atdotde

Download compete twitter timeline

2009-10-09T14:41:00.002+02:00

Upon popular request, I wrote a small script to download all tweets of a given twitter id. Have fun!


#!/usr/bin/perl

use Net::Twitter;
$|=1;

unless(@ARGV){
    print "Usage: $0 twitter_id [sleep_seconds]\n";
    exit 0;
}

my ($follow,$sleeper)  = @ARGV;

# No account needed for this.
my $twit = Net::Twitter->new(username => 'MYNAME', password => 'XXX');

$p=1;
while(1){
    my $result = $twit->user_timeline({id => $follow, page => $p});
    
    foreach my $tweet (@{$result}){
 print "At ", $tweet->{'created_at'},"\n";
 print $tweet->{'text'},"\n\n";
    }
    ++$p;
    sleep $sleeper if $sleeper;
}

You might have to install the Net::Twitter module. This is most easily done as


sudo perl -MCPAN -e shell

and then (possibly after answering a few questions)


install Net::Twitter

Not so canonical momentum

2009-10-05T22:52:00.003+02:00

Two weeks ago, I was on Corfu where I attended the conference/school/workshop on particles, astroparticles, strings and cosmology. This was a three week event, the first being on more conventional particle physics, the second on strings and the last on loops and non-commutative geometry and the like. I was mainly there for the second week but stayed a few days longer into the loopy week.

I think it was a clever move by the organisers of the last week to give five hours to the morning lecturers rather than one or two as in the string week. So they had the time to really develop their subjects rather than just mention a few highlights. John Baez has already reported on some of the lectures.

I would like to mention something I learned about elementary classical mechanics and quantum mechanics which was just a footnote in Ashtekar's first lecture but which was new to me: One canonical variable can have several canonical conjugates! In the loopy context, this appears as both the old and the new connection variables have the same canonical momentum although they differ by the Imirzi parameter times the second fundamental form (don't worry if you don't know what this is in detail, what's important that the 'positions' are different in the two sets of variables although they have the same canonical momentum).

How can this be? I always thought that if is a canonical variable the conjugate variabel is determined by . What I had not realized is that you could for example take and obtain the same fundamental Poisson brackets (and consequently commuation relations after quantization). Similarly, you could add any function to the momentum without changing the commutation relations.

The origin of this abiguity can be found in the fact that also the Lagrangian is not unique: You can always add a total derivative without changing the action (at least locally, see below). For example, to obtain by the derivative formula, add to the action. The most general change would be to add .

What about the quantum theory? This is most easily seen by realising that upon a gauge transformatio , the action of a charge particle changes by . Thus our change in Lagrangian (with a corresponding change in the canonical momentum) can be viewed as a gauge transformation (even if no gauge field is around one could add a trivial one). Correspondingly, the wave function would have to be changed to as acting on by a canocially quantized is the same as acted on by .

So, it seems as if you would get exactly the same physics in the primed variables as in the unprimed ones. But we know that not all total derivatives have no influence on the qunatum theory the -angle being the most prominent example. How would that appear in our much simpler quantum mechanics example? Here, it is important to remember that one should only use gauge transformations that are trivial at infinity. Here, if you change the phase of the wave function too wildly at you might leave the good part of the Hilbert space: For example the kinetic energy being an unbounded operator is not defined on all of Hilbert space but only on a dense subspace (most often taken to be some Sobolev space). And that you might leave by adding a wild phase and end up in a different self adjoint extension of the kinetic energy.

I have no idea if all this is relevant in the loopy case and the old and new variables or the variables are related by a (generalized) gauge transformation but at least I found in amusing to learn that the canonical conjugate is not canonical.

Jazz makes you age faster

2009-08-08T11:19:00.003+02:00

Before I head off for the travel season (first vacation: St. Petersburg, Moscow, Transsiberian Railway, Irkutsk, Baikal Lake, Ulan Ude and Mongolian Border, then two weeks of workshop in Corfu, then meeting collaborators in Erlangen and finally lecuring in Nis, Yugoslawia) - you won't notice any change in posting frequency - I would like to leave you with the latest statistic I learned about in "Sueddeutsche Zeitung" today:

In 1982, the average age of the audience of jazz concerts (don't know if in Germany or worldwide or whatsoever) was 29, today it is 64. So, even assuming immortality of improvised music enthusiasts, in 27 years, they got older by 35 years!

Note well that for an average of 64, if I attend a jazz concert being 36, we need 78ers to get back to the average.

Thermodynamic (in)stability of hydrogen

2009-07-14T14:12:00.004+02:00

The interview season for the "Theoretical and Mathematical Physics" master programme at LMU is approaching quickly. We have to come up with new questions and problems that help us judge our applicants.

It turns out to be easy to find questions in quantum mechanics and those easily lead over to mathematics questions. However, we were always short on good stat mech problems. One possibility is to have an easy start with the harmonic oscillator and then couple that to a heat bath and compute the partition function (with geometric series featuring).

But this time, we thought we could vary this a bit and came to a surprising realization: Hydrogen is unstable! This was news to me but google finds a number of pages where this is discussed. Often wrongly, but the good explanation is in a 2001 paper by Miranda.

The idea is the following: Everybody knows that the energy of the -th level of the hydrogen atom has energy proportional to . This level has degeneracy since runs from 1 to and then runs from to . So the partition function is . First, we thought that this might be a function named after some 19th century mathematician but mathematica told us its name is actually since the exponent quickly approaches 1 for every positive .

The conclusion seems to be that there is something wrong with the hydrogen atom. And we have not even started to consider the positive energy scattering states. Obviously, this problem has an IR divergence and it is probably better to embed it in some cavity of finite radius. But still, you would think that then for a large cavity, most of the statistical weight would be in the highly excited states and the probability to be in the ground state would go to zero as the cavity gets larger.

The conclusion would be that a hydrogen atom at any temperature would almost never be in its ground state but always highly excited or even ionized. And all this only because the density of states diverges at 0. This looks like a situations worse than the Hagedorn transition that strings experience due to the exponentially growing density of states.

The solution in the above mentioned paper is quite simple: Rather than these scaling arguments one should put in some numbers! Let us start with the Bohr radius, which is m and the radius grows like . This means in ameter sized cavity we can only fit states up to roughly . However, at room temperature, Boltzmann exponent and . Thus, to balance the Boltzmann suppression of the higher levels compared to the ground state one has to take into account at the order of states and not just the first . Or put differently, one should use and exponentially large cavity. Otherwise the partition function is essentially cut off at and the probablility to find the ground state is very very very close to 1.

