Monday, February 27, 2006

arXiv trackback controversy

A lively controversy has recently broken out in the physics blogosphere regarding the recently revealed (and previously somewhat mysterious) trackback policy on the arXiv. For some time, the arXiv has had a mechanism by which approved blogs could post trackbacks to preprints on the arXiv. This would allow researchers looking at a paper to see that and where it is being discussed on physics blogs, and help bring people interested in discussing it together on the same discussion boards. Seems like a good idea, right? Now the problem is of course which blogs to approve for posting trackbacks. There are a lot of cranks, lunatics and plain idiots populating the web, and many of them have their own ideas about fundamental physics (anybody remember Archimedes Plutonium?), which you would definitely not want to be linked to from the arXiv. So the arXiv board decided to vet blogs before allowing them to post trackbacks. So far everything seems fine.

Enter Peter Woit, whose blog Not Even Wrong is very strongly critical of String Theory, suggesting that it is, in Wolfgang Pauli's words, not only not right, but "not even wrong". That kind of criticism is obviously not welcomed by string theorists, many of whom therefore consider Woit a crank (even though he holds a permanent position in mathematics at Columbia University). So what happens when Peter Woit tries to post a trackback to the arXiv? It gets rejected, and since the arXiv trackback policy is sort of secret at that point, Peter feels justified to complain about censorship by string theorists on his blog. His case is taken up by Cosmic Variance, prompting Jacques Distler to reveal the arXiv's trackback policy on his blog.

It turns out that the arXiv trackback policy is to allow trackbacks only from currently active researchers (as judged by the number of their papers on the arXiv). Since Peter Woit apparently has only two papers on the arXiv, his blog does not qualify, and there is apparently no censorship involved.

However, the question arises of how useful this kind of policy actually is. For example, this post on a well-known physics blog simply tries to ridicule the work of people the author disagrees with, but since the author is an active researcher it generates a trackback. On the other hand, this post and this post are perfectly reasonable and non-cranky, and the latter one even sparked a long and technical (if somewhat heated) discussion, but they can't generate trackbacks. Not all active researchers are always interested in a serious discussion, and someone who hasn't recently published any papers may still be able to start a useful discussion.

This blog, for example, probably does not qualify for arXiv trackbacks, since Matthew has left the field and my publication record probably does not meet the required standards at this point in time. I do not believe that makes either of us a crank with nothing worthwhile to say. And any crank who gets someone to endorse his papers for the arXiv (which does happen) might still pass muster as an active researcher and be allowed to post trackbacks. Maybe a more reasonable policy would be to allow trackbacks from blogs written by people who have an official affiliation with a university or public research institution.

The arXiv people definitely have a very tough job, and I do not envy them for it. And whatever specific criticisms one may want to raise, on the whole they ought to be congratulated on doing their job very well and providing a hugely important resource to the physics community. The trackback issue is really relatively minor, but like all things in the blogosphere that exceed a certain critical mass, it is currently undergoing a chain reaction. But it is important that these issues are discussed, because any kind censorship of undesired views or results has to be totally unacceptable in science, and it is important that even the slightest suspicion that legitimate work might be suppressed is investigated and laid to rest.

On a totally unrelated topic: There is a cool post on quantum interrogation (a way to use quantum mechanics to obtain the answer to a question without ever really asking it, roughly speaking) over at Cosmic Variance. The explanation given there involves puppies and the new discipline of quantum cooking, where meals are prepared in superpositions of different recipe states.

Update: As Peter Woit pointed out in a comment, the arXiv trackback policy was in fact not first revealed on Jacques Distler's blog, but in a comment on Cosmic Variance by Ethan Vishniac of the arXiv advisory board.

Update: It was pointed out by Jacques Distler that Life on the Lattice is allowed to post trackbacks to the arXiv on the basis of Matthew's publication record, and using Haloscan I have been able to verify that this is indeed the case.

Update: As Jacques has asked for ideas about how to improve the trackback system, here is my proposal, which I have also submitted as a comment on his blog (replies to go there please): Each arXiv user gets to put the URL to their blog or homepage into their arXiv user profile along with their email address. Each time someone posts a paper, they receive a number of trackback credits (five, say), which can then be used to post trackbacks to papers. No credit, no trackbacks. This would formalise the “active researcher” criterion in an objective manner, while being inclusive of researchers with short publication records and keeping the signal-to-noise ratio high, since you wouldn’t want to waste your hard-earned credits.

Wednesday, February 15, 2006

An interview with Matthew Nobes

Life on the lattice founder Matthew Nobes, now a Quantitative Analyst with a firm in London, England, kindly agreed to give us an e-mail interview. Interviewing him is Life on the lattice's Georg von Hippel.

Georg: While I assume that 'Life on the Lattice' readers will know you, maybe you would like to briefly introduce yourself?

Matt: My name is Matthew Nobes, I grew up in Southern Ontario, and studied undergraduate physics at the University of Waterloo. I did an MSc and PhD at Simon Fraser University (SFU), in Vancouver. Following that I did just over a year of postdoctoral work at Cornell University.

