Everything solved!

While I was away for a wonderful vacation in southern France, I nearly missed gr-qc/0606121. In the first paragraph we are reminded

The issue of the dynamics is perhaps the central problem in canonical quantization approaches to totally constrained theories like quantum general relativity. There are three salient aspects of the problem that have prevented from advancing in the quantization. The first one is how to construct a space of physical states for the theory that are annihilated by the quantum constraints and that is endowed with a proper Hilbert space structure. The second issue is related to the introduction of a correspondence principle with the classical theory, in particular to check the constraint algebra at a quantum level. The third problem is how to address the ``problem of time'' that is, to introduce a satisfactory picture for the dynamics of the theory in terms of observable quantities.

Then come three pages of semi-technical stuff (finite number of degrees of freedom models, Legendre transformations) and eventually

Summarizing, the method of uniform discretizations allows to tackle
satisfactorily the three central problems of the dynamics of quantum
general relativity and provides new avenues for studying numerically
classical relativity as well.

Well done, guys! Now we can stop worrying about quantum gravity and spend all your energies to cheer up Klinsi's Jungs!

Sorry, I didn't have anything more intelligent to say.

Higher order stuff

It has been over a month since my last post. And as I will be on vacation in a few days which will probably take me off line for a while I thought I should send some sort of ping before disappearing to Provence.

We had been busy finishing our paper on WMAP multipole vectors and soon after got busy with Wolfgang, my office mate, thinking about entanglement entropy. The latter project is not yet in a stage to be discussed in detail but I think this potentiallly quite interesting.

Instead, today I would like to mention a book that I have been reading recently: It's "Higher Order Perl" by Mark Jason Dominus. This is the most interesting computer book I have read for years. It has the potential to change my thinking about programming as much as the first time I learned about Perl.

If you have formal trainig in computer science and talk Lisp each day, this is will not be too interesting to you. But if you like me learned programming the street style there are a few things to note.

When I have to explain why I like Perl so much I could say it's because you can write nice short effective programs and it's very easy to communicate to the compiler what you want. Plus you have regular expressions and don't have to worry about memory management and garbage collection. But usually, I explain how much I liked the idea (of course like all not unique to Perl) that if you have a collection of several things integers are natural labels in very few cases, thus an array is rarely what you really want. It's a bit lik e coordinates. One option is to call things by their name which gives you a hash ($lastname{Robert} is much more natural than $lastname[1]).

The other case is that you don't care that some element is the 4711th as long as you get all of them either at once or you get one after the other (and can iterate over those like in a foreach $element(@list) construct). This gives you lists. If you have a list, you can take the first element and the rest and you can add elements to the beginning and the end. No need to worry how many elements there are as long as there are more than zero.

The "higher order" in the title of the book refers to the possiblility to have functions that return functions (or rather references to functions. So what?, I hear you think. Well, for the mathematically inclined: This allows you to go to the dual space of your data! Instead of manipulating the data, you can now manipulate the ways to access the data. And you should know that the dual space can in general be of very different size. Think of your examples in functional analysis or about distributions: There you first restrict yourself to very nice functions, the "test functions" and then look at their dual space which gives you distributions, quite powerful objects that are more general than functions.

Now back to the programming examples: Think again of a list. I mentioned, the only thing you needed to do with lists is take them as a whole or access the next element. But this is really enough! It is enough to pretend you know the list if you know a way to always get hold of the next element.

For example, with this you can come up the the universal doubling function. It takes a list and returns a list that has each element doubled. But in fact, all you do is to answer the question for the next element by going to the original list, taking the next element from that, double it and return it. Or you can interlace two lists or concatenate them by using obvious strategies to return the next element of the resulting lists.

This way, you can of course handle infinite lists that don't fit into your memory like the list of all integers. This is where really the power of the dual space notion comes in. All you return is a function that computes the next element. From this you can obtain the list of even numbers by applying the doubling function or the list of primes by discarding integers that are not prime.