Wrocław summary

2009-07-06T18:37:00.001+02:00

So, I did not get around to live blog from the XXVth Max Born meeting "The Planck Scale". The main reason was, that there were no hot news or controversial things presented, rather people from the different camps talked about findings that a daily reader of hep-th had in some form or the other already noticed. I don't want to create the impression that it was boring, by no means. There were many interesting talks, there were just no breathtaking revelations. I myself am not an exception: I took the opportunity of having several loop-people in the audience to talk once more on the loop string, this time focussing on spontaneous breaking of diffeomorphism invariance.

By now, the PDFs are online and in a few days you will also find video footage. To get an idea what people discussed, the organizers had the idea to assemble tag clouds from the slides, some are above.

Let me mention a few presentations and speakers nevertheless. Steve Carlip talked about the notion of space-time being two dimensional at very short distances in several unrelated approaches. Related was a nice presentation of Silke Weinfurter on her papers with Visser on the scalar mode not decoupling in Horava gravity. That talk was probably on the most recent and hottest results and I had the impression that many other approaches still have to digest the lesson that it is non-trivial to modify gravity and still not throw out the baby with the bath tub.

Hermann Nicolai presented his work (together with Meissner) on a classically scale invariant version of the standard model in which the only dimensionful coupling (the Higgs squared term) arises from an anomaly. They claim that their model is compatible with the current data and would imply that LHC sees the Higgs and only the Higgs. Daniel Litim gave a nice overview over the asymptotic safety scenario for gravity. Bergshoeff and Skenderis talked about models related to 3d topologically massive gravity and Jose Figueroa-O-Farrill presented a summary of algebraic structures relevant for M2 theories.

Mavromatos discussed possible observations of time delays in gamma ray bursts and implications for bounding modifications of dispersion relations in quantum gravity. Steve Giddings talked about locality and unitarity in connection with black hole information loss and Catherine Meuseburger explained how in 3d gravity observers can make geometrical measurements with light rays to find the gauge invariant information on in which Ricci-flat world they are living.

I was surprised how many people still work on non-commutative geometry (in the various forms). The Moyal-plane, however, seems to be out of fashion (not so much because of UV-IR-mixing which I think is the main reason to be careful but many people seem to think they can work around that but are worried about unitarity on the other hand). Kappa-Minkowski is a space many people care about and Dopplicher explained why we live in quantum space-time. The general attitude seemed to be (surprisingly) that Lorentz-breaking in those theories is not an issue. However, Piacitelli, showed a calculation that should have been done quite a while ago: People say that although Lorentz invariance is broken that is not a problem since there is a twisted co-product version that preserves at least some related quantum symmetry. Piacitelly now spelled out what that means in everyday's terms: When you do a boost or rotation, twisting the co-product is equivalent to treating theta as a tensor and rotating that as well. Great, that explains why the formalism shows that rotational symmetry is preserved while the physics clearly says that a tensor background field singles out preferred directions. I had for a long time the suspicion that this is what is behind this Hopf-algebra approach but could never motivate myself enough to understand that in detail so I could confirm it.

In addition, there were many talks from loop-related people (also on spin foams, BF-type theories etc) about which I would like to mention just one: Modesto applied the reasoning found in the loop approach to cosmology (I would like to say more about this in a future posting) to a spherically symmetric space-time (i.e. what is Schwarzschild in the classical theory). What he finds is indeed Schwarzschild at large distances but the discretization inherent in that approach produces a solution that has a T-duality like R <--> l_p^2/R symmetry.

A great opportunity for meetings of this style with people coming from different approaches are always extended discussion sessions. Once more, those were a great plus (although not as controversial as a few years back in Bad Honnef), there were two, one on quantum gravity and one on non-commutative geometry.

There, once more, people complained that it is hard to do this kind of physics without new experimental input. Of course to a large degree, this is true. But to me it seems that also misses an important point: By no means, everything goes! At least you should be able to make sure you are really talking about gravity in the sense that in not so extreme regimes you recover well known physics (Newton's law for example). Above, I mentioned Horava gravity apparently failing that criterion and it seems many other approaches are not even there to be tested in that respect.

We often say, we work on strings because it is the only game in town. On that meeting you could have a rather different impression: It seemed more like everybody was playing more or less their on game and many didn't even know the name of their game. Another example of such a trivial non-trivial test is what your theory says about playing snooker: The kinetics of billard balls tests tensor products of Poincare representations of objects with trans-planckian momenta and energies. If your approach predicts weird stuff because it does not allow for trans-planckian energies my interpretation would be that you face hard times phenomenologically, even if your model agrees with CMB polarizations.

More conference blogging

2009-06-29T14:25:00.002+02:00

Instead of String '09 I decided to attend this year the Born Symposium on the Planck scale. There are a number of stringy speakers as well as quite a few people from the loop camp. Watch this space for some reports. The talks (including video) will be online as well (as opposed to Strings '09).

More quality journals by Elsevier

2009-05-06T11:25:00.002+02:00

After all the fun re the El Nashie fan board "Chaos, Solitons and Fractals" it seems Elsevier has put another nail in their coffin by allowing the pharma company Merck to run their pseudo scientific marketing journal under their flag: Merck Makes Phony Peer-Review Journal | blog.bioethics.net . Once more, John Baez has more details: The Foibles of Science Publishing | The n-Category Café

Great, I think nobody in the world can claim anymore that our libraries should throw big money at these commercial publishing houses because they provide the quality control that open access publication cannot provide.

Journal club cgi

2009-04-27T20:17:00.006+02:00

For our journal club, I wrote a small cgi script that provides a web page where people can dump arxiv.org identifies of papers they are interested in and then everybody can see title, abstract and authours as well as a link to the pdf.

You can copy the file to your cgi-bin directory, make it world executable and create a world writeable directory /opt/journal . You might need to install the XML::TreeBuilder module (as root run 'perl -MCPAN -e shell' and then do 'install XML::TreeBuilder'.


