On the influence of our imaginary on string theory's beauty

[ledjazz]

Dear physicists,
Please forgive my naive and general question but I have a something in mind that I would like to answer...

String theorists say something like:
"Although string theory cannot be tested, the mathematical beauty coming from this theory is such that it is very convincing and makes us think that we are on the right direction towards the explanation of the universe with one single theory".

So, my question is quite simple: How can string theorists be sure that their mathematical models are correct?

I do not know so much about the mathematical aspects behind string theory and theoretical physics in general. All I understand from my non-specialist perspective of a civil engineer is that string theorists have successfully responded to the deepest theoretical question of physics (the unification of quantum theory and gravity in one single theory) by developing mathematical tools that require extra dimensions in addition to the known 3+1 dimensions. One implication of this theory is that we are stuck in this 4-D "reality" so that we might never have the possibility of actually seeing the other dimensions, be they at macro scale.

But, if we accept the idea that our perception of a universe with 4 dimensions is not correct, how can the mathematical methods used to explain string theory be correct if they originally come from a wrong description of this 4D reality? I make here the assumption that there has been an evolution in mathematical methods so that the methods used today in string theory have their roots in our old Aristotelean/Cartesian description of the universe.

Maybe it will appear as an unclear or a non-sense question to some of you. I hope not.

Maybe it is only something that a non-specialist cannot understand. If so, don't be embarrassed if you provide a very technical response. I will take the time necessary to understand it.

Thanks in advance.
Francois

 

[xts]

String theorists say something like:
"Although string theory cannot be tested, the mathematical beauty coming from this theory is such that it is very convincing and makes us think that we are on the right direction towards the explanation of the universe with one single theory".

Only string theorists see that mathematical beauty and are convinced by it. Matter of taste and religious-like belief. For Popperian unbelievers (like me) there is nothing convincing in it, and I see no beauty in their speculations.

How can string theorists be sure that their mathematical models are correct?

They can't. They may just believe. But, on the other hand, no one may falsify their ideas. That is why Peter Woit gave a title "Not Even Wrong" to his book criticizing string theory.

But, if we accept the idea that our perception of a universe with 4 dimensions is not correct, how can the mathematical methods used to explain string theory be correct?

Mathematical methods they use are correct. Mathematical ideas are fully abstract and self-consistency is the only requirement for their validity. The questions is rather: are the models made with those methods applicable to our world. In other words: are their predictions consistent with an experiments? Problem with ST is that its predictions cannot be verified by any possible experiment.

 

[dhillonv10]

A lot of people seem to ask this question, Penrose answered this in a very elegant way, so let's assume we have 3 worlds (http://cambridgeforecast.files.wordpress.com/2007/05/worldspenrose.gif" ) This is only a construction to help you understand why string theorist do what they do. So the first one is our world, where stuff happens, the next is your mind where we perceive the stuff that happens and the third world is the Platonic world, this world contains every mathematical equation that we need, and everything is just perfect. Now what we do with logical reasoning is to get a glimpse of the platonic world, hence our theories are only approximate and not "perfect" since we only get a blurry glimpse. We use mathematics to make senses of what is around us, hence if the theory requires 26 dimensions, we go on with that because we are only trying to explain what is going on, no one really know what's "really" going on, or put differently, no one can get a clear glimpse of the Platonic world. It is interesting that the mainstream QM doesn't even believe in the existence of a deeper reality, they believe that reality is created so to speak (wavefunction collapse/decoherence) as we see it. Hope that makes sense.

Also, string theory predicts gravity, that's by far the most important prediction of it, there are others however LHC is trying to find them.

 

[xts]

Also, string theory predicts gravity, that's by far the most important prediction of it, there are others however LHC is trying to find them.

It doesn't predict gravity! It just gives explanation to its existence. By prediction I understand ability to predict results of some phenomenon differently than existing theories. When Einstein formulated GRT, he predicted gravitational light bending. Eddington could then make his trip to watch eclipse and then confirm prediction: yes, the light bends as Einstein says! It's predictive power was why we accepted GRT, not only for its mathematical ellegance.
BTW (matter of taste) - I see lots of mathematical beauty in GRT, but ST is one of the mathematically ugliest theories (even more ugly than QCD) I ever saw.

