Thursday, December 16, 2004
Friday, December 03, 2004
A rose is a rose is a rose.
True but even more as I have learnt again recently and especially in people's understanding of science. Driving to IUB I heard a radio progamm on creationists somewhere in the bible belt that put stickers on school books saying that "Darwinism is just a theory". Fair enough. But what do these people really mean? Theories are the best approximation to the truth that science has to offer. Anything based on empirism can a best yield theories. Based on our limited observations, we can never deduce anything that is actually true (meaning guarantied to be true).
Of course, there are other ways to truth than observation and deduction: Mathematical theorems are true (meaning derivable from the axioms). But that truth is only internal and doesn't tell us anything about the world.
And of course there are a lot of people (some with blogs) that even doubt that string theory is really a theory. It is probably impossible to argue with them and I wouldn't go down the road and discuss falsifyability with them as this positivist concept (although still in many physicists box of tools) is from a philosophy of science quite old fashioned.
Thomas Kuhn has taught us that falsifyability is really an illusion and that no experiment or observation has ever falsified a theory. You can always blame it on circumstances of the experiment or the set-up or add some fudge factors to the theory to accomodate that observation. Another common approach is to claim that you don't understand your theory well enough yet to understand if the observation is really incompatible with it. But you will never end up in a state without a theory (or should I say paradigm) because all your candidates have been falsified.
It is only that if there is a new paradigm that more easily accomodates the important (defined by the paradigm!) observations that many people switch over to the new paradigm. But again this is not directly based on logical deduction but much more because the feel more comfortable with the new paradigm.
But I am dirgressing, I don't want to discuss Kuhnianism today (but still I urge everybody to read and think about "The structure of scientific revolutions").
My other encounter with the real world happend in a pharmacy some days ago: A. has a really bad cold and we wanted to buy some cough syrop. The drugist offered two different products: One was the ordinary drug that she described as quite strong and effective but with words that implied that it might be too strong and have side effects. The other bottle contained a syrop based on some thyme extract.
I was only in the back as A. did the shopping but then the druggist said something that forced me to enter the discussion: She said that the first drug contains a "chemical substance". Obviously she wanted to sell drug two (which of course turned out to be more expensive than drug one) but she had intended to scare A. by mentioning chemistry.
Being the way I am, I could not resist and replied that I hoped that drug two would contain chemical substances as well otherwise I could not imagine it to be effective (maybe except for some placebo effect). Of course, she had to admit that (thereby making clear that drug two was not some homeopathic way of selling expensive water and maybe alcohol).
But this druggist's sales strategy made me worry and I hope that when I need a drug I get better advice. If in doubt I would rather take some effective and clean synthetic substance (I assume that is what she ment by 'chemical') rather than some dodgy plant based product that might contain hundreds of different substance that I effective at all might have uncontrolled interactions.
For example, I know many people that swear by echinacea based drugs to prevent getting colds. But from what I heard, none of these drugs has been proven (again according to some scientific standards that of course cannot derive truth but only some level of trust) to be effective apart from irritating the immune system. However, in several cases this irriation got fat too strong and people got life threatening alergic shocks.
So, please people tell me the truth and give sound advice rather than trying to scare me with misused scientific terms such as 'theory' or 'chemical'.
PS: Thanks to Anna Langley for mentioning that in theory theory and practice should be the same but in practice...
PPS: A. bought drug two.
Thursday, November 18, 2004
OK, we physicists know how to do this: In terms of a Cartan basis (H,E,F) we take an eigenvector of H and than act on it a couple of times with E to show that if this does not terminate we end up with negative norm vectors. Easy.
But this was too easy. If we have to consider infinite dimensional representations one should be careful with functional analysis. It could be that H is only essentially self-adjoint (like the momentum operator) and thus does not have eigenvectors because it only has a continious spectrum. Can you repair the above prove in this case or show that it cannot happen or find a counter example?
Wednesday, November 17, 2004
This is quite disappointing for people who were hoping that string theory as the theory of everything would once and for all answer all questions about space-time dimensionality, matter content, masses, coupling constants, mixings etc. There are even people who argue with this new insight string theory lacks any predictability at all.
What I would like to argue is that both these views, the optimistic hope for a unique vacuum and the claim of predictive emptiness of string theory, have unrealistic expectations of a theory of everything.
We now have some centuries experience with more and more unifying and more and more fundamental theories (starting from Newton’s unification of gravity with celestical motions) that we should have learnt the lesson how these things work: There are always two theories, an old one and a new one, or an engeneering and a physical theory if you allow me this pun. The old one often actually consists of several independant subtheories (like the theory that "apples keep falling down" and "planet move on cubic sections") and the new theory in some sense "explains" the old theories.Like there is a simple, local force law corresponding to differential equations that happen to have cubic sections as their solutions.