#!/usr/bin/perl
#
# Journal club cgi
# Written by Robert C. Helling (helling@atdotde.de)
# Published under the Gnu Public License (most recent version)
#

use XML::TreeBuilder;
use LWP::Simple;
use CGI;

my $g = CGI::new();
print "Content-type: text/html\n\n";
my @ids = ();

system "touch /opt/journal/numbers";
open (IN,'/opt/journal/numbers') ||die "Cannot open /opt/journal/numbers:$!!";;
while(){
chomp;
if(/(\d\d\d\d\.\d\d\d\d)/){
push @ids, $1;
}
elsif(/^\-\-\-/){
@ids = ();
}
}
close IN;

if($new_paper = $g->param('paper_id')){
my ($new_id) = $new_paper =~ /(\d\d\d\d\.\d\d\d\d)/;
push @ids,$new_id;
open (OUT, ">>/opt/journal/numbers") || die "Cannot write to /opt/journal/numbers:$!";
print OUT "$new_id\n";
print "\nNEW$new_id\n";
close OUT;
}

my %seen = ();
@ids = grep { ! $seen{$_} ++ } @ids;

dbmopen %papers, '/opt/journal/papers', 0666;

print join '<hr>', map {&show($_)} @ids;

print ($g->start_form(),
  $g->textfield('paper_id'),
  $g->submit(-name => "add paper"),
  $g->end_form());

sub show{
my $id = shift;
my $data;

unless($data = $papers{$id}){
$data = get("http://export.arxiv.org/oai2?verb=GetRecord\&identifier=oai:arXiv.org:$id\&metadataPrefix=arXivRaw");
$papers{$id} = $data;
}

my $all = XML::TreeBuilder->new;
$all->parse($data);

my $authors = $all->find('authors')->as_text;
my $title = $all->find('title')->as_text;
my $abstract = $all->find('abstract')->as_text;

return "$authors\n<a href=\"http://arxiv.org/pdf/$id\">$title</a>\n$abstract\n";
}

dbmclose %papers;

Posts disappearing

2009-03-01T23:27:00.002+01:00

As I have noted earlier, some posts by John Baez and others on certain crackpots having their own Elsevier journal to dump their E-infinity weirdness have disappeared from the net. Luckily, one brave soul keeps copies of this stuff.

Now, I had to learn, that they completely overtook the discussion section of the online version on a Scientific American article on dynamical triangulations and what is even more disturbing, made the weekly quality newspaper "Die Zeit" take down the online version of an article reporting these issues (in German). I would have thought it would take a lot to make a respectable paper with a law department to commit this kind of self censorship.

Initial data for higher order equations of motion

2009-02-17T20:59:00.000+01:00

Over lunch, today, we had a discussion on higher order quantum corrections in the effective action. You start out with a classical action that only contains terms with up to two derivatives. This corresponds to equations of motion that are second order in time. As such, for the physical degrees of freedom (but I want to ignore a possible gauege freedom here) you then have to specify the field and its time derivate on a Cauchy surface to uniquely determine the solution.

Loop corrections, however, tyically lead to terms with any number of derivatives in the effective action. Corresponding equations of motion allow then for more initial data to be specified. The question then is what to do with the unwanted solutions. If you want this is the classical version of unitarity.

Rather than discussing higher derivative gravity (where our lunch discussion took off) I would like to discuss a much simpler system. Say, we have a one dimensional mechanical system and the classical equation of motion is as simple as it can get, just . To simplify things, this is only first order in time and I would like to view a second order term already as "small" correction. The higher order equation would then be with small .

To find solutions, one uses the ansatz and finds . For small , the two exponents behave as which blows up and which approaches the solution of the "classical equation".

The general solution is a linear combination of the two exponential functions. We see that the solution blows up over a time-scale of unless the initial data satisfies the classical equation .

We can turn this around and say that if the classical equation is satisfied initially, we are close to the classical solution for long time (it's not exactly the same since differs from the "classical exponent" by order terms. For other initial data, the solution blows up exponentially on a "quantum time" inversely proportional to the small parameter .

This plot shows for . On the axis that goes into the picture there is a parameter for the initial conditions which is for data satisfying the classical equation initially. You can see that this parameter determines if goes to or over short time. Only the classical initial data stays small for much longer.

Unfortunately, this still leaves us with the question of why nature chooses to pick the "classical" initial data and seems not to use the other solutions. In the case of higher order gravity there is of course an anthropic argument that suggests itself but I would rather like to live without this. Any suggestions?

Better than refereeing fees

2009-02-17T16:30:00.003+01:00

A few days ago, I received an invitation to join a facebook group that demands that all journals should follow JHEP to pay their referees. So far, I did not sign up.

I am convinced the refereeing system has many flaws. But the pay of referees is not one of them. I don't know how much JHEP pays, I have heard the figure of 30$ per paper. What's that? Refereeing a string theory paper is a job that requires a specialist with a broad academic background. So, you would expect an hourly rate that is well above 100$ (judging for example the rate that lawyers demand). That means, by paying this specialist 30$ I expect that the refereeing takes him less than 20 minutes (including typing the report and uploading it to a web page). But that's exactly the problem with the refereeing system: The value you can add by refereeing a paper in 20 minutes negligible. You have to spend significantly more time with the paper to have a more significant opinion than you have after one minute of seeing the authors' names, reading the abstract and flipping through the pages.

On the other hand, referees are already paid for their refereeing: That's part of an academics job, and he/she already gets a salary from the university. That should already cover the refereeing as it is part of the job like it is to attend seminars and to discuss with other scientists.

The problem with the refereeing system really is that too often too little attention is given to the actual paper. Everybody knows first hand examples of excellent papers that were rejected for stupid reasons. On the other hand, there is a lot of very low quality stuff that gets printed, the Bogdanovs' papers and the El Nashie[no link so far] story being only the most prominent examples.

Of course, the refereeing process is most likely the only value that publishers add to a paper when it is promoted from a freely available preprint on arxiv.org to a published article. And we (that is our employers through their libraries) pay enormous sums for this more and more demanding justification. And giving this justification gets harder and harder with every b.s. paper that appears in print.

The flaw with the "you are already paid" argument is of course that refereeing is invisible and besides your obligation as a scientist there is little incentive to do a good job. Nobody (except maybe the editor) sees it and there is no reward, not even an idealistic one.

There is however one simple improvement that would be trivial to implement. I learned this from Vijay Balasubramanian a few years ago and I am convinced it should be introduced immediately: If a paper gets accepted, the identity of the referee should be published together with the paper while a referee that rejects a paper should stay anonymous.

