What experiment would prove string theory?

Question

The conceptual model of multidimensional vibrating strings provides an incredibly rich and diverse "language" that almost certainly is encompassing all of known physics as a singular point somewhere within its almost unfathomably large parameter space; e.g. see What experiment would disprove string theory?.

However, since in our human-sized world the fundamental organizing concept of "vibrating strings" comes to us from observing complex, multilevel interactions of condensed matter, and fields within space and time (e.g. see What are the strings in string theory made of?), another possible interpretation for this compatibility exists.

Perhaps the inclusiveness of string theory emerges not from the simplicity of vibrations, but from the mathematics of vibrations being some sort of beautifully succinct emergent expression of of the many diverse physics threads that must come together to create a universe rich enough for both observers and string-like vibrations to exist within it. If so, string vibrations would be more like the outer crystalline facets of some incredibly rich and complex compound, or perhaps the mouth of Krishna: An outward expression of seemingly simplicity within which the entire universe lies hidden.

So, after all of that, my question is this: If the all-inclusiveness power of string theory is emergent rather than primary -- that is, if any working string vibration model already contains all of known physics, even if in redundant or highly distorted form -- then shouldn't there exist experimentally tractable methods by which the quality of diverse string models and string model categories can be compared and selected? Such selections would be based on a sort of Occam's razor or signal extraction approach that seeks to minimize their complexity and maximize their fit to known physics, I would think. (I may elaborate more on that later; it's late.)

Answer 1

In my opinion you are exaggerating the power of strings. In my perception it is the all pervading harmonic oscillator potential of quantum mechanical potentials taken to a higher dimensional level. You must know that all symmetric potentials have as a first term the harmonic oscillator in the expansion. When in doubt of the form of the potential, approximate it with a harmonic oscillator.

It may be that it is not really simple strings that control the behavior, but again that a string model is a first approximation of the real underlying mathematics just because of it simply appears in any perturbative expansion of a mathematical form.

My second point is that one can never "prove" a physical model/theory. One can only validate it or falsify it.

At the moment there exist no predictions for any string theory model that can validate it or falsify it. Well, partially true, since all models require extra dimensions. So if one could get the so mathematically oriented string theories to give different predictions for the effect on our four dimensions of the extra dimensions, then yes, one could falsify a specific model. This has been done setting limits for the large extra dimensions models already at the level of LHC data, by not finding the thermodynamic jets it predicted, and this has been used to further other models.

Answer 2

The place to start is, of course, by finding a prediction of string theory that differs from that of made by competing theories.

The prediction made by naive string theory are

1. Extra dimensions. Naively this is a problem, but it can be patched up.

   All we have been able to do on this front so far is to require that the extra ones be compact and put limits on their size.

2. All the well tested symmetries of preexisting theories. These were built into string-theory with malice aforethought.

   The leading answer to the converse question concentrates on these "predictions" which is in some sense a cheat because they are in fact "postdictions".

   Not that string theory having these properties is trivial: a great deal of work by very smart people was required to make it happen. It's just having this property is a minimum requirements for a theory to be considered as a possible theory-of-everything, Any competitor must also make these predictions because those symmetries are already tested to death.

So, in my very naive view, the only target on the table right now is finding and counting the extra dimensions, and for that to be feasible in the near future would require them to be "large" (i.e. $10^{-19}\,\mathrm{m}$ or so).