It is well known that QM and GR are deemed incompatible due to a discrepancy in some calculations which I have read can differ by large magnitudes. What are these calculations to which people are referring i.e. what equations/results?
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1The point is, actually, that classical GR, when quantized as an effective field theory, does not predict any large deviations from the classical theory in almost any situation of interest. Maybe what you are referring to is the measured (not predicted by a GR computation) value of the cosmological constant (cosmological vacuum energy) as compared to order-of-magnitude guesstimates created by smashing fundamental constants together ("the quantum-gravity estimate of vacuum energy"). – Void Jul 25 '19 at 15:33
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Possible duplicate of A list of inconveniences between quantum mechanics and (general) relativity? – Emilio Pisanty Jul 26 '19 at 11:42
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You probably heard about the energy density of the vacuum. Quantum field theory seems to suggest a value about 120 orders of magnitude larger than value used in cosmological theories based on General Relativity. The low cosmological value is in good agreement with observation but it seems unnaturally low.
G. Smith
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Sorry, I am confused: GR- predicts x but we measure y. QF - predicts x and we measure x. Just because GR makes sense, we call it incompatible and we call QF unnatural even though it matches the observation? What am I missing here? – LostCause Jul 26 '19 at 17:38
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They are not incompatible just because of the discrepancy is some calculations. If that was true then Newton's law of universal gravitation would also be incompatible with GR.
QM and GR are incompatible because they have fundamental differences. GR requires a smooth gravity while QM requires a quantized gravity; therefore, we are hunting for the graviton.
Unless you are referring to measured vs calculated difference of constant as mentioned by @Void, I am not sure what other discrepancies of large magnitude you are referring to.
LostCause
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Then where does this “differing by x orders of magnitude” that I keep hearing come from? I can try to find some articles I’ve found it in if that would help – Sterling Butters Jul 25 '19 at 16:01
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Well I can’t find the article now -.- but I’ll post back if I find it - I’m betting it was the cosmological constant problem to which the articles were referring – Sterling Butters Jul 25 '19 at 16:35
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@SterlingButters why did you ask the question if already knew the answer you were looking for? – LostCause Jul 26 '19 at 16:09
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I didn't know the answer - I was just saying thats probably what the articles were referring to (same as answer) – Sterling Butters Jul 26 '19 at 21:15
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Just want to echo the observation of @Void: Quantum gravity as an effective field theory has only insignificant impact on classical gravity (see, e.g. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.50.3874).
The problem lies in the quantum anything else other than quantum gravity: for instance, the quantum fluctuation of a typical bosonic field would have exorbitantly large contribution to the cosmological constant, contradicting the concordant cosmological model $\Lambda$CDM which is based on CLASSICAL gravity.
In the high energy community, the savior is supersymmetry: the contributions to the vacuum energy from bosons and fermions as SUSY partners exactly cancels out, since they are of the opposite sign. However, there is a catch! SUSY has to be spontaneously broken to facilitate the Higgs mechanism, which entails an electroweak scale (still WAY too large) cosmological constant.
So is SUSY the true Messiah?
MadMax
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This should have been a comment since it's not answering the question. – LostCause Jul 26 '19 at 16:03