This would give an incentive to do good work as a referee. If the paper's value is low and you still accepted it because you did not properly read it you will receive shame while if the paper is good people can see you put some effort into it. Keeping the identities of rejectors hidden of course prevents referees from accepting papers because of fear of any kind of "revenge" from the authors.

I am sure the quality of the refereeing process would increase significantly if this were implemented. Thus, I would urge you to support the publication of accepting referees names in the next discussion of the flaws of the refereeing system I am sure you will take part in over the next few weeks!

Update: Some brave soul has collected all the El Naschie stuff that seems to have disappeared from the web.

Reinstalling my Aspire One

2009-01-21T17:05:00.004+01:00

Did I mention before that the package selection tool (originally from Fedora) that comes with the Aspire One sucks big time? Yesterday, I came across zebra barcode reader I could use this together with the built in camera to keep track of the books I lend to various people. Zebra was of course not packaged and compiling it required C++ bindings for ImageMagick. Those I could not install due to dependency problems. I spent more or less the whole day installing this/compiling that/upgrading the other. In the end, I had zebra running (only to learn that ordinary bar codes are either too small to be resolved by the web cam or bringing them closer to the cam is too close for the camera to focus. Bummer. But enlarging the barcode on the copier made the computer recognize it but somehow defeats the purpose) but left the Aspire One in a state unable to boot.

Luckily, it only did not boot into X but I could still get a prompt and mount an external disk and backup my home dir. And now I install Ubuntu to it. I will continuously update this post as I keep going.

Step one was to get the installation disk onto a bootable USB stick. UNetbootin is a wonderful tool for this it only took me some time to find it. In the first go I ended up with a "Missing operating system" error when trying to boot from it. Fortunately, Bug #277903 in usb-creator (Ubuntu): “Missing Operating System [message at boot]” has the solution: Remove the partition using fdisk(!!!) and create new one using gparted. That worked. Now I install from that stick.

Stay with me and keep fingers crossed!

Update: I had expected to have to wait for long times fighting with various bits and pieces and having time to blog the solutions as I found them. But there were no solutions to find. Everything I tried so far just worked. Without any hassle. So nothing to say except I should have switched to Ubuntu already much earlier. OK, two things do not work so far: The mic (for skype for example) and the bluetooth USB stick. But I have not really tried.

A feature I would love

2009-01-18T15:51:00.003+01:00

I have a problem and it seems so far no one has come up with a good solution for it: Many web 2.0 services come in the form of a stream of items most of which I would like to see exactly once. Examples are RSS feeds, podcasts (here seeing could as well mean synching with the ipod), mail (in some respect), twitter, usenet, etc.

If I access them with a single program on a single device, this program keeps track if what I have seen so far and (at least in default mode) only presents me the new stuff. Excellent. Only that I use more than one device to access these services: I have my desktop, a laptop at home, a netbook on the road or in meetings and seminars, sometimes I even use other peoples devices.

What I want is a way that all these different devices have a possibility to share the information which items I have already seen. C'mon, this can't be that hard to implement. And I am sure I am not the only person with more than one computer.

The problem is most pronounced with RSS feeds. As mentioned some time ago, I used Liferea read blogs. This is where I first noted I would like to share the "read it flag" info between different computers. I thought that program might have a file like .newsrc in the old days where it records for each feed which posts have been seen before. Then it shouldn't be too hard to put this under subversion control or write a small perl script to merge those files. Except that information is not kept in a simple format. Instead, liferea keeps the downloaded content in some xml file and that file has flags. In order to merge the state of read items one would have to download them as does liferea and then sync the flags. Why do they have to mix the content and the meta information, why why why? I even looked at liferea's source but I couldn't see the possibility of an easy patch.

I "solved" this by giving up on liferea and moving to Google Reader instead. Since there, feeds are not read locally but on a single server, there is no problem with sharing state information. Only that I am not very comfortable with letting google know which feeds I like. And maybe at some point the GUI gets on my nerves or whatever. I don't think this is an ideal solution.

For more or less the same reason I use a similar approach to mail: All my different addresses' mail ends up in the inbox of my desktop computer (except for mailing lists etc which are sorted in appropriate alternative inboxes but on the same computer). In case I want to read mail on a different computer I ssh to the desktop. Except that it is not directly connected to the net. I first have to ssh to LMU's firewall. But that computer still cannot see my desktop. So from there I ssh to some PC in the Arnold Sommerfeld Center. From where eventually I can ssh to my computer (although only with a numeric ip since my computer is not important enough to get a DNS entry. And so far I was too lazy to hook it up to dyndns. But over recent months dhcp was kind enough to always give me the same ip and thus this chain of computers is supported by appropriate entires in .ssh/config . But I am digressing.

What I wanted to say about mail is not so much I don't want to use IMAP and one central mail server. It is also about saved mail in local folders. Those I have to many and too much volume to put them all in IMAP. At least on publicly accessible computers. And on my desktop (where I can install whatever I want) it would be of no use since this is always two hops away from the rest of the internet, at least for ingoing connections. OK, I could set up ssh tunnels. But those usually do not work reliably over longer times (we are talking at least weeks, I want to have reliable access to my mail even if I travel for longer time).

But again, the main problem seems to be sharing the 'read it' information.

One more incarnation of the same problem: ITunes does of course not exist for Linux. So I manage my ipod with Amarok. I would like to use my different computers to upload recent podcasts to the ipod but have not found a way to do this consistently.

Thermodynamics of gravitational systems

2009-01-02T15:43:00.002+01:00

In this last (first?) post of the year I would like to express some confusion I have with respect to applying thermodynamic reasoning to cosmology or in general situations governed by gravity. The main puzzle I would like to understand is the question regarding the entropy balance of the universe: According to the second law of thermodynamics, entropy is never decreasing (I hope this is the correct sign, I can never remember it. Let's see, S is minus trace rho log rho. If rho is proportional to the projector on an N dimensional subspace we have S = - N 1/N log(1/N) = log(N). Thus it is increasing if the probability spreads over a larger subspace. Good). So if it is increasing, it should have been minimal at the big bang which seems to be at conflict with the universe being a hot soup of all kinds of fluctuations right after the big bang.

With the popular science interpretation of entropy as a measure of disorder or negative information the early universe must have been highly ordered and should have contained maximal information, a notion which is highly counter intuitive. So this needs some clearing up.