Isn't that neat? Go get this book and read it!

Fast strings

When I explain strings to non-stringy physicist, I often start out by stating that a string is like a rubber band and has a potential energy which is proportional to its length (like a 'relativistic Hook law'). Then, all you have to do is to covariantize this statement and you arrive at the Nambu Goto action.

You can, of course read this backwards: A string with potential energy E has a length proportional to E. Now, you can often read this as an explanation of why hard string scattering behaves much better than hard scattering of particles: At high energies, the strings in fact expand and thus the interaction delocalizes.

This, however, is only semi-true: I would think of what you have in hard scattering are strings which have been accelerated so that they have large centre of mass energy. But the centre of mass energy is decoupled from the internal energy of the oscillators and thus a boosted short string will still be short although it has large (kinetic) energy. On the other hand, you can have a long string with zero kinetic energy which just happens to be very heavy. So, in general, heavy strings are long, not fast ones.

So far, this is just kinematics, but can we see this in practice? What happens to a string that runs through a linear accelerator? So, the set-up would look as follows: You start with a string which is in a low mass state which is charged under some U(1) (maybe in a KK type theory, D-branes are welcome as well). Now it feels a electric field strength (of some cavity say). This electric field is a condensate of low energy (given by the normal frequency of the cavity) photons. So, you have to compute the scattering of the string with lots and lots of low energy strings in the vector field state.

Question: Even if the individual photon has energy much less than 1/sqrt(alpha'), does this scattering excite any of the higher oscillator modes (which make the string grow)? A Feynman diagram would look somewhat like

e----x-----x-----x-----x- ... -x-----h
     |     |     |     |  ...  |
     A     A     A     A       A

where e is the charged low energy state, A is the gauge field and h is a heavy state. Has this been done before?

Eurostrings

I just came back from one week of Eurostrings at DAMTP, Cambridge which was a combination of a network meeting of the EU String Network then turning into a celebration of Michael Green's 60th birthday. So, before anything else:

Happy Birthday, Michael!

This was a particularly nice event and quite different from other european meetings there was also a large number of people from the Americas attending which I assume was due to a) celebrate Michael and b) that this year's Strings '06 conference in Beijing is not too attractive for a number of people for various reasons.

Once more, I was surprised how many people actually read this blog and came to me during the conference mentioning some of my entries in the past.

As here was no wireless network operational during the conference and unlike the Loops '05 I did not feel the strong urge to report. Victor Rivelles already has and Peter Woit has as well.

There were no really big surprises, just look at the titles of the talks and you get a pretty good idea what was going on; there are online proceedings for those who want more details. Looking through my notes reminds me of a few that are worth mentioning never the less: There were talks by Damour, West and Kleinschmidt about the relations between M-Theory and hyperbolic Kac-Moody algebras. By now, it becomes clear how this works dynamically (at least at low levels). The KMA structure even fixed numbers like the coefficient of the CS term in 11d sugra which is usually determined by supersymmetry. I would really like to see worked out how this works in detail, it would not be the first time, there is a relation between exceptional Lie algebras and susy.

A number of people talked about the relations between spin chains and N=4 SYM and strings and another theme discussed by several speakers was the relation between black holes and topological strings (known under the names of OSV). Especially, Strominger gave a nice derivation on the blackboard of the mysterious square formula.

Seiberg gave two talks both quite interesting, the first on a paradox if you apply T-duality in the euclidean time direction to relate high and low temperature physics and how this is related to the Hagedorn transition and the second on his findings in N=1 theories which even if they have a vanishing Witten index often have a non-susy meta-stable state at the origin of scalar field space. This is potentially very interesting phenomenologically as it provides a mechanism of dynamical susy breaking but unfortunately I understand too little of N=1 gauge theories to give you more information. But you can read it all in the paper.