Another example would be the theory of atomic spectra: Lacking any quantum mechnical model (not even Bohr's theory) one could have just a big book that contains the frequencies of the spectra of all elements (and possibly molecules). That is a theory of the type engeneers like to have: They have big tables with lots and lots of numbers describing for example all possible gears that are on the market with their mechnical properties.
Another example of such a theory is the particle data book. This contains many many numbers that describe out understanding of the standard model. Well, here I am cheating a bit because we believe that most of the numbers (especially all the branchings and all the baryonic data could in principle be computed from QCD etc), but there are still the first couple of pages. You get the idea. Now one might have hoped that once one has a sufficient understanding of string theory in situations with low or even no susy, there would be a unique ground state and similarly, one could have computed all those numbers (like mass of the electron, weak mixing angle, the ud matrix element of the CKM matrix) from string theory. Now the landscape seems to end these hopes.
But why should we have stopped with those microscopic numbers? If there would have been a unique state of string theory, we should be able to compute many more properties of this state (also known as our univers): Why not compute the mass of the earth. Or the number of water molecules in the Atlantic ocean. Or the length of my left index finger. If there is only one state (=one universe), all these numbers should at least in principle be computable from
Obviously, this is nonsense and nobody would have believed this in the first place. It might have been a possible scenario but nobody should have been so overoptimistic to expect a unique state of string thoery.
The real difference between the old and the new theory is that what used to be 'external parameters' in the old one (for example parameters of its equations of motion) are properties of the solution/initial conditions of the more fundamental one. This is like Maxewells equations: For all we know, they are the fundamental theory of electromagnetic radiation but nobody would expect to compute from them which song Radio 1 is playing at the moment. The song is just encoded in the initial and boundary conditions for a specific solution to dF=0, d*F=j.
I think, one should (have) expected a similar situation for string theory (or better M-Theory): As a theory of everything it should not have dimensionless parameters in its formulation, but still, there are many solutions to its equations of motion and at least some of the properties of our world (including maybe some of the standard model parameters) are simply properties of a specific solution.
But on the other hand, this does not mean that anything goes and (again in principle) string theory will never make any prediction: Simply take scattering at very very large energies. Those that correspond to distance scales much smaller than our compactification at hand: Than I would expect to see an excitation spectrum typical of strings with the tower of states etc. OK, this might not yet happen at LHC but I am talking in prinicple.
Furthermore, it might be that over all solutions to the string equations of motion not all but only a submanifold (or even only a discretuum) of the macroscopic parameter space is swept out: There are relations. It might be that the mass of the proton is always 612 times the mass of the electron times the number of generations. Who knows? That would clearly be a prediction. It's just at this stage we are not yet powerful enough to make these kinds of predictions.
Even in quantum mechanics, may properties of the emission spectra one is computing with Schrödinger's equation depend on intial and boudary contions: One has to specify for example the charge of the nucleus and the number of electrons before one can predict the energy spectrum. There is no unique solution to Schrödinger's equation but still, QM predicts for example Rydberg's law that you can write the energies as a constant times (1/m -1/n) for small integers m and n. Similar predictions be be possible in string theory even if there are many vacuua.
Thursday, November 11, 2004
Today, on my way to work, I heard a radio progam on Deutschlandfunk, the nation wide public radio, from which I learnt some factoids that I would like to share with the blogsphere.
The historic Martin was born as a roman (the name relates to Mars, the roman god of war) in the fourth century and started out as an officer in the roman army but later turned christian an became a archbishop in Tour, France. As such he of course was also a political figure and after his death in 397 was the first saint that did not die as a martyr.
His day is Martini, November 11th, which later became the last day of the peasant fiscal year: On this day, the contracts of farm labourers and servants ended and taxes, feud and leasehold had to be paid. It is also the beginning of a fourty day lent period and the way these things work was celebrated with a feast. This is the origin of the tradition to have a roast goose on Martini and for childern to have processions with hand lanterns. In some regions, this is also the day on which this year's wine is drunk for the first time.
Finally, 11/11 is the first day of the "fifth season", the carneval period that culminates in the days before the spring lent in February. But at least this custom is too Catholic for me to notice...
Wednesday, November 03, 2004
TV says that values rather than issues decided this election. I just find it sad that there are so many people that have views on christianity, tolerance, social issues, ecology and international relations that on the long run I expect to turn against all of us. He will be your president, not mine, it's just that at least some of the time we have to share the same world.
Sean Caroll has written an entry on how to move on (with a long term perspective) in the Preposterous Universe that I support 100%!