The simplest resolution would be that it is compatible with observation to assume that the universe has infinite volume and if it has a finite entropy density the entropy is infinite and any discussion of increasing or decreasing entropy is meaningless as it will be infinite at any time and it does not make sense to talk about more or less infinite entropy.

We could however try to still make sense in a local, desitised version: We could make the usual cosmology assumption of the universe being pretty much homogeneous and talk solely of entropy densities (after all, we only observe a Hubble sized ball of it and should thus only make appropriate local statements). But since the universe is expanding should we use co-moving or constant volumes when computing the densities when applying a desitised second law? But I don't think this is the real problem.

I am much more worried about another point: I am not convinced it makes sense to apply thermodynamic reasoning to situations that involve gravity! Obviously, the universe as we see it is not in thermal equilibrium, all the interesting stuff we see are local fluctuations. So standard textbook equilibrium thermodynamics does not apply: Remember for example, temperature is a property of an equilibrium, the fact it is well defined is sometimes called the zeroth law and out of equilibrium situations do not have a temperature! Only if locally things are not too different from an equilibrium state one can assign something like a local temperature. But things are even worse: The usual systems that we are used to describe thermodynamically (steam engines, containers of gas etc) have the property that the equilibrium is an attractor of the dynamics: All kinds of small, local perturbations diffuse away exponentially fast. This is in line with our intuitive understanding of the second law: The homogeneous state is the one with the highest entropy and thus the diffusion is governed by the second law.

This is not the case anymore as soon as gravity is the dominating force: What is different here is that gravity is always attractive. Thus if you have a nearly homogeneous matter distribution with small local fluctuations, over-dense regions will gravitate even stronger and thus will be even denser while under-dense regions will gravitate less and will become even emptier. Thus the contrast is increasing over time (a feature which is of course essential to structure formation of galaxies, stars etc). But this means the equilibrium is unstable. This is at least in conflict with the naive understanding of the second law above.

Some deeper inspection reveals that when you axiomatise thermodynamics you usually make some assumption on convexity (or concavity, depending on whether you use intensive or extensive variables of state) of your favorite thermodynamic potential (free energy etc). IIRC this is something you impose. Your system has to fulfill this property in order to be described by thermodynamics. And it seems that gravity does not have this property (the stability) and it quite possible (if I am not mistaken, sitting here in a train without any books or internet access) thermodynamic arguments do not apply to gravity.

Note well that I am talking classically (actually even only about the weak field situation in which the fluctuations are well described by Newtonian gravity), I have not even mentioned black holes and their negative heat capacity due to Hawking radiation which should make you even more uneasy about thermodynamic stability.

There is however a related problem my classically relativistic friends told me about: When discussing cosmology, it is usually a good first approximation that the universe is homogeneous which supposedly it is at large scales. At small scales however, this is obviously not the case with voids, galaxies, stars, stones etc. But for the evolution at large scales you average all those local fluctuations and replace everything by the cosmological fluid.

The problem with the non-linear theory of gravity is however that it is by far not obvious that this averaging commutes with time evolution: That, starting from good initial conditions it does not matter if you first average and then compute the time evolution of the averaged matter density or if you first compute the time evolution and then to the spatial averaging. The first thing is of course what we always compute while the second thing is what really happens. An incarnation of this problem was an argument that was discussed a few years ago that what looks like the cosmological constant in our local patch of the universe is just a density fluctuation with a super-horizon wave length. At first you would reject such a suggestion since something that happens over regions that are causally disconnected from us should not influence our local observations. However, due to the non-linear nature of gravity this argument is too fast and needed a more thorough inspection. My impression is that eventually it was decided that this idea does not work. I would be happy to be informed by somebody follows these things more closely.

To wrap up, I feel that I would need to have to understand much more basic things about thermodynamics applied to gravity before I could make sensible statements about the entropy of the universe or Boltzmann brains and the similar.

Symmetry Breaking in Quantum Mechanics

2008-12-10T20:14:00.002+01:00

Today, in our Mathematical Quantum Mechanics lecture, I put my foot in my mouth. I claimed that under very general circumstances there cannot be spontaneous symmetry breaking in quantum mechanics. Unfortunately, there is an easy counter example:

Take a nucleus with charge Z and add five electrons. Assume for simplicity that there is no Coulomb interaction between the electrons, only between the electrons and the nucleus (this is not essential, you can instead take the large Z limit as explained in this paper by Frieseke. The only way the electrons see each other is via the Pauli exclusion principle. The Hamiltonian for this system has an obvious SO(3) rotational symmetry. The ground state, however is what chemists would call 1S^2 2S^2 2P^1. That is, there is one electron in a P-orbital and in fact this state is six-fold degenerate (including spin). Of course, there is a symmetric linear combination but in that six dimensional eigen-space of the Hamiltonian there are also linear combinations that are not rotationally invariant. Thus, the SO(3) symmetry here is in general spontaneously broken.

This is in stark contrast to the folk theorem that for spontaneous symmetry breaking you need at least 2+1 non-compact dimensions. This for example is discussed by Witten in lecture 1 of the IAS lectures or here and is even stated in the Wikipedia.

Witten argues using the Stone-von Neumann theorem on the uniqueness of the representation of the Weyl group (the argument is too short for me) and explicitly only discusses the particle on the real line with a potential (the famous double well potential where the statement is true). In 1+1 dimensions, there is the argument due to Coleman, that in the case of symmetry breaking you would have a Goldstone boson. But free bosons do not exist in 1+1d since the 2-point function would be a log which is in conflict with positivity.

I talked to a number of people and they all agreed that they thought that "in low dimensions (QM being 0+1d QFT), quantum fluctuations are so strong they destroy any symmetry breaking". Unfortunately, I could not get hold of Prof. Wagner (of the Mermin-Wagner theorem) but maybe you my dear reader have some insight what the true theorem is?

Spectral Action Part II

2008-12-08T23:26:00.001+01:00

After in part I, I have explained how to go back and forth between spaces with metric information and (C*)-algebras it's now time to add some physics: Let us now explore how to formulate an action principle that will lead to equations of motion when extremised.

Let me stress however, that although it may look differently, this is entirely classical physics, there is no quantum physics to be found anywhere here even though having possibly non-commutative algebras might remind you of quantum mechanics. This, however, is only a way of writing strange spaces and has nothing to do with the quantisation of a physical theory. We will even compute divergences of one loop Feynman diagrams, but still this only a technical trick to write the classical Einstein action (integral of the Ricci scalar over the manifold) and has nothing to do with quantum gravity! Our final result will be the classical equations of motion of gravity coupled to a gauge theory and a scalar field (the Higgs)!

