# What does the equivalence principle mean in quantum cases?

We know that electron trapped by nuclear, like the hydrogen system, is described by quantum state,and never fall to the nuclear.So is there any similar situation in the case of electron near the blackhole but not fall into it?And what is "falling " in gravitation mean when considering quantum mechanics?What does the equivalence principle mean in quantum cases?

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This is asking for coherent bound motion near a black hole, and it is very much current research. It is an important question +1, but it is hard to answer without stepping on toes and entering into realms where calculations have not been done properly and not everything is 100% clear. –  Ron Maimon Apr 13 '12 at 6:01

The equivalence principle is a classical principle, it does not apply in quantum cases. Several specific violations of the principle are reported

http://prd.aps.org/abstract/PRD/v85/i4/e044052

http://iopscience.iop.org/0264-9381/29/2/025010

In the general case we wait the equivalence principle to not hold when the general relativistic spacetime metric $g_{ab}$ is corrected by the higher order graviton corrections.