 derivation which restricts to the canonical isomorphism g *[1 ]g *[2 ] on g *[1 ] and to the deRham differential on C (X) and to zero on the shifted generators.

Action Lie algebroids provide examples for this: for g an ordinary Lie algebra acting on an ordinary manifold X by means of a Lie algebra morphism ρ:gΓ(TX), the action Lie algebroid Lie(X//G) comes from the free C (X)-module generated by g concentrated in degree 0, with the differential being the dual of ρ on C (X) and the ordinary Chevalley-Eilenberg differential on g *.

As Alejandro saw, it is a quick computation using Cartan’s formula for the Lie derivative on differential forms to show that the Weil algebra W(Lie(X//G)) in the above sense is precisely the Kalkman/BRST differential that appears as equation (21) in Mehta’s article.

Notice that Mehta follows common fashion and thinks of all things L in terms of -graded supergeometry. I tend to want to not do that, as the Lie-theoretic imagery seems to me to be paramount. But in the end it is just an inessential matter of language and a straightforward exercise to check that Mehta’s shifted tangent Q-algebroid [1 ]Tg in his section 5.2 corresponds to the W(g) above.

Finally a word on the original issue of models for equivariant deRham cohomology and the relavent sub-complexes of the Weil algebra complex:

as recalled and discussed in L -connections

the Chevalley-Eilenberg algebra CE(g) plays the role of differential forms on the -group G integrating g

the Weil algebra W(g) plays the role of differential forms on the universal G-bundle

the canonical morphism CE(g)i *W(g) plays the role of the dual to the fiber injection GiEGBG.

This defines yet another qDGCA, namely W(g) basic=:inv(g)W(g), the algebra of basic forms or invariant polynomials on g as the subalgebra of W(g) which is invariant under those inner derivations on W(g) that cover inner derivations on CE(g).

the algebra W(g) basic=inv(g)W(g) plays the role of differential forms on BG.

And inv(Lie(X//G)) is the Kalkman/BRST model of G-equivariant deRham cohomology on X.

To see this, notice that the only inner derivations [d g,ι t] on the CE-algebra CE(Lie(X//G)) of the action Lie algebroid Lie(X//G) are those coming from contractions ι t with elements t in the Lie algebra g. Hence so are the inner derivations [d W(g),ι t] of the Weil algebra W(Lie(X//G)) covering these. So an element of W(Lie(X//G)) is in inv(Lie(X//G)) precisely if it is annihilated by all the contractions ι t and all the inner derivations [d W(g),ι t] for all tg. This subalgebra is usually denoted inv(Lie(X//G))=(Ω(X)Sg *) G and with the induced differential this is indeed the Cartan model for equivariant deRham cohomology. See for instance page 19 of Mehta’s article.

Finally, I should add a more general word on Mehta’s article. As mentioned here he is interested in groupoids internal to “Q-manifolds”. In the language I am using a “Q-manifold” is the geometric interpretation of the dual of the Chevalley-Eilenberg algebra of an L -algebroid. Hence these are groupoids internal to L -algebroids.

Such internal groupoids correspond of course to Lie algebroids internal to L -algebroids. Mehta calls these “Q-algebroids” and this is what his article is concerned with. The Weil algebra W(g) of an L -algebroid is itself a qDGCA and hence itself a Chevalley-Eilenberg algebra of an L -algebroid which in L -connections is denoted inn(g): the L -algebroid of inner derivations of g. From Mehta’s point of view this is a special case of a Q-algebroid, corresponding to the shifted tangent bundle of the corresponding “Q-manifold”.

n-Café regulars will recall our extensive discussion of the relation between tangents, inner derivations and universal bundles, for instance from More on tangent categories.

Jonathan ShockTakoyaki with Galician pulpo, a first?

Yesterday we had a seminar from a Japanese researcher who is currently doing a postdoc in Chile. After the seminar a few of us headed for dinner to a local restaurant and had the usual, very tasty selection of Galician delights, Pimientos de Padron, Pulpo a la feira, xoubas and much besides. I chatted with the speaker and his wife, also from Japan and when I mentioned that I'd inherited a Takoyaki pan from a Japanese friend who had left Santiago a couple of months back, their eyes lit up and they told me that it had been many moons since they'd had takoyaki. So, I invited them for lunch today for a hands-on takoyaki fest. This was the first time I'd made it, but in fact it turned out rather well and I'm sure to do it again soon. So, this is my/our recipe for takoyaki.

