Approaching the holiday season

It' there: I started my Christmas holiday. I decided to start it early this year, after I have spent three weeks managing the technicalities of merging contributions of 80 professors into a 200 page 100MB pdf document containing this year's research report of the school for engineering and science of IUB. At least we were using TeX and subversion otherwise the nightmare would have been complete. Submission deadline to the dean was on Monday, so after reporting on esearch I could do some actual research myself or..... go on holiday.

I picked option one for three quite productive days and then moved to option two. Just five minutes before I intended to leave I received an email from a journal editor that requested a referee report on some paper to be written until January 3rd. Just in case I get too bored
under the tree...

Now, I am at my parents' place and turned on the computer so check what has happened on the net over night and there is a message from Clifford asking me to My instructions:

1. Grab the book closest to you.
2. Open to page 123, go down to the fifth sentence.
3. Post the text of next 3 sentences on your blog.
4. Name of the book and the author.
5. Tag three people.

So, let's do it. 1. done 2. done. 3.:

500g Kastanien werden kruz angeröstet, dann von der äußeren und inneren Haut befreit und in Wasser weichgekocht; ich tropfe sie ab und streich sie durch ein feines Sieb. Dann rühre ich 150g Butter mit 150g Zucker und 2 Päckchen Vanillinzucker, einer Prise Salz sowie 3 ganzen Eiern recht schaumig und gebe den dicklichen Kastanienbrei dazu.

4. It's "Backe backe Kuchen mit Erna Horn" by Erna Horn, a recipe book for bakery. The quotation above is from recipe number 242 "Kastanientorte" a maroon cake. 5. is more difficult (given the exponential growth of these kinds of chain letter things). I tried to get out of the string theory circles by handing this over to Georg, Anna, and Amelie.

Effectiveness of Symmetry

For some strange reasons, only today I had my copy of the November issue of "Physics Today" in my mailbox, a few days after the December issue arrived. It contains an opinion piece "Reasonably effective: I. Deconstructing a miracle" by Frank Wilczek (online available only to subscribers of Physics Today unfortunately).

He discusses the famous Wigner quote about the unreasonable effectiveness of Mathematics in the Natural Sciences and comes to the conclusion that it can be traced back to symmetries and locality. Then he writes

Since any answer to a "why" question can be challenged with a further "why," any reasoned argument must terminate in premises for which no further reason can be offered.

Let's nevertheless still take this argument a little bit further, just for the fun of it. Why is the world symmetric and local? We are used from string theory that at least continuous symmetries are always local and global symmetries arise only as asymptotic versions of local symmetries. But on the other hand, local gauge symmetries are not really symmetries but just redundancies of a convenient notation. It is possible to rewrite systems with gauge symmetries only in terms of invariant objects (like e.g. Wilson loops) although that formulation is not particularly simple. It's just that in terms of more fields (like longitudinal polarisations of gauge bosons) the formalism simplifies (e.g. becomes linear) and one has to use gauge transformations to get rid of the unphysical polarisations. Thus saying the world has lots of symmetries really means the best formalisation of the world that we know of has many redundancies.

Or turned the other way round: It's not really the symmetries which are properties of the theories. For example people used to point out that GR is diffeomorphism invariant, it keeps its form in any coordinate system. Thus the infinite dimensional group of diffeos make up the symmetries of GR. But this argument is wrong. For example Misner, Thorne and Wheeler spend the entire chapter 12 of the Telephone Book on demonstrating that you can formulate Newtonian gravity in a diffeomorphism invariant way. This is just a fancy way of expressing what every first year student knows: You are not forced to use Cartesian coordinates to discuss Newtonian gravity you can use spherical coordinates as well. Thus this theory is also coordinate invariant.

The real difference between Newton's gravity and GR is that in Newton's version there is a covariantly constant one form dt which is background in the sense that it is not determined by an equation of motion but it is just there. It is externally given. Therefore what is often called "many symmetries" really means absence of such background structure.

