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What experiment would disprove string theory?

We carefully observe things, observe patterns and then build theories that predict.

String theory is frequently criticized for not providing quantitative experimental prediction.

What are the problems that prevent this theory from producing quantitative experimental predictions?

Is there no experiment suggested by string theorists to verify validity of their theory? Is the problem mathematical? (or it just requires many dimensional equipments...just kidding).

I am not criticizing the theory because to do that I should understand it first, but I haven't studied it. I just want to know.


2 Answers 2


Let me make an analogy that is due to Wati Taylor.

Take Einstein and, say, Ketterle, lock them in a room and give them two stones, an ordinary watch, paper and pencil. Then give them the task to verify general relativity (GR) experimentally. They will fail, inevitably.

This is not because GR is "wrong" or, as some might put it, "not-even-wrong", but because the experimental equipment is not adequate for a stringent test.

Fortunately for GR, there were observations about perihelion shifts and light bending that eventually convinced the skeptics (or, more probably, the skeptics died out).

String theory is a quantum theory of gravity that makes a bunch of predictions on the Planck scale. However, we have no current experiment that is good enough to be sensitive to Planck scale physics.

BTW, the same problem basically applies to ANY quantum theory of gravity - they are usually safely away from experiment...

Now, string theory is more ambitious and makes not only quantum gravitational predictions, but also restricts the low energy physics. It is not clear, however, if these restrictions are tight enough to be of observational relevance. I am sure that others will have to say more about the landscape of string vacua, so I will stop here.

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    $\begingroup$ What are the predictions on the Planck scale? $\endgroup$ Feb 12, 2011 at 15:51
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    $\begingroup$ Yes that is the case for string theory. The infinite tower of excitations would be obvious in an accelerator, as would the extra dimensions. $\endgroup$
    – Columbia
    Feb 12, 2011 at 16:23
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    $\begingroup$ MBN: I disagree. Extra dimensions are a prediction, and a very precise one. It is not be easy to test this prediction with current technology, which is the main point of my answer. But if some cleverly designed experiment found convincing evidence for 6 extra dimensions how would this not be a confirmation of string theory? Maybe I am missing your point. $\endgroup$ Feb 12, 2011 at 16:31
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    $\begingroup$ In other theories, say the Standard Model or general relativity, the number of dimensions indeed is an input. But in string theory is certainly is not an input, it is a prediction! You can try to formulate string theory in any dimension, but anomaly cancellation will pin you to 10. Anyhow, it is not the only prediction of string theory, so if finding 6 extra dimensions experimentally won't convince you, you'll have to wait for Kaluza-Klein excitations... $\endgroup$ Feb 12, 2011 at 20:32
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    $\begingroup$ @space_cadet These features might not manifest themselves at all at the LHC, which is somehow the point of Wati's analogy. But in the absence of experimental data one still can be guided by internal consistency and conceptual simplicity - much like Einstein was in his construction of general relativity. $\endgroup$ Feb 12, 2011 at 22:52

The most obvious stringy signature would be the observation of Regge resonances at energies close to the string scale. If the extra dimensions are very large, i.e. string scale is very low (I'm extremely skeptical about this possibility), such signatures could even be observed by the LHC. See this paper for the detailed computations of the scattering amplitudes and the crossections: http://arxiv.org/abs/0807.3333. Read the summary at the end of the paper.

A more generic/less specific, prediction is the existence of superpartners at some scale below the string scale. In the phenomenologically interesting scenarios, e.g. Calabi Yau compactifications of the Heterotic string, one obtains some type of N=1 D=4 supergravity. Unfortunately, there is no unique prediction for the details of the sparticle spectrum because there exist different mechanisms of supersymmetry breaking and the spectrum depends on that. However, in such compactifications, one generically expects some type of gravity mediation possibly mixed with high scale gauge mediation. Furthermore, one also has to specify in which corner of M-theory one is working, e.g. Heterotic, Type IIB, Type IIA, M-theory on G2, F-theory etc, which results in certain restrictions on the form of the superpotential and the Kahler potential. For example, in the G2 corner without fluxes the superpotential is purely non-perturbative because all the compactification moduli enjoy the PQ symmetry inherited from the gauge symmetry of the 11D supergravity 3-form. Thus, one can make a generic statement that the Yukawa couplings will have exponential hierarchies and the scale of SUSY breaking may be exponentially suppressed relative to the Planck scale. Furthermore, in this sector SUSY breaking is naturally gravity mediated because in 7 dimensions the 3-cycles supporting visible and hidden sectors generically do not intersect, etc. Once the mechanism of SUSY breaking and the M-theory patch are specified, one may be able to compute the sparticle spectrum at the string/GUT scale and put strong constrains on it from the top down and combine those with the bottom up requirements. In this way one can get several testable scenarios parameterized by very few phenomenological dials. The whole exponentially large landscape issue may be effectively decoupled when one is interested in these types of questions (SUSY breaking and the sparticle spectrum). To be more specific about the last point, in Type IIB flux vacua, the contribution of the fluxes to the superpotential can take on an exponentially large number of values, however, the corresponding F-terms for the complex structure moduli are still zero and the only phenomenologically relevant parameter will be the value of the flux superpotential, which is just one input parameter, whose detailed microscopic dependence on the fluxes is irrelevant for the computation of the sparticle spectrum!

Another generic prediction of string compactifications comes in the imprint of the non-trivial topology on the particle spectrum in 4D. In particular, string compactifications typically imply the existence of a number of particles with similar properties. The multiplicity of SM generations is one such example and while it's still not clear why there are only three generations, it's clear that having multiple generations is generically expected. Of particular interest are so-called axions, which are ultra-light pseudoscalar particles - the partners of some (or all in the G2 case) of the geometric moduli. One of these axions can naturally provide a dynamical solution to the strong CP problem and the PQ symmetry that makes it so light can be directly traced back to the gauge symmetry of the corresponding RR-type field in 10D. Depending on the topology, there may actually be hundreds of such particles whose existence would be a complete mystery from the 4D effective field theory point of view. The experimental implications of such an "Axiverse" is described in detail here: http://arxiv.org/abs/0905.4720

On a related note, in a generic compactification one also expects a large number of moduli fields - scalars in 4D EFT. These fields gain large masses (generically at or well above the gravitino mass scale) and interact with the visible sector via Planck suppressed operators. Their presence can have a major impact on cosmology because some of the geometric moduli end up as light as the gravitino and can be quite long-lived if SUSY breaking scale is low. They may therefore come to dominate the energy density of the universe after inflation and the standard thermal cosmological history must be revised. This is a very active area of research and there are many good papers on the topic.


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