Friday, October 09, 2009

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

#!/usr/bin/perl

$|=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 Monday, October 05, 2009 Not so canonical momentum 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. Saturday, August 08, 2009 Jazz makes you age faster 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. Tuesday, July 14, 2009 Thermodynamic (in)stability of hydrogen 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. Monday, July 06, 2009 Wrocław summary 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. Monday, June 29, 2009 More conference blogging 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). Wednesday, May 06, 2009 More quality journals by Elsevier 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. Monday, April 27, 2009 Journal club cgi 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;

Sunday, March 01, 2009

Posts disappearing

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.

Tuesday, February 17, 2009

Initial data for higher order equations of motion

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?