Thursday, December 21, 2006

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.

Tuesday, December 19, 2006

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.

Tuesday, December 05, 2006

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

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

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).