Start off by making a dashi, a Japanese stock, which traditionally isn't as strong as a western stock. Before my guests turned up I made a shiitake stock by steeping a handfull of dried shiitake mushrooms in boiled water. This takes just 20 minutes or so.

When they arrived, the stock was ready and to the dashi (around 275 ml) we added 200 grams of flour, one egg, a pinch of salt, a quarter of a teaspoon of baking powder, a finely chopped spring onion, and a couple of finely chopped shiitakes, previously well soaked.

Take your takoyaki pan, should you be lucky enough to have one (see below), or equivalent and heat it directly over a flame until it becomes very hot. A good takoyaki pan should be as heavy as possible in order to distribute the heat slowly and evenly. Coat the pits in a little oil and spoon in the batter. This should sizzle straight away and start to rise a little. Immediately add a small piece of cooked octopus to each batter section. After a minute or so, take your takoyaki pick and turn the batter and octopus upside down. The bottom of each one should now be spherical.
Homemade Takoyaki
Cook for another minute or so and then put straight on a plate.

For the sauce, mix a few teaspoons of Worcestershire sauce to a few tablespoons of mayonnaise and a dash of soy sauce (really one should get hold of an okonomiyaki sauce, but this is rather hard to come by in my neck of the woods) and spoon it over the takoyaki. Sprinkle the top with dried tuna flakes and enjoy, piping hot!

Though my guests admitted that they weren't exactly as in Japan, they said this was mostly due to the sauce not being quite the same, but they seemed to enjoy them as much as I did, and I'll be sure to make them again.

I'm sure that you could do the same thing with any normal cup cake tin, though you'd have to be careful with the quantity of mix and the temperature distribution, but it's worth giving it a go.

Jonathan ShockLeaving Incheon

I have an intensely busy month coming up, with a Spanish course about to take over my lunchtimes and the usual number of projects on the go. Couchsurfing is on hold for a little bit too, though I did meet up with a Norwegian couchsurfer last week who contacted me wanted to know all about string theory. We spent an enjoyable couple of hours over a coffee chatting about all things high-energy.

Anyway, I'll post the last of my Korea photos for now, which aptly is the photo taken as I was waiting in Incheon airport for this summer's travel adventures to draw to a close.
Leaving Seoul

Chad Orzellinks for 2008-09-07

Scott AaronsonThe Singularity Is Far

In this post, I wish to propose for the reader’s favorable consideration a doctrine that will strike many in the nerd community as strange, bizarre, and paradoxical, but that I hope will at least be given a hearing.  The doctrine in question is this: while it is possible that, a century hence, humans will have built molecular nanobots and superintelligent AIs, uploaded their brains to computers, and achieved eternal life, these possibilities are not quite so likely as commonly supposed, nor do they obviate the need to address mundane matters such as war, poverty, disease, climate change, and helping Democrats win elections.

Last week I read Ray Kurzweil’s The Singularity Is Near, which argues that by 2045, or somewhere around then, advances in AI, neuroscience, nanotechnology, and other fields will let us transcend biology, upload our brains to computers, and achieve the dreams of the ancient religions, including eternal life and whatever simulated sex partners we want.  (Kurzweil, famously, takes hundreds of supplements a day to maximize his chance of staying alive till then.)  Perhaps surprisingly, Kurzweil does not come across as a wild-eyed fanatic, but as a humane idealist; the text is thought-provoking and occasionally even wise.  I did have quibbles with his discussions of quantum computing and the possibility of faster-than-light travel, but Kurzweil wisely chose not to base his conclusions on any speculations about these topics.

I find myself in agreement with Kurzweil on three fundamental points.  Firstly, that whatever purifying or ennobling qualities suffering might have, those qualities are outweighed by suffering’s fundamental suckiness.  If I could press a button to free the world from loneliness, disease, and death—the downside being that life might become banal without the grace of tragedy—I’d probably hesitate for about five seconds before lunging for it.  As Tevye said about the ‘curse’ of wealth: “may the Lord strike me with that curse, and may I never recover!”