ST have no predictive power. It is unable to explain any known phenomenon, not explainable with well established theories (like was with GRT and Mercury orbit precession) , nor it is able to propose any feasible experiment leading to results different than existing theories predict (like was with GRT and light bending).

Let's see what LHC will bring to us... As far as I understand, ST-guys play here no-lose game: they prophet some phenomena, which may happen at LHC energy, but equally well they may need the energy 12 orders of magnitude higher. So if LHC won't find them - ST still survives falsification test.

 

[mitchell porter]

The two cornerstones of modern physics are quantum field theory and general relativity, each of which introduced new mathematical and physical ideas. String theory really does have the qualities you might expect in a deeper unifying theory: the mathematics is deeper, and the physical ideas of the previous theories are still present.

There are string models (particular geometries for the extra dimensions) which really do look a lot like the real world, and one of them might even be the real world. It's just an extremely difficult matter to get predictions from such a model for the really decisive quantities, such as the particle masses. They depend e.g. on the exact values at which certain geometric quantities stabilize, and this is very hard to calculate.

I believe that the single factor most responsible for promoting skepticism about string theory, is the doubt which developed among string theorists themselves that the theory will make a unique prediction for the structure of the extra dimensions and thus for particle physics. There was a moment http://motls.blogspot.com/2010/11/extra-dimensions-lhc-and-real-world.html" when a few informed people thought there might be only one option. Then came maybe 15 years of model-building, but such models are flat-space approximations and might be unstable in the full theory. The real turning point was the "KKLT" paper in 2003, which showed how to make large classes of stable-looking models. That was when people started talking about a "landscape" of solutions, realized in different regions in an inflating universe, and about the possibility that some parts of physics might be anthropically determined (by the need to be consistent with the existence of living observers) and other parts might be "random" (that is, the particle masses, interaction structure and so forth, would still be determined by the structure of the extra dimensions in our part of the universe, but their structure here would be a contingency, just as the particular sizes and orbits of the planets in our solar system is a contingency).

I also believe that the technical issue here is, fundamentally, how to extend string theory to cosmology. String theory was originally an invention of particle physicists. The extra dimensions just define a background geometry that sets the properties of the strings. So you can stipulate a particular background, see how the strings behave in that context, and this is what string model-building is all about: looking for background geometries which make the strings behave like the particles we know. But string theory also contains Einstein's gravity, so the extra dimensions, and the size and curvature of the universe, are all dynamical on long timescales. I think that here, string theory is still struggling for insight. There has been plenty of work on string cosmology, but no-one has come up with a cosmological framework which is obviously the right way to do cosmology in string theory. Susskind's combination of eternal inflation and the anthropic principle is a strong possibility, but it's not quite established. And until we have the correct cosmological completion of string theory, it's not really equipped to answer the ultimate questions.

 

[Fra]

So, my question is quite simple: How can string theorists be sure that their mathematical models are correct?

No scientist are "sure" of any theories correctness in the sense you refer to.

It's even irrational to think that, correctness is the question anyone would ask. That type of question is induced from a structural realist perspective that I think lacks rational scientific basis.

The only way to "test" a theory, is to use it (ie put it to test). This involves a risk. Loss of investments if the theory is wrong etc. This is in fact how all life works too. Those who place their bets wisely grow stronger.

IMHO, the only rational motivation a theorist "comitting" to working with, or developing a theory in a framwork needs is to ask "am I confident enough in this so I am willing to invest my personal future in this", or are there other baskets where it would be wiser to place some bets?

The evaluation of the plausability of a idea is always subjective and observer dependent. Scientific consensus is emergent as negotiated agreements in a community. I think it's a deep fallacy to confuse this process with things beeing correct or incorrect. It's not that simple, which becomes obvious only when you expect rationality from the proofing process.

So the plausability of ST beeing a natural extrapolation to the established SM and GR, is a very subjective position. But any competing position is ALSO subjective. But that's how scientific process works.

