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String theory has at least $10^{500}$ 6D compactifications. Denef and Douglas proved the computational complexity of finding a compactification which fits the parameters of the low energy effective action like the cosmological constant, the electroweak scale, the Higgs self-coupling, Yukawa couplings and gauge coupling strengths is NP-complete. There are limits on the energies future particle accelerators can reach, and cosmic ray frequencies. The amount of data gleanable from the cosmic microwave background anisotropies is limited, and can only probe up to the energy scale of slow roll inflation.

If it is beyond our abilities to determine the exact string compactification describing our universe, is it not wrong to call the compactification unobservable? Only things which are experimentally observable, possibly with the aid of theoretical interpolations, and can make experimentally verifiable predictions count as science. Within the realm of physics, are we forbidden to ask which string compactification describes our universe? Must we stick to the effective field theory if we wish to remain physicists and not philosophers?

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My comments here: math.columbia.edu/~woit/wordpress/… –  Mitchell Porter May 27 '11 at 7:23
@Mitchell: The two comments you made in conversation with Peter Woit more than constitute an answer to the OP's question, and a good one at that. Transfer them over and I'll certainly give it +1 ;) –  qftme May 27 '11 at 13:22

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There is an real life analogy that provides a nice answer to this question

In 1999 Lord Monckton marketed a toy called the "Eternity Puzzle". It was a tiling problem with 209 pieces. He thought it was sufficiently complex that nobody would solve it even with a very powerful computer, so he offered £1 million to anyone who could. One year later it was solved by some Cambridge mathematicians. How many combinations did he estimate people would have to try to solve it? $10^{500}$ of course!

The problem of finding the correct string vacuum for the universe won't be solved so quickly. It will probably require some more input from experiments and cosmology, but there is no reason to think it is not soluble simply because of the large number (assuming the universe is really constructed that way). It may (or may not) also be necessary to understand the foundations of string theory better first.

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The precise string compactification is not something we can find out. To ask about it isn't forbidden, but it's a meaningless question. The same thing goes for questions like "is there really a definite string compactification". Until and unless we can find out, this is a meaningless question.

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