The trick goes as follows: Last time, we saw that in order to encode metric information we had to introduce a differentiation operator so we could formulate the requirement that a function should have a gradient which has length less or equal to 1. One could have taken the gradient directly but there was a slight advantage to take the Dirac operator instead since that maps spinors to spinors instead of the gradient mapping scalars to vector fields.

Another advantage of the Dirac operator is that when it is squared it gives the Laplacian plus the Ricci scalar (which we want to integrate to obtain the Einstein Hilbert action) divided by some number which I vaguely remember to be 12 but which is not essential. In formulas, we have . Even better, when we are in d dimensions, taking the d-th power gives us the volume element. Thus, taking these two observations together and using the Clifford algebra, we find that taking powers of gives us . The second term is obviously what we need to integrate to obtain the EH action.

But how to get the integration? Here the important observation is that we can pretend that this operator is the kinetic term for some field. Then, we can compute the one loop divergence of this field. On one hand, we know that this is the functional trace of the log of this operator. On the other hand, we can compute the divergence of this expression either diagrammatically or with slightly advanced technology in terms of the heat-kernel.

I will explain the heat-kernel formalism at some other time. However, the result of that treatment is a series of "heat-kernel coefficients" which are scalars expressions of the curvature of mass dimension . That is is 1, is basically the Ricci scalar, is a linear combination of scalar contractions of the curvature squared and so on. All those can interpreted as the coefficients of a power series in a formal parameter , i.e. .

The important result now is that the effective action is the integral of over s from 0 to infinity and over all space-time points. Because of the negative powers of , this integral diverges at 0. It turns out, this diverge is nothing but the UV divergence of the one-loop diagrams. Now you can apply your favourite regularisation procedure (dimensinal regularisation, Pauli-Vilars, you name it). Here, for simplicity, we just use a cut-off and start our integration at instead of 0. Connes and Chamseddine do something very similar. Just instead of a sharp cut-off they use a function in the integral that decays exponentially when s approaches 0 (NB has mass-dimension -2 and thus acts as ).

For concreteness, take . Then the term leads to times 1 integrated over the space (i.e. a cosmological constant). The term from gives times the Einstein-Hilbert term and is times an integral of curvature squared. The remaining terms are finite when Lambda is removed. Thus, we find the Einstein action (including a huge cosmological constant) plus a curvature squared correction as the divergence of the one-loop effective action.

But the effective action can also be written as the functional trace of the log of the operator. For this, we don't need any field for which the operator is the kinetic operator of. Imagine we happen to know all the eigenvalues of . Then we have just found that the Einstein Hilbert action can be written as the divergent part of the sum of the log of all those eigenvalues. And this is the spectral action principle: .

As it happens, Connes and Chamseddine really know the eigenvalues of the Dirac operator on spheres. So, they can really do this sum (which turns out to be expressible in terms of zeta-functions). The spheres are of course compact and thus the eigenvalues are discrete. In our field theory argument above, however, we implicitly used the usual continuous momentum space arguments for the effective action. In the limit of large momentum (which is relevant for the divergence) corresponding to short distances this should not really matter, one can pretend that momentum space is actually continuous. However, with a cut-off, this is not precisely true and the discreteness comes in in sub-leading orders. The difference between the continuous computation and the discrete one is of course tiny for a large cut-off. And it is exactly this difference that lets the two authors find agreement to "astronomical precision" (p. 15).

OK, up to now, we have reformulated the gravitational action in terms of the spectrum of the Dirac operator. But what about gauge interactions. But every physicist should now now how to proceed: Do gravity in higher dimensions and perform a Kaluza-Klein reduction. If the compact space has a symmetry group G then besides some scalars you will find YM-theory with gauge group G.

In the non-commutative setting, one can as well take a non-commutative space for the compact directions. Here, Connes and Chamseddine argue for a minimal example (given some conditions of unclear origin, one might be suspicions that those are tuned to give the correct result). It is minimal in terms of irreducibility. However, the total space being the product (by definition reducible) of this compact space by a classical commutative 4d space time (again reducible) make the naturalness of this requirement a but questionable.

For the concrete specification of the compact space, some Clifford magic is employed (including Bott periodicity) but this is standard material. You end up with a non-commutative description of two points for the two spinor chiralities. The symmetry then determines the gauge group. Here I am not completely sure but it seems to me that they employ the usual representation theory arithmetic from GUT-theories to sort all standard model particles in nice representations.

The non-commutative formulation allows the KK-gauge boson A_mu to also have a leg in the compact direction between the two points. From the 4d perspective this is of course a scalar. This of course will be the Higgs. The two points have a finite distance (see the Landi notes for details) and give a mass term inversely proportional to the distance (that is opposite to a superficially similar D-brane construction as noted by Michael Douglas some years ago).

That's it. We have an algebraic formulation of the classical action for the standard model. Let's recap what went in: The NCG version of a space with metric information in terms of a Dirac operator. Some heat-kernel material to write the gravitational action in terms of eigenvalues, GUT-type representations theory and KK-theory. What kind of 'surprises' were found? GUT type relations are rediscovered, treating the discrete spectrum of on spheres can well be approximated by continuous momentum space for momenta large compared to the inverse radius. And there is a final observation detailed in appendix A of the paper: For there are some cancellations of unclear origin which make vanish. This however is a statement about a heat-kernel coefficient and does not have a priori any connection with the non-commutative approach. Furthermore, the physical implications are left in the dark.

KK description of Black Holes?

2008-12-05T07:54:00.002+01:00

Still no second part of the spectral action post. But instead a litte puzzle that came up over coffee yesterday: What is the Kaluza-Klein description of a black hole?

To be more explicit: Take pure gravity on R^4xK for compact K and imagine that it is large (some parsec in diameter say). Then you could imagine you have something that looks like a blackhole in this total space-time. What is its four dimenional description in KK theory?

With KK theory I mean the 4d theory with an infinite number of fields. I want to include the whole KK tower. This theory should be equivalent to the higher dimensional one since both are related by a (generalised) Fourier transform on K. One might be worried that a black hole is so singular that this Fourier transform has problems, does not converge or something. But if that is your worry, take a black hole that is not eternal but one that is formed by the collision of graviational waves say. In the past, those waves came in from infinity and if you siufficiently go back in time all fields are weak. This weak field configuration should have no problem being described in KK language and then the evolution is done in the 4d perspective. What would the 4d observer see when the black hole forms in higher dimensions?