Scientists comitt to investigating and develing a theory or programs. Some bear fruit, some doesn't. Questions such as "is the theory correct" would I argue, not even enter any equation in this decision process. It's all about expectations.

/Fredrik

 

[tom.stoer]

So, my question is quite simple: How can string theorists be sure that their mathematical models are correct?

I think we should first clarify what physics can say about the "correctness" of a theory.

A theory has to make predictions which can be falsified in principle. String theory does this, it predicts e.g. a tower of massive states (the string modes) which could be tested in principle, but unfortunately not in practice b/c of the huge energy which is not available in ordinary experiments like colliders.

If there are enough correct predictions with experimental support we tend to believe in the theory as a hole, e.g. we tend to believe that other predictions, the underlying mathematical structure etc. is correct as well. So for example we believe that GR is correct (classically) and that we can trust in the prediction of black holes - even though there is no direct evidence for black holes.

Unfortunately this is not the case for string theory.

As fas as I can see string theory does not predict uniquely the existence of our universe with all its particles and interactions, but it provides a framework from which such a universe (such universes) can emerge mathematically (this is the landscape issue mitchell porter discussed).

Now look at quantum mechanics: it explains the physics of ordinary matter (atoms, molecules, solid state physics), but it does not predict the existence of one single material. So ice cannot be derived uniquely from QM, but QM can describe the properties of ice correctly. Now think about us living in a huge christal of ice - this is our universe. Of course we would like to have a theory at hand which not only describes ice, but which predicts ice. But this is not the case. The pure scientists living in this huge cristal of ice derive hydrogen, iron, copper, water, ... but they fail to find ice in the space of solutions of their theory. But this is simply due to the fact that this space of solutions is large and that their search can never be exhaustive.

I guess string theorists believe that they are in a similar situation. String theory model building produces solutions which are rather close to our known universe; they contain gravity, gauge theory, fermion generations, ... but up to now they failed to produce our universe exactly.

For me the main difference between string theory and other theories (like GR, QED, QCD, ...) is that the "solutions" to string theory are "other theories". You take string theory, plug in some "initial data" and get (for each set of initial data) one theory. String theory is rather a meta-theory or a framework to generate or derive theories.

 

[Fra]

For me the main difference between string theory and other theories (like GR, QED, QCD, ...) is that the "solutions" to string theory are "other theories". You take string theory, plug in some "initial data" and get (for each set of initial data) one theory. String theory is rather a meta-theory or a framework to generate or derive theories.

I share this distinction. But if we do, we can rephrase the question, and ask "how does we know the FRAMEWORK is correct". I'd claim that the requirements of rationality is not much different on a framework than it is on a theory. And a framework can as well be seen as a theory of theory (that's not to say I think ST is the RIGHT framework). This does however force a less mechanical view of the falsficiation process which is at the heart of science.

A theory makes predictions, which renders it either falsified or corroborated. This theory does however leave zero insight in how to generate a new candidate theory, once one is shot down.

This is where a theory of theory enters. IMHO, it would ideally describe how to rationally move in a theory space as feedback is collected. It would provide exactly the missing link in Poppers failed attempt to make the scientific process deductive. Induction still exists when a falsififed theory need to give rise to a new candidate.

Efficient adaption would have to produce a rational deformed theory, based on the falsified theory and quantifications of deviations. For this we need to look at a theory space.

If we accept this, the question becomes: IS ST really the most rational theory of theory seen as an interaction tool? (note that this is pretty much artifical intelligence or self lerning adaptive system we are talking about here - a novel view of physical law, that goes well with the information theoretic views)

Personally I think it's not.

Edit: I forgot the key point: So when is a theory of theory righy? ie. when do we know we are moving in the RIGHT direction in theory space as the result of backreaction from the environment? If we picture this as a game, we can picture that there are equilibrium points in theory space which tends to be stable. Some theories are not observer in nature because they are unfit. So the "right" framework would like to survival and persistence. The wrong framework would kill itself; and thus only be a transient in the big picture.

/Fredrik