What experiment would disprove string theory?
One can disprove string theory by many observations that will almost certain not occur, for example:
By detecting Lorentz violation at high energies: string theory predicts that the Lorentz symmetry is exact at any energy scale; recent experiments by the Fermi satellite and others have showed that the Lorentz symmetry works even at the Planck scale with a precision much better than 100% and the accuracy may improve in the near future; for example, if an experiment ever claimed that a particle is moving faster than light, string theory predicts that an error will be found in that experiment
By detecting a violation of the equivalence principle; it's been tested with the relative accuracy of $10^{-16}$ and it's unlikely that a violation will occur; string theory predicts that the law is exact
By detecting a mathematical inconsistency in our world, for example that $2+2$ can be equal both to $4$ as well as $5$; such an observation would make the existing alternatives of string theory conceivable alternatives because all of them are mathematically inconsistent as theories of gravity; clearly, nothing of the sort will occur; also, one could find out a previously unknown mathematical inconsistency of string theory - even this seems extremely unlikely after the neverending successful tests
By experimentally proving that the information is lost in the black holes, or anything else that contradicts general properties of quantum gravity as predicted by string theory, e.g. that the high center-of-mass-energy regime is dominated by black hole production and/or that the black holes have the right entropy; string theory implies that the information is preserved in any processes in the asymptotical Minkowski space, including the Hawking radiation, and confirms the Hawking-Bekenstein claims as the right semiclassical approximation; obviously, you also disprove string theory by proving that gravitons don't exist; if you could prove that gravity is an entropic force, it would therefore rule out string theory as well
By experimentally proving that the world doesn't contain gravity, fermions, or isn't described by quantum field theories at low energies; or that the general postulates of quantum mechanics don't work; string theory predicts that these approximations work and the postulates of quantum mechanics are exactly valid while the alternatives of string theory predict that nothing like the Standard Model etc. is possible
By experimentally showing that the real world contradicts some of the general features predicted by all string vacua which are not satisfied by the "Swampland" QFTs as explained by Cumrun Vafa; if we lived in the swampland, our world couldn't be described by anything inside the landscape of string theory; the generic predictions of string theory probably include the fact that gravity is the weakest force, moduli spaces have finite volume, and similar predictions that seem to be satisfied so far
By mapping the whole landscape, calculating the accurate predictions of each vacuum for the particle physics (masses, couplings, mixings), and by showing that none of them is compatible with the experimentally measured parameters of particle physics within the known error margins; this route to disprove string theory is hard but possible in principle, too (although the full mathematical machinery to calculate the properties of any vacuum at any accuracy isn't quite available today, even in principle)
By analyzing physics experimentally up to the Planck scale and showing that our world contains neither supersymmetry nor extra dimensions at any scale. If you check that there is no SUSY up to a certain higher scale, you will increase the probability that string theory is not relevant for our Universe but it won't be a full proof
A convincing observation of varying fundamental constants such as the fine-structure constant would disprove string theory unless some other unlikely predictions of some string models that allow such a variability would be observed at the same time
The reason why it's hard if not impossible to disprove string theory in practice is that string theory - as a qualitative framework that must replace quantum field theory if one wants to include both successes of QFT as well as GR - has already been established. There's nothing wrong with it; the fact that a theory is hard to exclude in practice is just another way of saying that it is already shown to be "probably true" according to the observations that have shaped our expectations of future observations. Science requires that hypotheses have to be disprovable in principle, and the list above surely shows that string theory is. The "criticism" is usually directed against string theory but not quantum field theory; but this is a reflection of a deep misunderstanding of what string theory predicts; or a deep misunderstanding of the processes of the scientific method; or both.
In science, one can only exclude a theory that contradicts the observations. However, the landscape of string theory predicts the same set of possible observations at low energies as quantum field theories. At long distances, string theory and QFT as the frameworks are indistinguishable; they just have different methods to parameterize the detailed possibilities. In QFT, one chooses the particle content and determines the continuous values of the couplings and masses; in string theory, one only chooses some discrete information about the topology of the compact manifold and the discrete fluxes and branes. Although the number of discrete possibilities is large, all the continuous numbers follow from these discrete choices, at any accuracy.
So the validity of QFT and string theory is equivalent from the viewpoint of doable experiments at low energies. The difference is that QFT can't include consistent gravity, in a quantum framework, while string theory also automatically predicts a consistent quantum gravity. That's an advantage of string theory, not a disadvantage. There is no known disadvantage of string theory relatively to QFT. For this reason, it is at least as established as QFT. It can't realistically go away.