The question I would be most interested in is if there is always a black hole in terms of the 4d gravity or if the 4d gravity can remain weak and the action can be entirely in the other fields.

One scenario I could imagine is as follows: The 4d theory has besides the metric some gauge fields and some dilatons. If the black hole is well localised in K then many higher Fourier modes of K will participate. From the 4d perspective, the KK momentum is the charge under the gauge fields and the unit is dependent on the dilaton. So could it be that there is a gauge theory black hole, i.e. a charged configuration that is confined to small region of space time where the coupling is strong with all the causality implications of black holes in gravity?

Spectral Actions Imprecisely

2008-12-02T14:14:00.003+01:00

A post from Lubos triggered me to write a post on non-commutative geometry models for gravity plus the standard model as for example promoted by Chamseddine and Connes in a paper today.

Before I start I would like to point out that I have not studied this paper in any detail but only read over it quickly. Therefore, there are probably a number of misunderstandings on my side and you should read this as a report of my thoughts when scanning over that paper rather than a fair representation of the work of Chamseddine and Connes.

Most of what I know about Connes' version of non-commutative geometry (rather than the *-product stuff which has only a small overlap with this) I know from the excellent lecture notes by Landi. If you want to know more about non-commutative geometry beyond the *-product this is a must read (except maybe for the parts on POSETs which are a hobby horse of the author and which can be safely ignored).

But enough of these preliminary remarks. Let's try to understand the spectral action principle!

Every child in kindergarden knows that if you have a compact space you get a commutative C*-algebra for free: You just have to take the continuous functions and add and multiply complex conjugate them point-wise. As norm you can take the supremum/maximum norm (here the compactness helps). This is what is presented in every introduction section of a talk on non-commutative geometry, but onfortunately, this is completely trivial.

The non-trivial part (due to Gelfand, Naimark and Segal) is that it works also the other way round: Given a (unital) commutative C*-algebra, one can construct a compact space such that this C*-algebra is the algebra of the functions on it. Furthermore, if one has got the algebra from the functions on a space, the new space is homeomorphic to (i.e. the same as) the original one.

How can this work? Of course, anybody with some knowledge in algebraic geometry (a similar endeavour but there one deals with polynomials rather than continuous functions) knows how: First, we have to find the space as a set of points. Let's assume that we started from a space and we know what the points are. Then for each point x we get a map from the functions on the manifold to the numbers, we simply map f to f(x). A short reflection reveals that this is in fact a representation of the algebra which is one-dimensional and thus irreducible. It turns out that all irreducible representations of the algebra are of this form. Thus, we can identify the points of the space with the irreducible representations of the algebra.

I could have told an equivalent story in therms of maximal ideals which arise as kernels of the above maps, i.e. the ideals of functions that vanish at x.

Next, we have to turn this set into a topological space. One way to do this is to come up with a collection of all open or all closed sets. In this case, however, it is simpler to define the topology in terms of a closure map, that is a map that maps a set of points to the closure of this set. Such a map has to obey a number of obvious properties (for example if I apply the closure a second time it doesn't do anything or a set is always contained in its closure). In order to find this map we have to make use of the fact that if a continuous functions vanishes on a set of points then by continuity it vanishes as well on the limit points of that set, that is on its closure. Therefore, I can define the closure of a set A of points as the vanishing points of all continious functions that vanish on A. This definition then has an obvious reformulation in terms of irreducible representations instead of points. Think about it, as a homework!

Now that we have a topological space, we want to endow it with a metric structure. But instead of giving a second rank symmetric tensor, we specify a measure for the distance between two points x and y as this is closer to our formalism so far. How can we do this in terms of functions?

The trick is now to introduce a derivative. This allows us to restrict our attention to functions which are differentiable and whose gradient is nowhere greater then 1, i.e. the supremum norm of the gradient is bounded by one (this is where the metric enters implicitly since we use it to compute the length of the gradient). Amongst all such functions f we maximize l=|f(x)-f(y)|. Take now the shortest path between x and y (a geodesic). Since the derivative of f along this paths is bounded by one l cannot be bigger than the distance between x and y. And taking the supremum over all possible f we find that l becomes the distance.

Again, I leave it as a homework to reformulate this construction in the algebraic setting in terms of irreducible representations and the distance between them. There is only a slight technical complication: We started with the algebra of scalar functions on the manifold but the gradient maps those to vector fields which is a different set of sections. This makes life a bit more complicated. Connes' solution is here to forget about scalar functions and take spinors (sections of a spinor bundle precisely) instead. If those exist, all the previous constructions work equally well. But now we can use the Dirac operator and this maps spinors to spinors (with another slight complication for Weyl spinors in even dimensions).

In the algebraic setting, the Dirac operator D is just some abstract linear (unbounded) operator D which fulfills a number of properties listed on p2 of the Chamseddine_Connes paper and once that is given by some supernatural being in addition to the algebra, you can actually reconstruct a Riemannian manifold from an abstract commutative C*-algebra and D.

Next, we have to write down actions. Unfortunately, I now have to run to get to a seminar on the status of LHC. This will be continued, so stay tuned!

What is (the) time?

2008-11-30T15:38:00.002+01:00

After seeing Sean revise his view on Templeton funded events and submitting an essay to the FQXi essay contest it seems that this is now officially PC.

So, nothing stands in my way to submit my own.

Picking winners

2008-11-14T18:12:00.003+01:00

I just came across a post at fontblog where it is described how they picked a winner from 36 contributors: They take a dice and throw it once. The number shown is the number of further throws of the dice that are added up to yield the winning number. Obviously, any number 1..36 can be picked, but the distribution is not even: Contributor 1 is picked if the first throw yields a one and the second one as well: probability 1/36. Contributor 2 will be picked by two sequences: 1 2 and 2 1 1 giving 1/6 x 1/6 + 1/6 x 1/6^2 and so on. Conributor 36 is only picked when 7 sixes are thrown in a row, i.e. with probability 1/6^7.

Of course I could not resist and write a perl program to compute the probability distribution, here it is:

Somewhat surprisingly, contributor 29 was eventually picked although he only had a probability of 0.28% a tenth of the average 1/36.

