Tuesday, January 24, 2006

Some philosophy and/of string theory

by Robert C. Helling (helling@atdotde.de), the winning visitor #250,000

I am very happy to have this opportunity to guest blog in the Reference Frame. I thought I could use it to present a slightly longer essay on the philosophical background in the falsifyablility discussion about string theory. Regular readers here will be used to posts that are slightly longer than two sentences and arguments in favour of our beloved pet theory, although I have no intention to match the unique style of the regular poster.

The ancient Greeks introduced formal logic to be able to rigorously check if an argument is valid and to have a scheme to produce new true statements from others one is already convinced to be true. It is not too difficult to play with expressions and to concatenate them with "and", "or" and "not" (even if already at this level there are some pitfalls: At German traffic lights you can sometimes find signs saying "Bei Rot und Gelb hier halten", that advice you to stop at the indicated place at red and yellow lights rather than or).

Slightly later, people came up with an extended version of this scheme that also allowed roughly speaking the infinite concatenation of "or" and "and" using quantors "there is" and "for all". This already brings with it some of the dangers of set theory but if you are careful to specify that these always apply to elements of sets (saying "for all x in the real numbers" rather than just "for all x") you are pretty safe.

The problem epistemology faces is that empirical observations are of the first type but scientific theories are of the second type. In your lab, you observe "on this day in round #12345 of the experiment with parameters x, y, and z the measured result was 42". However, from those observations one would like to come to statements like "apples always fall down when falling from a tree" or "test-particles follow geodesics in space-time".

No matter how many observations you make (even if it could be an infinite number) you will never be able to strictly deduce a "for all" statement that is not only "for all experiments that I have done so far" but that tells you something about the outcome of future experiments.

Luckily, scientists are not logicians and take a pragmatic view on this problem being at some point sufficiently convinced that some theory is a good working hypothesis. Philosophers on the other hand have tried for centuries to formalise this process without too much success as it seems. For example coming up with statistical measures of confidence did not get very far (N.B. there might be something to learn for the landscapers) easily yielding paradoxes like the observation of a green apple supporting the thesis that all ravens are black as the latter is equivalent to all non-black things are non-ravens and a green apple is neither green nor a raven.

Progress was made on this point by the neo-positivists around Popper who emphasised that while you need to check all instances to verify a "for all" statement (or to falsify a "there is" statement) to show the opposite is much easier: If you claim that something holds for all x and I show you one thing for which x does not hold your claim is dead. Similarly, if I show you a y that fulfils some property P then I showed that "there is a y with property P". So Popper argued that a theory that offers many such potential failure modes and still survives is a good because it is predictive in a non-trivial way. This "falsifyablility" was promoted as the litmus test of scientific theories.

This sounds very nice from a logical perspective and is still very popular amongst practising scientists when quizzed on the logical foundations of what they are doing. Still, there came a blow to this attitude when Thomas Kuhn published his "Structure of Scientific Revolutions". Kuhn pointed out that although this formally sounds like a good way of proceeding, falsification is not what happens in the real worlds of science: If it did, scientists would be without theories nearly all of the time. There are many experiments that apparently disprove well established theories. For example on fun fairs you can see water that looks like it is flowing uphill. A strict falsifier would have to put his theory of things falling down in the dustbin and search for a new theory of things most of the time falling down but sometimes also up. But this is not the case. Rather, one believes in ones well established theory and investigates "what went wrong with the experiment" and eventually finds that the fact that the floor has a steep slope caused the illusion that the water was flowing up but that in fact it flows down.

Only if after a long time an experiment keeps failing and one cannot find "a reason" for it failing one will be tempted to tweak the theory and build in special exceptions that allow for this outcome of a theory. Still, usually, you just tweak the theory and keep the main body of it rather than give it up. Only if a theory gets more and more tweaked and revised and amended it becomes unattractive and more and more people will find a competitor more attractive. But such a challenge will only come from a competing theory which provides a better explanation and never from observation or experiment alone leaving one without a theory at all. Rather, people will stick with this the old, ugly, often repaired theory. The switch to the competitor is a sociological process (rather than a formal logical one) as pointed out by Kuhn and is the main subject of the "SoSR" but I will not discuss it any further here in this essay. I would just like to point out that this view is by now rather standard amongst people who think about how science is done (rather than the practitioners of science itself who often have a rather amateurish attitude in this meta discussion).