Finally, I would like to point out a little triviality in elementary quantum mechanics which seems not to be generally appreciated. Imagine that some degrees of freedom are not accessible to you, maybe because they are behind a curtain or even the horizon of a black hole. Formally, you write your Hilbert space as a tensor product . The whole system is in a state described by a density matrix which could well be a pure state . As you see only part of the degrees of freedom, you observe only the partial trace , where the trace is over .

The time evolution is is given by the Heisenberg equation and this implies that the entropy does not change with time. Especially, a pure state (with entropy 0) cannot evolve to a mixed state and vice versa.

This however is not true for the reduced state . It evolves unitarily as only if the total Hamiltonian is a tensor product that is if the two tensor factors of the Hilbert space do not interact.

Otherwise, for example if you throw stuff behind the curtain (or horizon) the time evolution of is more complicated and will change in time. This means, if we only observe part of the Hilbert space, a state that was pure in our part of the Hilbert space can become mixed by interactions with the other degrees of freedom.

This is of course well known to people working on decoherence but somehow not so much amongst people thinking about quantum cosmology.

Sick at home

The past weekend, we had a family reunion at my parents' place and I planned to go back to Bremen late Sunday or Monday morning. However, I had been quite tired the better part of last week (which at that point I had attributed to the late stages of finishing our paper on multipole vectors in the three year WMAP data and the visit by Guiseppe Policastro as we had not always finished discussing by 6 p.m.). Sunday evening, however it became appearant that indeed there were a number of red spots on my face and my Monday morning all over my body (for illustrations see here). The doctor confirmed my internet based diagnosis of rubella (German measels) and told me to stay at home for the time it lasts. Now, I am with my parents, they take care of me and I have fun reading papers and other things.

So, let me tell you about a few things I came across in case you also have some time to waste. Let's start with a poem by Thomas Gsella published in the weekly supplement to the Süddeutsche Zeitung (in German, I attempt no translation):

Berufsbeschreibung
Der Astrophysiker

Gewöhnliches ist nicht sein Ding.
Er aast im Unbekannten.
"Ereignishorizont" und "String",
das "Schwarze Loch", die "Quanten":

Er faselt Super-Quark und hört
dem "Hintergrund" sein "Rauschen".
Auf Partys steht er da und stört,
doch welche gibt's, die lauschen.

So ist ihm schnurz, ob wir's kapiern:
Er faselt guten Mutes.
Er will den Damen imponiern,
und ach, oh weh, er tut es!

Let me just add that from my experience this poem is rather unrealistic.

Next is a geometry problem I learned from my office mate Wolfgang Spitzer: Draw a sqare and mark one random point on each of the four sides. Now, erase the sqare just keeping the marked points. Use compass and ruler to reconstruct the square from the points. For bonus credit find conditions on four random points to lay on the four sides of a square.

Finally, there is a puzzle from "Spektrum der Wissenschaft", the German version of "Scientific American": A biologist starts with one bacterium. Each night, each bacterium splits into two. (Up to now, it sounds like a pretty dull, well known problem, but...). However, he notices that in some nights, exactly one bacterium becomes inactive and does not split on that night or any of the further night but it stays alive. Yesterday, the biologist counted 1638 bacteria, today, there are 3245. How many days ago did he start with the single bacterium? You can sumbit your solution to Spektrum until April 11th and win a carrier bag.

Wolfgang does not offer a prize but his problem if found much harder.

PS: I received a complaint that I had left destructive comments in other blogs. Let me assure you that I try not to be descructive but I don't know how you percieve it. Nevertheless, I always sign comments (as well as usenet posts) with my name and link to this blog. So comments from annoymous people or other Roberts (without link to atdotde) are not by me.