And here is the program:


#!/usr/bin/perl

%h = (0 => 1);

for $t(1..6){
    %h = nocheinwurf(%h);

    print "$t:\n";
    foreach $s(sort {$a <=> $b} keys %h){
        print "$s:".$h{$s}/6**$t." ";
        $total[$s] += $h{$s}/6**($t+1);
    }
    print "\n\n";
}

print "total:\n";
foreach $s(1..36){
    print "$s $total[$s]\n";
}

sub nocheinwurf{
    my %bisher = @_;
    
    my %dann;

    for $w(1..6){
        foreach $s(keys %bisher){
            $dann{$s+$w} += $bisher{$s};
        }
    }
    return(%dann);
}

Acer Aspire One and Fonic UMTS

2008-10-27T09:22:00.003+01:00

Sorry for these uninspired titles of computer related posts. I picked them for search engine optimization since I had not been able to find information on these topics easily in google and at least want others to have a simpler life.

So this post is about how I managed to hook up my shiny new (actually there are already the first few spots on the keyboard...) netbook to the inceadible Fonic UMTS flat rate. They offer a USB stick (a Huawai E160 internally) and a SIM card for 90 Euros. There is no further monthly cost and you only pay 2.50 Euro per calender day you use it. That includes the first GB at UMTS speed per day, if you need more it drops down to a GPRS connection.

The fact that you can read this post is proof that I got it to work as I type this in the departure lounge of Schönefeld airport waiting for my flight to Munich.

Basically, there are two pieces of software that are required: usb_modeswitch which turns the stick from a USB storage device to a serial device. I wanted to compile it myself which lead me to learn (I didn't expect that) that the GNU Linux of the Aspire One comes without the C compiler and I had to manually install gcc. Furthermore, this had to be selected from the list of packages since just selecting the "development environment" of the grouped package selection lead to a version conflict that the stupid package manager (I was complaining about before) was unable to resolve. But once gcc is there, compilation is a matter of seconds. I also had to move the config file to /etc and change a few semicolons which are the comment markers to activate the sections that refer to the E160.

So now, to make a connection I turn on the Aspire One and insert the Fonic stick. Then, as root, I run

usb_modeswitch -c /etc/usb_modeswitch.conf -W

The actual connection is made with umtsmon. I have to wait a few seconds after running the usb_modeswith as otherwise the stick will not be detected. In the config the APN has to be set to pinternet.interkom.de and the checkbox noauth as to be ticked while "replace default route" has to be unchecket since the version of pppd that comes with the Aspire One does not understand this option (which apparently was introduced by SuSE and adopted bey Debian). Then you click connect and it should work!

Update: I forgot to mention that because you had to disable the "replace default route" option, the default route (if existent) will not be disabled. Thus you either have to do it by hand (using 'route') or better just make sure you don't have already a network connection running when trying to connect eg. WiFi (and why would you want to connect UMTS if you already had a better newtowrk connection???)

Why gold?

2008-10-26T18:06:00.002+01:00

I have seen this being discussed in several newspaper articles: In view of the financial crisis people withdraw their money from the bank and buy gold. They do this to such an extend that Germany's main internet gold coin dealer has stopped accepting orders. Amazing. What do they think they are doing?

Ok, you don't trust your local bank XY anymore and, depending where you are, you either have so much money that you are beyond the limit or you even don't trust the banking guarantee system anymore. Therefore, you don't want to leave your money in your account. Fine, you are a pessimist.

But why on earth are you buying gold? Obviously you are so afraid that you are willing to renounce the interest you could be getting for your money. But why don't you keep your money in coins and bills and put it in a save place (safe, mattress, cookie jar).

But that's not good enough for you. You don't even trust your (or any other) currency anymore and want to avoid the risk of inflation. That is you don't trust that somebody is willing to give you enough real stuff for your bills. That is, you mistrust your complete local economy.

You really want to make sure. Therefore you buy gold. Because that keeps its value. That you know.

But why on earth do you believe that? Why do you think that the value of gold is in any way less symbolic or just based on common agreement than the agreement of many people that you will give you food if you provide them with enough pieces of paper on which somebody printed the portrait of some former president in green color?

I have bad news for you: You cannot eat the gold, at least it has zero nutrition value (see wiki article linked above). You can use it for electric contacts that will not corrode. And yes, you can make jewelery from it (as it is done with a third of the gold that is mined). But again, the value of the jewelery is just that "everbody knows gold is precious". And this is only the case as long as everybody believes that. But there ist not much you can actually do with gold that you cannot for example to with copper or palladium (which is an excellent catalyst for many reactions involving hydrogen by the way). The value of gold is only high because everybody believes that. But that's the same for dollar bills or any other currency (leaving out the Icelandic crone for the moment).

And it is not beyond historical example that people stopped believing that gold has high value: As pointed out buy my history teacher in high school this was the main strategic mistake of the Spanish crown: not realising that you can destroy the marked if you suddenly have a lot of it. The Spanish kept importing huge amounts of gold that they had found in the Americas without noticing early enough that the others lost their interest in gold as soon as the Spanish suddenly had so much. At the same time, others found that it's a much better to invest into the real economy.

It took some more years to understand that the value of a currency is not so much based on all the gold that the central bank holds but much more on the economy that backs it.

And of course the telephone desinfactants that stranded on the earth in our past as told by the hitchhiker's guide to the galaxy also had the great idea to use leaves as bills. Which lead them to burn down all their woods.

Aharonov Bohm phase from self-adjointness

2008-10-18T09:02:00.002+02:00

This week started the course in "Mathematical Quantum Mechanics" that I am co-teaching with Laszlo Erdös this term. Since I had to rush a bit in the end of yesterday's lecture, I composed some notes on how to extend the momentum operator in a self-adjoint way for the particle on the interval and how one can see an Aharonov-Bohm phase being the ambiguity of this procedure.

Seen it all before

2008-10-16T19:20:00.000+02:00

You thought you saw something new? Watch this:

Unbounded operators are not defined on all of H

2008-10-16T10:40:00.002+02:00

I am looking for an elementary proof of the fact that an unbounded operator cannot have the whole Hilbert space as its domain of definition. In the textbooks I had a look at this follows from the closed graph theorem which then is proved using somewhat heavy functional analysis machinery. What I am looking for is something that is accessible to physicists that have just learned about unbounded operators and that could be turned into a homework problem. If you know such a reference or could give me a hint (in the comments or to helling@atdotde.de) I would greatly appreciate it!