So, what has all this to do with string theory? Well, string theory is admittedly very weak on the falsifyablility side: More or less by construction at low energies it is indistinguishable from (maybe supersymmetrised version of) the standard model coupled to classical general relativity, at least we know it contains all the ingredients and I think there is no doubt that there are states (or vacua or compactifications whatever is you favourite name) in which below say 100GeV it just reproduces the standard model. You might find it problematic that it also has lots of states that do not at all look like the standard model (but for example like 10d flat space). To me this is unfortunate but not much worse than the fact that Maxwell's equations have more solutions (i.e. states) than just The Brecker Brothers playing Some Skunk Funk frequency modulated at 100MHz.

What I think is much more troublesome is that fact that if we tune into a state that looks like the standard model chances are that it won't look much different for the next couple of orders of magnitude or maybe just like a GUT. Even if we tune up the energy by another factor of 1000 (which is practically impossible for the foreseeable future given today's technology) it would be quite surprising if one finds undeniable signs of stringy physics.

Some will even claim this is true for all energies as do not really know what happens at strong coupling (unless there is a duality that maps it again to some weakly coupled theory). But at least, I think there is a consensus that weakly coupled string theory has distinctly stringy features at asymptotically high energies (like the spectrum of excited modes and Regge behaviour). Only that it will be impractical to probe these energies in accelerator experiments.

We might be unexpectedly lucky: Tomorrow, some graduate student might find a stable, testable low energy prediction of string theory. Or at LHC it might turn out, there are large extra dimensions and the fundamental scale is much lower than expected and therefore stringy features already show at scales reachable with today's experiments. However that would be quite a coincidence and we would in fact live in a very narrow corner of stringy parameter space. Or somebody discovers a cosmological imprint of stringtheory on for example the microwave background. Then there would be no question about the ontological status of stringtheory. But most likely we will no be lucky. What then?

I think, currently, expectations are a bit too high. Around the final stages of building LHC many string theorists wanted to get their share of the hype that comes with this big event of LHC being the experiment that for a long time will be the first that is very likely to see interesting "new physics" (we will be very likely learning a lot about Higgs and SUSY from it even if we will not find them, an outcome I consider unlikely). However, this "new physics" is likely to be plain old fashioned field theory and all attempts to link it to stringy or gravitational physics are not very convincing, yet. But these people have raised general expectations that, "soon, we will be able to see stringy physics" which of course is b.s..

Still, I maintain, that string theory is a very worthwhile endeavour. We know, there is gravity in the world and there is quantum theory and we cannot have both in their current form at once as they produce contradictory results when mixed together naively. So there has to be a unified theory of quantum gravity. And string theory is a candidate for it. Unfortunately, any such unifying theory has to match the limiting theories at low energies and simple arguments show that this theory will likely start to differ only near the Planck scale. So any such theory shares the above mentioned problems of string theory. This of course, unless you do something wrong: For example, if your theory breaks some symmetry like Lorentz invariance then this is likely to affect already low scales, you might find for example anomalous dispersion relations (or energy dependent time of flight) but probably you will have to hide this violation so it does not spring in your face at low energies. So even after working for forty years on string theory, people have not been able to circumvent this fundamental problem of any quantum gravity.

You could conclude that if you have very strict criteria for falsifyablility, the question for a quantum theory of gravity is unscientific because exactly of this reason. Then you are welcome to leave and go bird-watching or whatever you consider more scientific. But with such an attitude you will not likely find much left of science in fundamental physics.

Alternatively, you could decide you stay with sting theory for a little while; I argued above it is good practise in a science to stay with some theory at least for the time being until something much better comes up. And to many if not most of us, string theory is still by far the best player in town when it comes to quantum gravity. There is just no competitive alternative in sight. Everybody is welcome to look for alternatives. But this will be very hard (and this I mean not sociologically). And likely not fruitful. So, it is still a safe bet to commit most of your time and energy to string theory.