Secondly, there’s nothing bad about overcoming nature through technology.  Humans have been in that business for at least 10,000 years.  Now, it’s true that fanatical devotion to particular technologies—such as the internal combustion engine—might well cause the collapse of human civilization and the permanent degradation of life on Earth.  But the only plausible solution is better technology, not the Kaczynski/Flintstone route.

Thirdly, were there machines that pressed for recognition of their rights with originality, humor, and wit, we’d have to give it to them.  And if those machines quickly rendered humans obsolete, I for one would salute our new overlords.  In that situation, the denialism of John Searle would cease to be just a philosophical dead-end, and would take on the character of xenophobia, resentment, and cruelty.

Yet while I share Kurzweil’s ethical sense, I don’t share his technological optimism.  Everywhere he looks, Kurzweil sees Moore’s-Law-type exponential trajectories—not just for transistor density, but for bits of information, economic output, the resolution of brain imaging, the number of cell phones and Internet hosts, the cost of DNA sequencing … you name it, he’ll plot it on a log scale.  Kurzweil acknowledges that, even over the brief periods that his exponential curves cover, they have hit occasional snags, like (say) the Great Depression or World War II.  And he’s not so naïve as to extend the curves indefinitely: he knows that every exponential is just a sigmoid (or some other curve) in disguise.  Nevertheless, he fully expects current technological trends to continue pretty much unabated until they hit fundamental physical limits.

I’m much less sanguine.  Where Kurzweil sees a steady march of progress interrupted by occasional hiccups, I see a few fragile and improbable victories against a backdrop of malice, stupidity, and greed—the tiny amount of good humans have accomplished in constant danger of drowning in a sea of blood and tears, as happened to so many of the civilizations of antiquity.  The difference is that this time, human idiocy is playing itself out on a planetary scale; this time we can finally ensure that there are no survivors left to start over.

(Also, if the Singularity ever does arrive, I expect it to be plagued by frequent outages and terrible customer service.)

Obviously, my perceptions are as colored by my emotions and life experiences as Kurzweil’s are by his.  Despite two years of reading Overcoming Bias, I still don’t know how to uncompute myself, to predict the future from some standpoint of Bayesian equanimity.  But just as obviously, it’s our duty to try to minimize bias, to give reasons for our beliefs that are open to refutation and revision.  So in the rest of this post, I’d like to share some of the reasons why I haven’t chosen to spend my life worrying about the Singularity, instead devoting my time to boring, mundane topics like anthropic quantum computing and cosmological Turing machines.

The first, and most important, reason is also the reason why I don’t spend my life thinking about P versus NP: because there are vastly easier prerequisite questions that we already don’t know how to answer.  In a field like CS theory, you very quickly get used to being able to state a problem with perfect clarity, knowing exactly what would constitute a solution, and still not having any clue how to solve it.  (In other words, you get used to P not equaling NP.)  And at least in my experience, being pounded with this situation again and again slowly reorients your worldview.  You learn to terminate trains of thought that might otherwise run forever without halting.  Faced with a question like “How can we stop death?” or “How can we build a human-level AI?” you learn to respond: “What’s another question that’s easier to answer, and that probably has to be answered anyway before we have any chance on the original one?”  And if someone says, “but can’t you at least estimate how long it will take to answer the original question?” you learn to hedge and equivocate.  For looking backwards, you see that sometimes the highest peaks were scaled—Fermat’s Last Theorem, the Poincaré conjecture—but that not even the greatest climbers could peer through the fog to say anything terribly useful about the distance to the top.  Even Newton and Gauss could only stagger a few hundred yards up; the rest of us are lucky to push forward by an inch.