Georg: What brought you into physics originally? And what made you choose to specialize in Lattice QCD?

Matt: I had very good physics teachers at the high school level, which is what got me interested in physics, over another science. As for Lattice QCD, I got into that through my PhD supervisor, Howard Trottier, who was a very inspirational teacher. Howard taught an introductory Quantum Field Theory course my first year at SFU. From that I knew I wanted to work with him. That's how I got started in Lattice QCD.

Georg: Maybe you would like to tell our readers a little about the research you have performed or participated in during your life on the lattice.

Matt: My major focus was on the perturbative improvement of the actions and operators we use in Lattice QCD. In simple terms Lattice QCD is an approximation to the real world, and as such it has errors. One can correct the errors systematically using perturbation theory, however it is quite difficult. My research involved developing methods to streamline and automate these perturbative calculations.

This is a very important thing to be doing, as many of the recent HPQCD results have errors dominated by the lack of perturbation theory results.

Georg: Recently, you have changed careers and locations; now you are working as a Quantitative Analyst in London. What is that kind of work like, and how does it differ from being in a physics department?

Matt: The work is very different than academic physics. For one, the pace is much faster, people expect results on a much quicker time scale. Also, the number of things you have on the go at any one time is larger. In addition the work is far less specialized. I've had to use many skills which I haven't had to use in years.

Georg: Would you say that studying particle physics, and Lattice QCD in particular, was a good preparation for the work you are doing now? And if so, what kind of skills or knowledge acquired on the lattice are you using in your present position?

Matt: I would say yes, it was good preparation. There's lots of numerical analysis tasks in my new work, for which a background in Lattice was very good preparation. In addition, the general theoretical physics training gives one a very good set of tools and methods which can be applied to finance.

Georg: Where do you see yourself in ten years? And where do you see Lattice QCD going in the same timeframe?

Matt: I have no idea where I'll be in ten years :) Happy in a Quant position somewhere, I suppose.

As far as Lattice QCD, I imagine in ten years the field will have moved on quite a bit. Two areas of growth, I think, are into very complex QCD problems. Exploring the boundary of QCD and Nuclear physics, for example. Another area would be Lattice QFT more generally. If the LHC hits upon strongly coupled new physics, the Lattice will prove a valuable tool.

Georg: Do you have any other messages you would like to pass to our readers?

Matt: I hope everybody is well. And a big thanks to you for carrying the blog on very ably.

Georg: It's a pleasure. Matthew, thank you very much for the interview.

Matt: You're welcome, anytime.

Friday, February 03, 2006

Physics blogs and physicists' blogs

Looking at the physics blogosphere, there is a notable tendency for those blogs that receive the most attention in terms of readers, commenters and incoming links to be physicists' blogs rather than physics blogs. By a physics blog I understand a blog whose contents are devoted to physics, as in physicists advertising their research, teaching the wider public about physics, etc. A physicist's blog, on the other hand, is a blog authored by a physicist, which may well mainly discuss politics, economics, religion, ideology, terrorism, war, drugs, sex, stamp collecting and other such contentious issues. From what I see, it appears pretty clear that many more people read the latter kind of blog than the former.

While I understand that in the current global situation people (and especially people in the US, which still seems to dominate the global blogosphere) become much more worked up about the daily issues in politics, economics, religion etc. than about even the most long-standing physics problems (with the notable exception of anthropic arguments and the landscape), what I don't understand is why they would consider the political, economic or religious views of a particle physicist over e.g. those of an entomologist, an electrical engineer or a seismologist, or even over those of a historian, economist or theologian. I know that theoretical physicists (and most physics bloggers appear to be theorists) have the (partially deserved) reputation of being the professional and academic community with the highest IQ, percentile by percentile, but that does not mean that theoretical physicists are any more likely to be experts on political etc. matters than e.g. limnologists, which as far as I know do not have the same reputation for brilliance.

My point is that being more intelligent in and of itself does not mean being more knowledgeable or having a more balanced point of view; in fact a normally intelligent person with a degree in international history probably has a much better chance of making an important contribution to the debate about, say, the Iraq war, than a highly intelligent rocket scientist, simply because they have the greater wealth of pertinent knowledge on which to base their opinion, and because they are more used to drawing the kind of inferences and analogies that are needed in that context. Even the most brilliant string theorist will need to do some serious study of, say, granular flows before making a serious contribution to that field. The same applies to these debates.

Now, of course, it was noted as early as the days of Socrates that in matters of public policy everybody is assumed to be entitled to hold a point of view, whereas in other areas (Plato mentions shipbuilding and architecture, if I recall correctly) every sensible person defers to the experts. I don't disagree with that at all; in fact I hold strong views on contentious issues myself, and I have no problem stating them where they are asked for, or where I feel that I can make a contribution. But I wouldn't normally proffer them on a global forum like a blog, because I recognize that having a PhD in Theoretical Physics (even if it is from Cambridge) does not make me an expert on foreign relations or the global economy, and I am simply amazed at the number of people who seem to believe that academic credentials in a physics subject confer some degree of importance to writers' views on topics far outside the scope of physics.