In particular, it's been showed in the AdS/CFT correspondence that string theory is automatically the full framework describing the dynamics of theories such as gauge theories; it's equivalent to their behavior in the limit when the number of colors is large, and in related limits. This proof can't be "unproved" again: string theory has attached itself to the gauge theories as the more complete description. The latter, older theory - gauge theory - has been experimentally established, so string theory can never be removed from physics anymore. It's a part of physics to stay with us much like QCD or anything else in physics. The question is only what is the right vacuum or background to describe the world around us. Of course, this remains a question with a lot of unknowns. But that doesn't mean that everything, including the need for string theory, remains unknown.
What could happen - although it is extremely, extremely unlikely - is that a consistent, non-stringy competitor to string theory that is also able to predict the same features of the Universe as string theory can emerges in the future. (I am carefully watching all new ideas.) If this competitor began to look even more consistent with the observed details of the Universe, it could supersede or even replace string theory. It seems almost obvious that there exists no "competing" theory because the landscape of possible unifying theories has been pretty much mapped, it is very diverse, and whenever all consistency conditions are carefully imposed, one finds out that he returns back to the full-fledged string/M-theory in one of its diverse descriptions.
Even in the absence of string theory, it could hypothetically happen that new experiments will discover new phenomena that are impossible - at least unnatural - according to string theory. Obviously, people would have to find a proper description of these phenomena. For example, if there were preons inside electrons, they would need some explanation. They seem incompatible with the string model building as we know it today.
But even if such a new surprising observation were made, a significant fraction of the theorists would obviously try to find an explanation within the framework of string theory, and that's obviously the right strategy. Others could try to find an explanation elsewhere. But neverending attempts to "get rid of string theory" are almost as unreasonable as attempts to "get rid of relativity" or "get rid of quantum mechanics" or "get rid of mathematics" within physics. You simply can't do it because those things have already been showed to work at some level. Physics hasn't yet reached the very final end point - the complete understanding of everything - but that doesn't mean that it's plausible that physics may easily return to the pre-string, pre-quantum, pre-relativistic, or pre-mathematical era again. It almost certainly won't.
Since many people seem to have very odd ideas about this, let's address this from a much simpler point of view.
Let's suppose you have a friend who only knows math at the level of arithmetic of positive integers. You try to tell him about the existence of negative numbers, and he tells you,
That's stupid, there's obviously no such thing as "negative" numbers, how can I possibly measure something so stupid? Can you have negative one apple? No, you can't. I can owe you positive one apple, but there's clearly no such thing as negative apples.
How can you start to argue that there is such a thing as negative numbers?
A very powerful first step is mathematical consistency. You can list all of the abstract properties you believe to characterize everything about positive integer arithmetic:
- For all $a,b,c$, $a(b+c) = ab+ac$
- For all $a,b$, $a+b=b+a$, $ab=ba$
- There exists a number, called $0$, such that, for all $a$, $a+0=0+a=a$, $a0=0a=0$
- There exists a number, called $1$, such that, for all $a$, $1a=a1=a$
(note that, in sharp contrast to the case of real numbers, the first property can be proved with induction, and need not be an axiom. Similarly, other listed properties can be proved from other ones designated to be more basic if one wishes, which can not be done in the case of the reals.)
So, once you both agree that these axioms characterize the positive integers completely, you can show that these hypothetical negative numbers, based on their formal properties, are consistent with the above axioms. What does this show?
The positive integers, with the addition of the negative integers, can do at least as much as the positive integers by themselves.
(STOP At this point, pause to realize how powerful this constraint is!! How many other ways could one generalize arithmetic, at this level, to something else that is consistent with the properties you want? Zero. There is absolutely no other way to do it. This is incredibly suggestive, and you should keep this in mind for the rest of the cartoon argument, and see how every argument that follows is secretly an aspect of this one!)
Your friend responds:
Sure, you can write down toy models like that, and they may be consistent, but they don't correspond to reality.
Now, what else do you need to demonstrate to your friend to convince him of the validity of the negative numbers?
You find something else they can do that you can't do with the positive numbers alone. Simply, you can state that every positive-integer-valued algebraic equation does not have a solution:
$$ x + 1 = 0 $$
does not have a solution.
But, it is a trivial fact that extending to the negative numbers allows you to solve such equations. Then, all that's left to convince your friend of the validity of negative numbers is to show that this is equivalent to solving an ("a priori") different problem which only involved arithmetic of positive integers:
$$ x+1=0 \iff y + 1 = 1 $$
So, $y = 0$, and $y=x+1$ is equivalent to the other problem.
To be complete, we also have to consider problems that are "unique" to the negatives, such as $(-1)(-1) = 1$, but in the realm of integers, these are trivial matters that are reducible to the above. Even in the case of reals, given the other things we've shown, these consequences are almost "guaranteed" to work out intuitively obviously.
Now, assuming your friend is a reasonable, logical, person, he must now believe in the validity of negative numbers.
What have we shown?