The second reason is that as a goal recedes to infinity, the probability increases that as we approach it, we’ll discover some completely unanticipated reason why it wasn’t the right goal anyway.  You might ask: what is it that we could possibly learn about neuroscience, biology, or physics, that would make us slap our foreheads and realize that uploading our brains to computers was a harebrained idea from the start, reflecting little more than early-21st-century prejudice?  Unlike (say) Searle or Penrose, I don’t pretend to know.  But I do think that the “argument from absence of counterarguments” loses more and more force, the further into the future we’re talking about.  (One can, of course, say the same about quantum computers, which is one reason why I’ve never taken the possibility of building them as a given.)  Is there any example of a prognostication about the 21st century written before 1950, most of which doesn’t now seem quaint?

The third reason is simple comparative advantage.  Given our current ignorance, there seems to me to be relatively little worth saying about the Singularity—and what is worth saying is already being said well by others.  Thus, I find nothing wrong with a few people devoting their lives to Singulatarianism, just as others should arguably spend their lives worrying about asteroid collisions.  But precisely because smart people do devote brain-cycles to these possibilities, the rest of us have correspondingly less need to.

The fourth reason is the Doomsday Argument.  Having digested the Bayesian case for a Doomsday conclusion, and the rebuttals to that case, and the rebuttals to the rebuttals, what I find left over is just a certain check on futurian optimism.  Sure, maybe we’re at the very beginning of the human story, a mere awkward adolescence before billions of glorious post-Singularity years ahead.  But whatever intuitions cause us to expect that could easily be leading us astray.  Suppose that all over the universe, civilizations arise and continue growing exponentially until they exhaust their planets’ resources and kill themselves out.  In that case, almost every conscious being brought into existence would find itself extremely close to its civilization’s death throes.  If—as many believe—we’re quickly approaching the earth’s carrying capacity, then we’d have not the slightest reason to be surprised by that apparent coincidence.  To be human would, in the vast majority of cases, mean to be born into a world of air travel and Burger King and imminent global catastrophe.  It would be like some horrific Twilight Zone episode, with all the joys and labors, the triumphs and setbacks of developing civilizations across the universe receding into demographic insignificance next to their final, agonizing howls of pain.  I wish reading the news every morning furnished me with more reasons not to be haunted by this vision of existence.

The fifth reason is my (limited) experience of AI research.  I was actually an AI person long before I became a theorist.  When I was 12, I set myself the modest goal of writing a BASIC program that would pass the Turing Test by learning from experience and following Asimov’s Three Laws of Robotics.  I coded up a really nice tokenizer and user interface, and only got stuck on the subroutine that was supposed to understand the user’s question and output an intelligent, Three-Laws-obeying response.  Later, at Cornell, I was lucky to learn from Bart Selman, and worked as an AI programmer for Cornell’s RoboCup team—an experience that taught me little about the nature of intelligence but a great deal about how to make robots pass a ball.  At Berkeley, my initial focus was on machine learning and statistical inference; had it not been for quantum computing, I’d probably still be doing AI today.  For whatever it’s worth, my impression was of a field with plenty of exciting progress, but which has (to put it mildly) some ways to go before recapitulating the last billion years of evolution.  The idea that a field must either be (1) failing or (2) on track to reach its ultimate goal within our lifetimes, seems utterly without support in the history of science (if understandable from the standpoint of both critics and enthusiastic supporters).  If I were forced at gunpoint to guess, I’d say that human-level AI seemed to me like a slog of many more centuries or millennia (with the obvious potential for black swans along the way).

As you may have gathered, I don’t find the Singulatarian religion so silly as not to merit a response.  Not only is the “Rapture of the Nerds” compatible with all known laws of physics; if humans survive long enough it might even come to pass.  The one notion I have real trouble with is that the AI-beings of the future would be no more comprehensible to us than we are to dogs (or mice, or fish, or snails).  After all, we might similarly expect that there should be models of computation as far beyond Turing machines as Turing machines are beyond finite automata.  But in the latter case, we know the intuition is mistaken.  There is a ceiling to computational expressive power.  Get up to a certain threshold, and every machine can simulate every other one, albeit some slower and others faster.  Now, it’s clear that a human who thought at ten thousand times our clock rate would be a pretty impressive fellow.  But if that’s what we’re talking about, then we don’t mean a point beyond which history completely transcends us, but “merely” a point beyond which we could only understand history by playing it in extreme slow motion.