Monday, November 01, 2004
Friday, October 29, 2004
I had a long discussion with Annette about this spot and whether the coworkers liked the idea or just nodded because they didn't want to ruin their bosses succes of coming up with something they thought was stupid. The spot was on the internet as well but now you have to pay 15 pounds to see it, so unfortunately, you cannot judge for yourself.
I tell you about this because not being able to read people's expressions is one of the symptoms of autism. Not that I claim I am autistic, but sometimes you wonder whether being a string theorist brings you quite some way in that direction.
I enjoyed a lot the 'curious incident of the dog in the night-time written from an autistic boy's perspective. It is alarming how he tyranises everybody around him without noticinig. A must read! And the chapters are numbered from P, the set of prime numbers rather than N.
There is also Asperger's syndrome, something like Autism Light. That is probably pretty common in certain academic departments. Reading this page makes clear that I and most people are far from that stage (there was a student in Cambridge who was a diagnosed sufferer of asperger's syndrom and knowing here makes clear that all the nerds and geeks around you are way in the middle of the bell curve) but sometimes you wonder...
If you want to see for yourself, wired magazine has an online test. They say, the average person scores 16.4 and people with asperger or mild autism typically score 32 and more. My score was 28. What's yours?
Thursday, October 28, 2004
Update: Unfortunately, the above link now forwards to the general Renault website and the clip appears to be gone.
Second update: YouTube helps out:
Here is the one with Animal:
which I was talking about. There is another one here:
Wednesday, October 27, 2004
As a souvenir from that workshop I brought with me a book with proceedings. That is not so unusual, but in this case these were the proceedings of the Nobel symposium on Particle Physics in 1986. The conference name however is not telling the truth, it was more about strings than about particles. It is really amusing and amazing to read in this volume. Obviously, this was before the second string revolution of the 90s but there are some hint already around.
It starts out with a picture of all participants (18 years from today). Once I found a scanner I will let you participate in this picture, so far I can tell you that I am able to recognize the following people (in no particular order): Green, Van Nieuvenhuizen, Schwarz, Gross, Witten, 't Hooft, Ellis, Hawking, Salam, de Wit, and Fiedan. The list of participants is much longer but the picture is not of supreme quality.
The first contribution is a review by Michael Green that starts out with an expose of Regge behaviour of scattering amplitudes (much more detailed than chapter one of GSW) and then covers all the 'recent' developments. Michael finishes by listing 245 references which costed him quite some efford as he told me. Then comes Olive about KM algebras and Alvarez-Gaume about anomalies and index theorems, Gross explains the heterotic string (mainly text, very few formulas). Many more contributions follow, Witten talks about string field theory as do many others.
In the end, it gets particulary interesting, when they predict what will happen next. John Schwarz' contribution has the title 'The Furture of String Theory'. So let's see, what he predicts: He lists six approaches to string theory: 1) operator methods a la Olive, 2) Polyakov's path integral, 3) 2d CFT by Friedan and friends, 4) 10d effective action 5) light cone gauge field theory 6) string field theory and he predicts "All six approaches wil play an important role in the future developments". OK, he got that mainly right.
Then he talks about background independence, but I guess that will have to waiut for the next twenty years. His next prediction is that type II and heterotic will be shown to be finite at all orders of perturbation theory. Thank's to Berkovits, he got this right as well. His next prediction is "World sheets of infinite genus will plau an important role in future nonperturbative string theories.": That was only half fulfilled: Nonperturbative methods were at the heart of the recent developments, that's right, but I don't know anybody who thinks about those in terms of infinite genus worldsheets.
The next point is the uniqueness of the theory. He quotes Harvey who said that "various heterotic string theories are really different versions of the same theory" and then predicts "It would be most satisfying if there were only one string theory, which is the correct microscopic theory of nature...Presumably the heterotic theory shoud be the survivor. If this is going to happen the type I and type II superstrings would have to be found to be either inconsistent or equivalent to the heterotic theory". Well, M(other) decided for option 2.
The next prediction is an easy shot: "Future progress in string theory will be accompanied by significant advances in mathematics". And the last one is probably the best one: "String theory will be an even more vital and active subject at the turn of the century than it is today ".
