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Since general relativity is nonlinear, how could we quantitize gravity with QM interpretations which use the linear Schrödinger Equation? Or is this fundamentally unworkable?

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Some key-word is Wheeler–DeWitt equation. Maybe this paper could be useful (see Chapter 6 - Quantum Cosmology) –  Trimok May 27 '13 at 11:13
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Quantum electrodynamics is nonlinear (look at the interaction term) and conventional quantization seems to work quite well there, so just the fact that a classical theory is nonlinear isn't necessarily a barrier to successful quantization. –  twistor59 May 27 '13 at 11:20
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Quantum mechanics is a lot more mathematical modelings than Schroedinger's equation. en.wikipedia.org/wiki/… –  anna v May 27 '13 at 11:48
    
@twistor59 where are linear equations used to quantitize anything in quantum electrodynamics? My understanding is that it works because it is nonlinear; it's quite reconcilable with special relativity. –  Drew Bowers May 27 '13 at 16:31
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@DrewBowers The point that I was making was that, in QED, the classical equations you're starting with are nonlinear, however quantization proceeds by using the normal machinery of Hilbert spaces and unitary evolution. This is linear and is effectively governed by a (formal) Schroedinger equation. Hence it's not correct to say that conventional quantization fails for GR because the classical equations are nonlinear it fails for a different reason, related to the dimensional nature of the coupling constant. –  twistor59 May 28 '13 at 6:27

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