Yet while I believe the latter kind of singularity is possible, I’m not at all convinced of Kurzweil’s thesis that it’s “near” (where “near” means before 2045, or even 2300).  I see a world that really did change dramatically over the last century, but where progress on many fronts (like transportation and energy) seems to have slowed down rather than sped up; a world quickly approaching its carrying capacity, exhausting its natural resources, ruining its oceans, and supercharging its climate; a world where technology is often powerless to solve the most basic problems, millions continue to die for trivial reasons, and democracy isn’t even clearly winning over despotism; a world that finally has a communications network with a decent search engine but that still hasn’t emerged from the tribalism and ignorance of the Pleistocene.  And I can’t helping thinking that, before we transcend the human condition and upload our brains to computers, a reasonable first step might be to bring the 17th-century Enlightenment to the 98% of the world that still hasn’t gotten the message.

Chad OrzelBelated Baby Blogging 090608

We went down to visit Kate's parents on Wednesday, so I wasn't able to post the weekly bison-for-scale picture. I did get one, though, so here it is a few days late:

sm_week04.jpg

This also gives us a chance to show off her "Smart Cookie" onesie, which I picked up because it's a nice break from the frilly pink princessy crap that dominates the girl-baby clothing market. SteelyKid is adorably cute, to be sure, but that's not all she has to offer.

A different sense-of-scale option is below the fold:

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September 06, 2008

Joe FitzsimonsIn Waterloo

I am in Waterloo (the quantum one!) for the next month or so. I will be based at IQC for that period, although I will likely show my face in Perimeter at some point too. Once again I get to pretend to be a mathematician, since I am affiliated with the Combinatorics and Optimization department at UW.

I will still be contactable via my normal email addresses, or via jfitzsim [at] iqc [dot] ca.

It looks like there is going to be a really interesting discussion at a Nature Network meeting in Toronto tomorrow night on Science 2.0. I'm currently trying to figure out how I can get to it. I don't suppose anyone else is heading there? Or if anyone knows how best to get back to Waterloo on a Sunday evening, I'd also be grateful.

BackreactionInterna

Sorry for the silence folks, two days before our conference starts my inbox is about to collapse into a black hole. Can you believe I've spend a whole day doing nothing than replying to and forwarding emails? I now know how it feels like being a node in a network. Meanwhile, I am still preparing my recently acquired talk on Monday morning. I am trying to mention all other talks along the way. Somewhat like one of these games where you have to write a story including the following five words: Beer, Footprint, Credit Card, Collision, Deoxyribonucleic acid. There's always one that doesn't fit in.

Something completely different: I recently came across this LHC rap. Not quite my kind of music, but entertaining nevertheless.

Marco FrascaQCD and lattice computations


QCD in the infrared limit is generally not manageable for computations. We are not able to derive from it masses and other properties of hadrons. So, people thought to use computers to solve it in order to get exact results from it. Since the start, many difficulties were met by people working with this approach pioneered by K. G. Wilson (the Nobel prize winner for the introduction of renormalization group in statistical mechanics). The most serious ones are implied into the limitations of the resources of the computer one uses. On a lattice you have a spacing and you are interested in the continuum limit when the spacing goes to zero. But having the spacing going to zero implies more and more computational resources that are difficult to be found still today. The other question originates on how large is the volume you are using. One should be sure that small volume effects do not enter into our computations so that one is still not into the asymptotic limit is interested on. This latter problem is not so severe even if it has been advocated in computations of gluon and ghost propagators being theoretical expecations seriously at odd with those coming out from lattice.

In a comment about my analysis of quarkonia (see here) it was questioned by James Amundson at Fermilab that my potential does not seem to agree with the one emerging from lattice. People at Fermilab is doing a very good job for lattice QCD and so this comment should be taken rather seriously. Indeed, there is a point I did not emphaise in my answer. I have got an interquark potential

V(r)=-\frac{\alpha_s}{r}+0.8762499705\alpha_s\sqrt{\sigma}

but I do not take \alpha_s to be a constant. Rather, it depends on the energy scale where I am doing computations and this is the key trick that does the job and I get the right answers.

But let me comment abo