But still, why is the world symmetric? One possible answer is that amongst spin 1 fields only gauge potentials have normalisable interactions. Thus, it might well be that at some high, fundamental scale there are many more fields and gauge symmetries are not that preferred. However upon RG-flow these other fields decouple completely. Thus having only gauge interactions remaining really just comes from the fact that our energy scales are much lower than the Planck scale.

You could even try to put an anthropic twist on this: If observers require a large number of degrees of freedom being strongly coupled tuned tuned to critical values (think: neurons in your brain) it is not unreasonable to believe that you have to be quite far from the fundamental scale where all hell of quantum gravity breaks lose. If that were the case, you could argue that observers always see gauge interactions and chiral fermions first as only these survive the running to these scales necessary for observing subjects. Of course, there is still the hierarchy problem of why there is a Higgs. And this argument does not tell us why we observe non-abelian gauge theories, U(1)'s would do as well. For this we might have to invoke moduli trapping or similar mechanisms.

Farewell hep-th/yymmxyz

In case you did not notice: The arXiv is going to change the naming scheme. This has become necessary as the current scheme only allows for 999 papers per month in each category and the mathematicians had reached 989 in November already. The new numbering will for example read

arXiv:0701.0001

and there is the possibility to explicitly refer to specific versions as in

arXiv:0701.0001v1

Note that the section (like hep-th) is no longer part of the identifier but it can be added as in

arXiv:0701.0001v1 [q-bio.CB] 1 Jan 2007

I would have liked a more conservative change (like just adding an eighth digit) as now I will have to change a number of regular expression in programs that are supposed to spot references to the arXiv like my seminar announcement web suite and my .bib file updater (which uses Spires to find out if a paper has appeared in print).

Coherent states

If you are not working on quantum optics, you might be in a similar situation as I was a couple of days ago regarding coherent states: You had encountered them in a homework exercise on the harmonic oscillator where you had to prove that they are eigenstates of the creation operator and have minimal uncertainty. And you know that they are important to quantum optics. At least this was my state of knowledge until very recently. Since then, I have read this review (with which I do not agree in all parts) and have spent some thoughts on the subject I would like to share my current understanding.

Let's suppose we have two hermitean operators A and B and want to find states such that the uncertainty is minimal. To this, let's briefly go through the derivation of the uncertainty relation: You assume any state and from it form new states and similarly for B where is the expectation value of A. For these two new states, you use the Cauchy-Schwarz inequality (which basically says in the form ), expand and find


Finally, we use that the absolute value of the imaginary part of a number is less or equal to that number and realise that as A and be are hermitean the imaginary part of the left expectation value is to arrive at which is the usual uncertainty relation.

If you want to rest for a minute think about the following puzzle: Consider a particle on a circle (or on the interval with periodic boundary conditions). Take the wave function and compute that for this state while . This seems to clash with what we just derived. Where is the flaw? (Hint: see a previous post about quantum mechanics)

Back to the main argument. We want to find a state which saturates the inequality. To have that we have to saturate the inequality in the two places where used inequalities: The Cauchy Schwarz and the abs less Im parts of the argument. Cauchy Schwarz is saturated (the scalar product is maximal for vectors of fixed length) if the two vectors are proportional to each other, that is if there is a complex number such that in our case . We can rearrange that to that is has to be an eigenvector of the operator . Furthermore, for the absolute value of a number to be equal to its imaginary part, the number has to be purely imaginary. In our case, this means has to be purely imaginary which can only be if is purely imaginary.

So we found that the uncertainty of operators A and B in a state is minimal if the state is an eigenvector of an operator with real .

So much for the general theory. Now, we can specialise to the usual case A=x and B=p and conclude that states of minimal uncertainty are eigenstates of for some real . Note that so far we have not talked about the harmonic oscillator at all. We have just picked two operators and asked for states in which they have minimum uncertainty. This was a question at the level of Hilbert space operators and we did not specify any sort of dynamics.

Thus, coherent states are not about the harmonic oscillator at all. It just happens that they are eigenstates of annihilation operators for some harmonic oscillator. Above any real does the job and this translates directly to the frequency of the oscillator: What people call "squeezed states" are just coherent states for a different that can in a similar way be related to the annihilation operators at different frequencies.

