Recently, it became fashionable to claim string theory is not scientific because it makes no testable predictions. Let me not again get into the testable vs falsifyable discussion, I still think people who still insist on falsifyabilty should quickly patch their philosophy of science module to a more recent than the 1934 version (Karl Popper's "Logic of Scientific Discovery"). But I hope everybody would agree that a theory can only be scientific if it makes statements about empirical observations.

Now, many people claim that string theory does not fulfil this criterion for a good theory. This view is fed by string theorists speculation about landscapes of vacua of which the number has not error bars in the exponent (like some numbers in astronomy) but in the exponent of the exponent. It seems that if string theory has so many different low energy versions that we can never extract any unique features that are observable.

In addition people become more and more excited about LHC taking data in a foreseeable future and there are many many different versions of signatures of supersymmetry or even low scale quantum gravity being visible in the new detectors. And they all look very different and once again it seems string theory can fit more or less every possible experimental outcome.

However, I think that many sceptics confuse two things here: The property that something can be observed in principle and that it can be observed in practice (now or soon or with today's technology). If we had a Planck energy accelerator, nobody would have doubts that strings could be observed. As soon as you probe distance scales that so smaller than the compactification scale, string theory look effectively 10 (or 11) dimensional and has quite unique properties.

Unfortunately, it is very very unlikely that LHC energies are at least of the order of the fundamental Planck scale so it is save to assume that LHC will not speak the last word about string theory. And it is as save to believe that we will never come even close to 10^19GeV with accelerators before the sun blows up. So it is likely that in practice, we will not be able to confirm (or rule out) string theory unless some surprise happens (like somebody finds a way to link cosmological observations rather directly to string theory).

But claiming some theory is not scientific because current (or foreseeable future) observational technology in practice does not make definite statements is not appropriate. This question should be decided based on whether observation is possible in principle.

Atomic theory is still scientific if you currently have only optical light frequencies at your disposal and you cannot resolve atoms directly. In that situation you are even luckier as quantum mechanics make definitive statements about absorption spectra for observable frequencies, still you cannot directly observe the atoms.

And I can still make scientific statements about the contents of the office across the corridor although it is locked and I don't have the key. In practice, I cannot test my speculations but in principle I could.

## Friday, January 14, 2005

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## 7 comments:

I've never been able to get a string theorist to tell me what these predictions are for what a Planck-scale accelerator would see.

One obvious problem is that you don't even know what the string scale is (what's the dilaton expectation value?), so you don't even know at what energy scale you're going to start seeing stringy phenomena. The standard thing people say is that string theory predicts that you'll see Regge trajectories of states. But this is based on the assumption that perturbative string theory is valid for the energies of the states, so you're assuming somehow that perturbation theory is useless for saying anything about the lowest energy state (vacuum), but that it will accurately give you the higher energy states. I've never seen any argument for this other than wishful thinking. How do you know that to understand even the first energy state above the vacuum you don't need to know all sorts of non-perturbative information about how branes, black-holes, etc. are going to affect the energy of the state?

You should stop hiding behind poor Thomas Kuhn, and just admit that, in its current formulation, string theory can't predict anything about anything.

Perturbative string theory predicts 2-loop corrections to the amplitudes of graviton scattering, something that cannot be captured by ordinary QFT.

In general, once you pick a certain background perturbative string theory predicts all 2-loop terms for all conceivable scattering amplitudes.

Recall that choosing a background in ST is much like choosing a Lagrangian in QFT - except that there is (as yet unfulfilled) hope that as opposed to QFT Lagrangians there might be a dynamical mechanism to pick SFT backgrounds.

Sure, in principle you can compute two-loop perturbative string theory amplitudes. The question is whether they correspond to anything observable and thus "predict" something. You're assuming that the string perturbation series is a good asymptotic expansion to some underlying non-perturbative theory and that the string coupling constant is small enough that cutting off the series at two loops provides some decent approximation to the true result.

There's no good reason to believe this. How do you know the string coupling constant is small enough for this to be true? And even if it is small enough, why do you believe it is anything other than wishful thinking to claim that the perturbation series is no good for describing the lowest energy states of the theory, but is good for computing scattering matrix elements?

Peter,

If we could do scattering experiments into the Planckian regime, we would either find that the results are characteristic of weak coupling string theory or not.

Weak coupling string theory makes all sorts of predictions about Planckian scattering amplitudes: Regge behavior, soft, exponential falloff in high energy fixed angle scattering amplitudes.

If these characteristics are not seen there must be some other theory which describes these scattering processes. At this point there are two possibilities: this theory can be understood as arising in some well-defined way as a background or solution of M-theory, which includes weak coupling string theory as another solution; or, this theory is something different altogether, falsifying string/M-theory.

If this theory is to be interpreted in the framework of M-theory, it would be the responsibility of string theorists to prove how this happens. If they could not produce a more precise or useful understanding, people would be happy to leave M-theory to the side and use this experimentally verified scattering theory as a new starting point. At any rate, weak coupling string theory would be falsified, and M-theory would either be falsified or proven to be of little

immediate use.

At any rate, I think that the question of string theory would be more or less decided.

Best,

Ted

Hi Ted,

The original question "does string theory predict anything at any energy?" is still being evaded. Sure, perturbative string theory makes predictions, it makes predictions at all energies. People don't like the ones it makes for the lowest energy states (because they have exact supersymmetry, unseen long-range forces due to moduli, etc.) so they say that non-perturbative effects are important. But then they say they can predict what will happen at high energies using perturbative string theory. This makes no sense.

As a sociological prediction that, if we could do experiments at high energies and they didn't agree with perturbative string theory , some people would be discouraged, you're right. But that's not going to happen.

Peter

Perturbative bosonic string theory predicts that the universe is 26 dimensional, has no fermions, and is unstable. Its fair to say that this perturbative string theory has been falsified.

That does not mean that all perturbative string theories make predictions which have been falsified. There may still be one which describes the physics of scattering when quantum gravity effects are important.

True, in this class of not-yet-falsified string theories, the energy scale at which quantum gravity effects are important may vary. But since we are talking about issues of principle, presumably the quantum gravity scale is somewhere and we can in principle observe it. We can then ask whether scattering at this scale and beyond is well-described by a weak coupling string theory. The answer will be yes or no.

At any rate I am somewhat skeptical of the argument that string theory is a valid and intresting physical theory because in principle it can make falsifiable predictions about an experiment which will never be preformed. String theory is interesting since it gives us at least some picture of the physics of quantum gravity. To dogmatically rule that all thought about quantum gravity is illegal because we cannot surely observe its effects seems to unfairly restrict the possibility of human knowledge, even if this knowledge must remain scientific conjecture.

Of course, string theory does not definitively tell us that we will see its effects, but that does not mean that we won't.

This can be compared to QCD. Asymptotic freedom was known and gauge theories 'predict' this. At the same time there was the question "where are the quarks?" Then it became clear that the theory can even confine them.

However lemme add - it was known at that time that only gauge theories can be asymptotically free. The same is not true abt strings. In Glashow's words, "Its the only game in town"

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