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An example of a test: Ask each variant whether its estimate of the electron mass lies within $\pm\,x\%$ of the known value. This surely can't take long per theory. Although $10^{500}$ is huge, whittling them down could be essentially a background task for a few thousand computers. But is it being done, and if not, why not?

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10^500 is a conservative estimate, the number might be much larger. But even 10^500 is beyond anything imaginable, the whole universe does not contain enough atoms to store 10^500 integers for example, let alone the parameters for 10^500 string models. Also each of those backgrounds potentially has a number of continuous parameters. –  orbifold Apr 11 '13 at 11:16
    
@orbifold Why would you need to store $10^{500}$ integrals? –  user12345 Apr 11 '13 at 13:38
    
+1 for the mention of the electron mass! I think that' is a very good idea for a test!. –  Dimensio1n0 Jun 18 '13 at 8:11
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up vote 4 down vote accepted

"10^500 is huge". You're definitely correct there:

Suppose it took a Planck time to test each version. It would take $t = 10^{500} \times t_{P} = 10^{457}$ s, or $10^{440} \times$ the present age of the Universe.

Thus, it is not feasible to check them all manually.

[I like the idea with the electron mass; maybe something could be done with that in a different way].

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This is a good way to highlight that "whittling down" the possibilities just ain't gonna do it. –  Beska Apr 11 '13 at 17:35
    
@Beska you said it bro. –  user12345 Apr 11 '13 at 18:09
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String theory is not so well understood that we can exhaustively enumerate all possible models, nor are we able to calculate all the properties of any given model.

What actually happens is that a particular group of researchers will single out a particular narrow class of models which look promising for specific reasons, and then they will investigate that class of models as best they can, using the existing mathematical tools. For example, the recently measured mass of the Higgs boson implies that the quartic self-coupling of the Higgs field goes to zero at high energies; and just today a string paper appeared that conducts a preliminary investigation of a class of models in which that behavior of the coupling has a specific cause.

So carrying out the exhaustive top-down analysis of all possible string models remains far beyond what anyone can do, but the analysis is being done anyway, in a distributed, bottom-up fashion. Meanwhile, work on the fundamentals of the theory also proceeds. In the long run there should be an atlas of the "landscape" of all string models, a definite string cosmology, etc., but for now there are still many knowledge gaps to be filled, that may even require revolutions of perspective comparable to those which have already occurred in the history of the subject.

P.S. I will add that the sheer number of vacua in itself does not necessarily imply a long search time. Case by case it would be impossible to prove Fermat's last theorem, because there are infinitely many potential counterexamples; but sufficiently advanced mathematics was able to group all the infinite possibilities into a finite number of classes, and deal with them that way. The same applies to string theory, though it may be that we will need physical rather than mathematical input in order to winnow the possibilities, e.g. the knowledge that at low energies the world is described by a "standard model" whose Higgs has the property mentioned above, and which has one quark (the top quark) which is much more massive than all the others.

Such distinctive properties should be very important, if we ever reach the point that string theory can only be tested by systematically searching the whole landscape of possible models.

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Nice answer and I like the Fermat's last theorem example. Lumo has just yesterday written an article about it. –  Dilaton Apr 11 '13 at 12:03
    
+1 for the link to the paper. –  Dimensio1n0 Jun 18 '13 at 8:14
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