This so far is my current understanding. In the above mentioned review there is another generalisation which does involve dynamics which I do not yet fully understand. It somehow splits a Hamiltonian into sums of products of 'elementary' operators and then considers the Lie algebra generated by these elementary operators upon commutators. Then you exponentiate this algebra to a group and consider the orbit of the ground state of that Hamiltonian under the action of this group. The part I do not yet understand is how physical this is and how the different choices on the way (the set of elementary operators for example) influence the result.

Science and arXiv

I was made part of the team that assembles our school's research report involving contributions from all faculty members including references to their publications. My job is mainly merging all contributions into a single LaTeX document and managing the references. We decided to do them in BibTeX so we asked all faculty to provide a list of their papers in BibTeX format. The idea was of course that only a tiny part of this data would have to be typed as most literature databases (such as spires for our field) provide data in this format and other programs like Endnote can export BibTeX as well. Thus with a bit of cut&paste the job would be easy.

I had not expected the amount of computer illiteracy amongst science professors. OK, I knew that most biologists do not use TeX for their papers. But I must admit that I was impressed receiving an MS Word document containing BibTeX entries but for example having all the title="..." fields set in italics. That is not to speak of the many complaints I received about people having to retype their references. Plus the concept of separating content and layout is completely alien to many.

But what I really wanted to talk about is this: I learned during one of these discussions with an experimental surface physicist (who by the way keeps his references typed in a Word document) why he does not submit his preprints to the arXiv: He told me Science does not accept papers which are in electronic archives others than their own! I find this completely ridiculous and could not believe it since at least my only science paper (btw my first paper at all and still the one with most citations although not in high energy)had a preprint on the arXive. But it seems he is right, at least as far as the current policy is concerned.

Please, please, somebody tell me this interpretation is not true and the greed of the AAAS is not in the way of good scientific practices.

Paper cranes

Yesterday, I served as jury member for the exciting physics competition which is part of the WellenWelten ('wave worlds') physics exhibition in Bremen.

Children (possibly in teams) from 10 to 19 could choose from six construction tasks (announced two months earlier) and present their result in the Congress Centre.

I had to judge paper cranes. The task was to use only paper, glue, sand and twine to build a crane. It should only touch the table in an area of A4 size and be able to hold a 400g weight 40cm above the table and 25cm in front of the base. Furthermore, the crane had to be stable both with and without the weight. With these constraints the task was to build the crane as light as possible.

We had to judge the cranes not only on their stability and weight but also on design, presentation and construction. The level of the 15 submissions was very high and it was not easy to determine the winners. In the end we settled for this crane



which was constructed by two girls from 9th grade (13 years). The three runners up are



.

You find all the pictures here (two pages). Red t-shirts indicate participants and their teachers and dark blue is the jury.

Seminars while you drive

If I drive longer distances and get bored of listening to the radio I love audio books. Too bad they are usually quite expensive. But i discovered an alternative: Listen to seminars.

A good place to start is the KITP, for example their Blackboard Lunches.

The audio formats they offer are realaudio and ipod. As I do not own one of these white gadgets, I have to use the other option. My car radio can play mp3's (from its USB port or CDs). So I have to convert the .rm files to mp3. Here is how you can do that (so you don't have to spend as much time on it as I did):

In case it is not done already, install mplayer.

When you call it like

mplayer -quiet -vo null -vc dummy -af volume=0,resample=44100:0:1   -ao pcm:waveheader http://online.itp.ucsb.edu/download/bblunch/dine.rm

it will create a file audiodump.wav which in turn you can convert to an mp3 with bladeenc.

After you've done that for a couple of talks, use

mp3burn *mp3

to write the seminars to a CD and you can hit the road, Jack!

Update: Of course you don't use mp3burn as that would produce an ordinary audio CD with maximally 72 Minutes playing time. You want a data disk with the mp3's on it so you really use a program like xroastcd.