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When I studied physics I was shown that special relativity would become Newton's laws at low speeds. Similarly, quantum mechanics could also be shown to be Newtonian at large quantum numbers.

My question is, has it been shown yet that string theory becomes quantum mechanics at certain dimensions? Has anyone been able to solve the hydrogen atom with string theory or other similar quantum problems?

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Looking just at the title of the question reads like wanting to crack a nut with a sledgehammer ... :-D –  Dilaton Mar 5 '13 at 12:27
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Then again, one might feel awfully silly lugging around a sledgehammer only to later find it incapable of cracking said nut. –  wsc Mar 5 '13 at 14:23

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In physics you frequently find that a simple theory is part of a bigger, more complex theory, and that in turn is part of an even bigger, even more complex theory. For example non relativistic quantum mechanics (e.g. Schrodinger's equation) is a low speed limit of quantum field theory, and quantum field theory is a low energy limit of string theory.

When solving a problem you always choose the simplest theory you can get away with. You wouldn't attempt to use string theory to calculate the structure of a hydrogen atom because the calculation would be hopelessly complex. However we know QFT is a low energy limit of string theory and we can use QFT to calculate the structure of a hydrogen atom. Actually even non-relativistic QM is adequate for most purposes.

Given the above, the key bit of your question is:

has it been shown yet that string theory becomes quantum mechanics at certain dimensions?

and the answer is that yes, string theory does reproduce QFT at low energies. I don't think a model has yet been constructed that fully reproduces the Standard Model, but it's widely believed that it's possible and that we simply haven't found it yet.

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String theory is not a generalization of quantum mechanics . It doesn't modify the quantum mechanical rules for calculating probabilities so it doesn't have to become Quantum mechanics at some limit because it's quantum mechanics .

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I don't see how that makes sense. Are you saying they use Schrodinger's Equation the same way in string theory as in QM? There has to be some modification of the theory or else GR would have been incorporated into QM a long time ago. –  cspirou Mar 5 '13 at 22:22

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