The conference summary is done by Gell-Mann. Among many other things that I do not have time to report on right now, he mentions Luis Alvarez-Gaume as giving the lecture that should get the sublimal award for the meeting for flashing transparencies at the highest rate. He reproduces a page from his notes (I should scan that as well), that reads
picture of worldsheet ----> some flat diagram, phi=integral dphi not single valued...IMPORTANT....???...1) phi --> phi+const. 2)------ [two more transparencies]...??...Assume winding of soliton around a-cycles and b-cycles ==> 3rd term... 2nd term computated in holonomy... 1st term??? ...S=S1+S2+S3
And he mentions S-duality of type I and Het-SO(32): "Ther is even the half-joking suggestion of Ed Witten that the two SO(32) theories might be physically equivalent, is such a way that the dilaton field phi is one formulation is related to phi^(-1) [should be -phi] in the other." You can find this conference on spires
The following years, it became the rule that you had to queue for a train ticket for at least ten minutes, much more in peak hours. Then they introduced vending machines where you could buy your ticket with your credit or debit card. But those were restricted to 'simple' tickets. For more complicated things like reservation of a seat with a socket for the laptop or trips with complicated stops in the middle you still had to queue.
But now, you can surf to the above address, register your name etc. and then search for a connection and get your ticket as a pdf file. This pdf document contains your name, part of your credit card number and a 13 character key containing letters and digits. On the train, the conductor slides the credit card through some gigantic PDA, checks a photo ID and types in the security key to verify the ticket. So far, that sounds reasonable.
On last weekend's trip to Berlin, I had to learn hat a fourth step is important as well: The conductor insists on stamping the ticket. Before leaving, stupid me had been so clever to move the printout from my bag to a pocket. However, this is not an atomic procedure and multitasking interrupted right in the middle. Effect: I left the printout on my desk. I still had my laptop with me that had the pdf on the harddisk and I had it as well on my USB stick. But at Bremen central station I couldn't find a place that could print out one page of pdf for me! I had to buy a new ticket because the cannot stamp my laptop's display. I can return the online ticket, but this costs 15 Euros. Why?
For old style tickets it makes sense to devalidate them by stamping them. But why do they insist on this once they gave me the pdf that allows me to produce hundrets of printouts of the ticket? It seems, this rule procedure was implemented by somebody lacking some basic understanding of how computers work.
Tuesday, October 26, 2004
Under Win2k, the problem is probably that I have not yet found out which encryption key to use. That problem most likely has an easy solution once I seriously investigate it.
As we all know, Win sucks and GNU Linux is much cooler. Thus I resized the partion (took me a day due to some sectors marked damaged by some hard disk driver) and installed debian. With the help of Christian I even manged to compile and install a 2.6.8 kernel. And with some heavy googling I resolved an interrupt conflict.
Some things that still need some fiddling: Make the irda port recognize my new Sony Ericson T630 mobile phone and transfer image and sound files. Get wireless networking to work (the experimental driver module for the intel 2100 wlan chip is supposed to come in a .deb package that cannot be loaded from the usual debian servers...), migrate mail reading/composing to the laptop (I still use pine running on a machine in Cambridge). Of course just using IMAP to transfer the mail to the laptop is not the hard bit, getting spamassasin do an equally good job as the spam filter in Cambridge is much harder and finally I want become as versatile in mutt than I am currently in pine. I still find that UI very confusing and it does not work properly for me (for example sorting mail semiautomatically in my 100+ mail folders). You see, I am quite behind. And there is also some physics to do....
I find this hard to believe. From what I can see a typical poll has a (statistic and systematic) uncertaincy of at least 2-3% (absolute, not relative). This means that in many states it is in principle impossible to make reliable predictions and due to the very non-linear "the winner takes it all" system, these uncertainties become amplified when it comes to the majority in the electoral college.
From 2000, we still remember that it is not the total number of votes (assuming there are no further problems in deciding which ones are valid) that determines the next president but also how they are distributed over the country. And none of the reports on recent polls that I have seen comment on this. They all state only that Bush is leading by a couple of percent but not how that translates into votes in the electoral college.
Talking of conspiracy theories, there is still the issue of Bush being radio controlled during the TV debates. I must say, I would prefer if he would have been. In the end, it is also his advisors that determine policy so why shouldn't they have their say in the debate? Bush by himself is probably not very powerful or influential, it is the people in the background that you never get to see because they are hiding in their think tanks and operate the teleprompter or the RC for the president's mouth from there. And they make sure that groups that put huge sums of money into getting candidate x elected get their money's worth of their investment.
The question is: Do I really need the "linear combinations of" or can I get away without it. Your task is to find an example of a Lie algebra, where some
[a1,b1]+[a2,b2] cannot be written as [a,b]. Can you characterise algebras where this happens?
BTW, this is an exercise for you, I think we managed to figure out the solution. I just post it as I like it because it is not a standard exercise of the form "Show that the following assertion is true using the standard methods explained in class", it rather requires more creativity to solve it.
PS: Jacques Distler is right, TeX in a blog would be nice!