What makes me believe this, am I just the victim of the brainwashing of the physics mainstream Mafia? I don't think so. In fact, what I find fascinating about string theory is how few assumptions you have to make. You just make a small number of basic ones and the rest more or less follows (at least for almost all of the interesting developments, if you are desperately model building this might not be entirely true). It's not that with each paper, people come up with ten new hypotheses. Nearly all the papers investigate just the consequences of what is already there. And by doing this, people have found a huge number of surprises. The strongest among those are places where some circle of arguments closes. When you are able to arrive at the same conclusion on two entirely different routes. Routes that seem to be independent of each other and this "coincidence" is not merely something that was crafted into the assumptions. And string theory is full of these closed circles, in fact it is a dense network of facts that hold together very tightly.

This feature is what distinguishes it from the other approaches to the quantum gravity puzzle (if you accept that it as part of scientific investigation, see above). And this is what convinces so many people that it is powerful and there "must be something behind it".

Of course, it could all be "wrong". Then it would just be a funny mathematical theory. That alone would already be entertaining. But string theory is not mathematics. It is about gravity and about quantum theory and also about elementary particles. In addition, we have learned a great deal about the structure of gauge theories using stringy tools like the geometrisation in terms of branes. So string theory clearly is physics. Even it is not distinguishable in table top experiments from less ambitious theories like the standard model. It is really the best theory we have and pursuing such and fleshing it out has often proven not to be a waste of time.

Bremen, Germany 24 January 2006


  1. Dear Helling:

    Yes you have indeed been brain washed. You said you are fascinated by string theory because it only made a very few assumptions and it leads to very rich mathematical structures and lots of amazing results. No one is arguing against that fact. Yes, string theory has only a few assumptions. Yes, it leads to very rich mathematical structures and lots of amazing results. But if you are fascinated by that fact alone, you have been brain washed, because you have not opened your eyes. If you do open your eyes, you should see plenty of such constructs in the natural world or in pure mathematics where you start with a few very simple things and it leads to lots of amazing things. But that does not mean that the rich construct necessarily has anything to do with nature.

    For example, you should open your eyes and see a kaleidoscope. You would be amazed that such a simple device could render so many beautiful light patterns. You would spend a lot of time studying them, see how they transfer, and count how many different kaleidoscapes you can construct. The number of kaleidoscapes is it's probably much more than the number of landscapes. You could spend your whole lifetime studying all those kaleidoscapes, thinking such rich construct must have something to do with the nature and you could discover all of natures secrets by studying those kaleidoscapes. But at the end of day you grow from a 3 year old boy to a 93 year old man, and all of a sudden you discover it's just a few pieces of broken colored classes and it has nothing to do with nature whatsoever.

    The super string theory is just such a kaleidoscope. It indeed contains very much mathematical structures, no question about it. So far you have discovered there are 10^500 landscapes. What I can tell is after two decades of research of thousands of the best minds of the world, you probably have not even start to peel the surface of all the possible mathematics structures of super string theory yet. You are already amazed at the amount of math beauties you discovered so far, but wait until you find more later, much much more.

    The point is super string theory probably contains a virtually inexhaustible number of mathematical structures for you to explore, and it could suck in many many more intelligent minds into it for many decades, before you finally decides that it is beyond man's power to try to figure all those mathematical structures out.

    And then you turn around and find out this is just a Kaleidoscope and there is only just a few broken pieces of colored class. And it has nothing to do with nature. Is it worthwhile to spend your lifetime on studying a Kaleidoscope, just for the beautiful patterns in it that amazed you?


  2. Thank you for your comment quantoken, it is a good example: I agree, there is not much point in studying kaleidoscopes as they are boring. But they are boring because there is only one structure in a kaleidoscope and that explains it all: It is the symmetry group that is generated by two intersecting mirrors. If all of string theory would boil down to such a simple explanation, nobody would be interested in it. But it is not and that exactly is my point.