Email add-ons

Many people have asked about confirmations that emails they sent were actually received and had to learn that there is no reliable way to check this even if some mailers offer "return receipt" features. For one reason they are not part of the RFC's starting with 822 that define the protocol used to transmit emails: They don't work. First, what consitutes 'receipt' of an email? The first host (in my case atdotde.de) receives the SMTP message? Well, from there it's forwarded to an account where I run my mail client (currently at DAMTP). So, the first host, that does local delivery instead of forwarding? Or the first program that opens the message (spamassasin in my case)? Or the perl-script I use to organise my mail folders? Or only a program that displays the message on a screen (mostly 'pine' in my case, but could be 'less' as well when things get rougher)?

The general recommendation is to ask the reader in the body of the message explicitly to reply to the message to confirm reading it. But even reading it does not always mean one understands it. So even better, do a quiz on the contents of the mail. But still, not getting the confirmation does not mean the message was not read.

But today, I learned of a company which offers the solution to this problem: You have to register with them and get an account (free for 10messages/month, $50 per year for 750messages/month). Then just add .didtheyreadit.com to any email address. This causes the email to be routed through their server where this part of the address is stripped and the message gets an html attachment with a link to an invisible picture (1x1 pixels transparent say) with a unique URL.

The idea is that your email client downloads the picture to display it and they know somebody opened the message in a picture aware browser.

I use pine which is text based and thus does not care about pictures. Thunderbird at least is concerned about my privacy and warns me it didn't download any pictures that were refered to in the message but not contained (note that spammers also use this trick to determine which of the addresses they succed of web pages are actually read and are not directly going into the bit bucket). Still nothing happens. But if I click to download the picture (or use another mail client that is not so careful about my privacy) the sender of the message gets this.

Upshot: If you recieve an email with an attachment that looks like

<br />
<br />
<div><img src="http://xpostmail.com/b8a6a2cd5cd9ff294ecdf69dbb55d469worker.jpg" nosend="1" name="dtri" width="1" height="1"><link href="http://xpostmail.com/b8a6a2cd5cd9ff294ecdf69dbb55d469.css" hreflang="dtri" rel="stylesheet" type="text/css"></div>

the sender spys on you!

Fusing branes

For the first time this semester, yesterday, I had time to attend our school's colloquium. Everybody in academia will know that there is always a temptation to skip colloquia as they typically are not in your own area of expertise (and often that means interest) and if the speaker is not too good there is often not much you get out of it than at best some intellectual entertainment.

Still, my general philosophy is that in the long run it pays to invest 1.5 hours per week into broadening one's perspective and to get an idea what's hot in other areas of science. Physicists that refuse to spend time with anything else than their own little area of research are in my eyes just ignorants. Nevertheless, I usually take something to read with me so I have a chance to do something slightly more useful with my time once the speaker loses me. In recent times, I have also taken sudokus to seminars but I should better not admit that.

Yesterday, however, there was no need to bring anything, even though the talk was on microbiology because it was just excellent. The speaker was Reinhard Jahn and he talked about fusing membranes.

I have an interest in those as well, at least if we are talking about D-branes:



There, 'recombination' is an elementary process in which two branes join into a single one. It is still simple enough to be understood in detail but via dualities it is related (or archetypical) to many topological transitions (like small instantons, M5-branes falling into end-of-the-universe branes in heterotic M-Theory/Ekpyrotic scenarios etc) in string theory.

In biology as well, one can worry about the microscopic workings of this resolution of a singularity. Different from string theory, cell biology has a natural discreteness at small scales and at some point it becomes important that biological membranes are double layers of peptides sticking together by hydrophobicity.

So, I learned that cell membranes are not really elastic and if a cell (or one of its compartments) grows it has to add membrane which comes in small spherical blobs that fuse with the membrane that is about to grow:



Reinhard Jahn explained the inner workings of the process. An important role is played by somewhat longish specific proteins (SNAPs) that have one end sticking into the membrane and an alpha helix sticking out into the surroundings. Now, if two membranes get near each other, the helices of four of these SNAPs can coil up and form a highly stable supercoil. This draws the membranes together so they can fuse as well as releasing binding energy in the coiling up process that is used to overcome an activation energy barrier for the fusing process. Very fascinating and brilliantly presented!