Recently heard about the Schiff conjecture saying that any reasonable theory of gravitation should adhere to the ideas of EEP and UFF. I realise that this isn't a "strong" idea (only a conjecture after all), but to anyones understanding, does either loop quantum gravity or m-theory appear to adhere to/violate the Schiff conjecture? or are no real consequences of these theories testable to this level yet? (i.e to show the equivalencies between the postulates of Schiff).
http://arxiv.org/abs/1105.3735 "see also chapter 13 of [2], which shows how helicity 2 implies the equivalence principle"
EEP = Einstein Equivalence Principle UFF = Universality of Free Fall I'll let someone else answer your question. I haven't heard of any clearly formulated version of QG contradicting those two things. There may be some variant QG theory that does violate one or both, and I just missed hearing about it. I don't know of any standard formulation of M-theory. Authorities like David Gross say we don't know what it is. IOW we think there's a theory there somewhere but haven't written it down yet. Maybe someone else knows of clear unambiguous formulation of M-theory and can answer your question. Currently the most widely accepted formulation of Loop is http://arxiv.org/abs/1102.3660 an introductory tutorial and survey of open problems that CR gave last year at a school for PhD students and postdocs embarking on research. He points out many gaps, places that need to be filled in, notably how to work matter into the picture. Loop researchers think they have strong indications that Loop recovers GR in the simple case where there is no matter to worry about. And some evidence that you can successfully include matter. They don't have airtight proofs. Interestingly, the application to cosmology (LQC) seems already testable by this or next-generation spacecraft mapping the cosmic microwave background. The current mission ("Planck") reports next year and may have something to say, favorable or unfavorable. There are some papers about this on this quarter's MIP ("most important paper") poll, in this forum. If Loop recovers GR, as those involved expect, then I find it hard to imagine that it would not satisfy UFF and EEP. Leonard Schiff must have meant something deeper and more profound. Like WHY is their a constant relation between inertial mass and gravitational mass? WHY is this equivalence the same for all materials? I don't think the Loop program even tries to answer such a deep question. To the extent that some simple type or types of matter are included, one simply treats this equivalence as given. That doesn't mean it's not an interesting question! Merely that at this stage in its development AFAICS Loop just aspires to be a quantum theory of gravity with GR as limit (matterless or with at most rudimentary matter fields.) To the extent it achieves that goal it probably just inherits EEP and UFF by copying GR. So some deep questions (like relation of grav. mass and inertial mass) are avoided. By what means does matter bend geometry, by the way? Loop at this point does not offer a mechanism. Nor does GR say---only that it does bend, in suchandsuch fashion.
String theory should obey the EP to a very good approximation since it reduces to supergravity at low energies. However there are apparently small violations of the EP in some string models http://arxiv.org/abs/1202.6311