- Consistency, both with previous models and with itself
- The ability to solve new problems
- The reduction of some problems in the new language to problems in the old language
Now, to decide if this a good model for a particular system, you must look at the subset of problems that did not have a solution before, and see if the new properties characterize that system. In this case, that's trivial, because the properties of negative numbers are so obvious. In the case of applying more complicated things to describe the details of physical situations, it's less obvious, because the structure of the theory, and the experiments, is not so simple.
How does this apply to string theory? What must we show to convince a reasonable person of its validity? Following the above argument, I claim:
- String theory reproduces (by construction) general relativity
- String theory reproduces (by construction) quantum mechanics (and by the above, quantum field theory)
So string theory is at least as good as the rest of the foundations of physics. Stop again to marvel at how powerful this statement is! Realistically, how many ways are there to consistently and non-trivially write a theory that reduces to GR and QFT? Maybe more than one, but surely not many!
Now the question is--what new do we learn? What additional constraints do we get out of string theory? What problems in GR and QFT can be usefully written as equivalent problems in string theory? What problems can string theory solve that are totally outside of the realm of GR and QFT?
Only the last of these is beyond the reach of current experiments. The "natural" realm where string theory dominates the behavior of an experiment is is at very high energies, or equivalently, very short distances. Simple calculations show that these naive regions are well outside of direct detection by current experiments. (Note that in the above example of negative numbers, the validity of the "theory" strictly in the corresponding realm didn't need to be directly addressed to make a very convincing argument; pause to reflect on why!)
However, theoretical "problems" with the previous theories, such as black hole information loss, can be solved with string theory. Though these can't be experimentally verified, it's very suggestive that they admit the expected solution in addition to reproducing the right theories in the right limits.
There are two major successes of string theory that satisfy the other two requirements.
AdS/CFT allows us to solve purely field theory problems in terms of string theory. In other words, we have solved a problem in the new language that we could already solve in the old language. A bonus here is that it allows us to solve the problem precisely in a domain where the old language was difficult to deal with.
String theory also constrains, and specifies, the spectrum and properties of particles at low energies. In principle (and in toy calculations), it tells us all of the couplings, generations of particles, species of particles, etc. We don't yet know a description in string theory that gives us exactly the Standard Model, but the fact that it does constrain the low-energy phenomenology is a pretty powerful statement.
Really, all that's left to consider to convince a very skeptical reader is that one of the following things is true:
- It is possible for string theory to reproduce the Standard Model (e.g., it admits solutions with the correct gauge groups, chiral fermions, etc.)
- It is not possible for string theory to reproduce the Standard Model (e.g., there is no way to write down chiral theories, it does not admit the correct gauge groups, etc. This is the case in, e.g., Kaluza-Klein models.)
I claim, and it is generally believed (for very good reasons), that the first of these is true. There is no formal, complete, mathematical proof that this is the case, but there is absolutely no hint of anything going wrong, and we can get models very similar to the standard model. Additionally, one can show that all of the basic features of the Standard Model, such as chiral fermions, the right number of generations, etc, are consistent with string theory.
We can also ask, what would it mean if string theory was wrong? Really, this would signal that,
The theory was mathematically inconsistent (there is no reason to believe this)
At a fundamental level, either quantum mechanics or relativity failed in some fairly pathological way, such as a violation of Lorentz invariance, or unitarity. This would indicate that a theory of everything would look radically different than anything written down so far; this is a very precarious claim--consider what would happen in the example of arithmetic in the above if there were something "wrong" with addition.
The theory is consistent, and a generalization of GR and QFT, but is somehow not a generalization in the right "limit" in some sense. This happens in, e.g., Kaluza-Klein theory, where chiral fermions can't be properly written down. In that case, a solution is also suggested by a sufficiently careful analysis (and is one potential way to get to string theory).
Of these three possibilities, the first two are extremely unlikely. The third is more likely, but given that it is known that all the basic features can show up, it would seem very strange if we could almost reproduce what we want, but not quite. This would be like, in the arithmetic example, being able to reproduce all the properties we want, except for $1+ (-1) = 0$.
If you're careful, you can phrase my argument in a more formal way, in terms of what it precisely means to have a consistent generalization, in the sense of formal symbolic logic, if you like, and see what must "fail" in order for the contrapositive of the argument to be true. (That is, (stuff) => strings are true, so ~strings => ~(stuff), and then unpack the possibilities for what ~(stuff) could mean in terms of its components!)
String theory should come with a proposal for an experiment, and make some predictions about the results of the experiment; then we could check against the real results.
If a theory cannot come with any predictions, then it will disprove itself little by little ...
The problem is that, with string theory, this is extremely difficult to do, and string theorists have year in front of them to go in that direction; but if in 100 years we are still at the same status, then it would be a proof that string theory is unfruitful...