So this was a bit of a rant. Anyway, Life on the Lattice is a proud physics blog, and has no intention of becoming a mere physicists' blog. If that means fewer readers, so be it. At least I can rest safe in the assumption that I won't have to be ashamed of what I wrote here in ten years time.

Thursday, February 02, 2006

Exactly chiral fermions

In the last post in this series, we looked at the Ginsparg-Wilson relation and how it might provide a way to get past the Nielsen-Ninomiya theorem. In this post we shall have a look at how this can happen in practice.

One way in which a four-dimensional theory of a chiral fermion can be realized is by dimensional reduction from a five-dimensional theory. Let us consider the five-dimensional continuum theory of a Dirac fermion coupled to a scalar background field depending on only the fifth dimension $$s$$:

$$D = \gamma_\mu\partial_\mu + \gamma_5\partial_s - \phi(s)$$

where the scalar field is assumed to be a step function of the same general form as $$\phi(s)=M\tanh(Ms)$$. The plane $$s=0$$ can be understood as a domain wall of width $$M$$ separating domains of $$\phi\sim M$$ and $$\phi\sim -M$$. The case of interest has$$M$$ large.

From the square of the Dirac equation, we have for a fermion with four-momentum $$p=(iE,\mathbf{p})$$, $$p^2=-m^2$$, $$\psi(x,s)=exp(ipx)\chi(s)$$, that

$$\left[ -\partial_s^2 + \gamma_5\partial_s\phi(s) + \phi(s)^2 \right] \chi(s) = m^2 \chi(s)$$

and the allowed masses on the four-dimensional domain wall are determined by the eigenvalue spectrum of a differential operator in $$s$$. All non-zero eigenvalues are of order $$M$$ and hence large. For the zero eigenvalues, the Dirac equation can be decoupled into

$$\left[ -\gamma_5\partial_s + \phi(s) \right] \chi(s) = 0 \\gamma_\mu p_\mu \chi(s) = 0$$

with solutions

$$\chi(s) = \exp\left(\pm\int_0^s\mathrm{d}t\;\phi(t)\right)u \\gamma_\mu p_\mu u = 0 \P_{\pm} u = u$$

Of these, only the negative chirality solution is normalizable, and hence the low-energy spectrum on the domain wall consists of a single left-handed chiral fermion.

The presence of the scalar background field $$\phi$$ is a little awkward, but we may simplify the situation to the case of an ultra-massive five-dimensional fermion

$$D = \gamma_\mu\partial_\mu + \gamma_5\partial_s - M$$

in the half-space $$s\ge0$$ subject to the Dirichlet boundary condition

$$P_+\psi(x,s)|_{s=0} = 0$$

and perform the same analysis with $$\phi$$ replaced by $$M$$.

In the early nineties, Kaplan discovered that the same domain wall effect still occured on a lattice when the Wilson operator was used to discretize the five-dimensional theory. The apparent violation of the Nielsen-Ninomiya theorem is due to the fact that the four-dimensional theory is not the whole story: with a finite extent $$L_5$$ in the fifth direction, there will necessarily be another domain wall with opposite orientation, on which a massless chiral fermion of opposite chirality will live, thus fulfilling both the Nielsen-Ninomiya theorem in the five-dimensional theory and ensuring the mutual cancellation of the chiral anomalies stemming from either fermion. The anomalous divergence simply becomes a flow of charge onto and off the domain wall from the extra dimension.

Around the same time, Narayanan and Neuberger discovered a formulation of chiral fermions in terms of the overlap between the ground states of two Hamiltonians representing "time" evolution to $$\pm\infty$$ along the fifth direction. Later, Neuberger discovered a way to write the overlap as the determinant of a Dirac operator, the overlap operator

$$D = \frac{1+\epsilon(D_w)}{2} \\epsilon(H) = \frac{H}{\sqrt{H^\dag H}}$$

where $$D_w$$ is the Wilson Dirac operator. This formulation avoids the need for an explicit fifth dimension, but at the expense of introducing the slightly awkward operator sign function $$\epsilon(H)$$.

Later, it was shown that the domain wall and overlap formulations were essentially equivalent. It can also be shown that both the overlap operator and the effective Dirac operator for fermions on the domain wall satisfy the Ginsparg-Wilson relation, thereby allowing to describe exactly chiral fermions on the lattice.

So what is the bad news? The bad news is that these exactly chiral fermion formulations are extremely hard to simulate. Domain wall fermions need to be simulated in five dimensions, greatly increasing the compuational demand, and for overlap fermions the operator sign function is rather difficult to compute. So while these actions are exactly chiral, and hence in way closer to the real continuum physics, simulating them at reasonable sizes and lattice spacing will require a huge computational effort. If one considers to what effort MILC had to go to get 1% level predictions using staggered fermions (which are very efficient to simulate), it becomes clear that high-precision predictions from dynamical simulations using exactly chiral fermions are still a fair while in the future.

In the next, and probably final post in this series, we will go and have a look at a fairly new lattice fermion action, known as twisted mass.