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I see a lot of questions in various sites about why the 2 theories are or aren't incompatible, I'm satisfied as to why that's the case.

However it has been mentioned that both theories make predictions about phenomena that contradict or are incompatible, and I've been unable to find any examples.

What are the conflicting/contrary/incompatible predictions made by General Relativity versus Quantum Mechanics? Or are the claims false?

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marked as duplicate by Dilaton, Emilio Pisanty, Qmechanic Jul 19 '13 at 14:05

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Are you saking about conflicts between classical GR and quantum theory, or (insofar as it exists) quantum GR and quantum mechanics? If the former, the conflicts are basically the same as anything classical vs QM. –  John Rennie Jul 19 '13 at 9:16
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Maybe this question should be faq? @John Rennie: I think your comment can make a short answer. –  Dimensio1n0 Jul 19 '13 at 9:26
    
I'm unfamiliar with Quantum General Relativity, so classic GR –  Tom J Nowell Jul 19 '13 at 9:46
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possible duplicate of A list of inconveniences between quantum mechanics and relativity? –  Ali Jul 19 '13 at 9:49
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The problem is more that there's only one reality, so you need a single theory which makes the successful predictions of both GR and QM. –  Mitchell Porter Jul 19 '13 at 10:07

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up vote 10 down vote accepted

As Mitchell Porter said, we need more than just the absence of self-evident contradictions. We need a theory that encompasses both quantum mechanics and general relativity. The most straightforward, naive union of these frameworks produces a theory that is "nonrenormalizable" – predicts all quantities to be equal to a finite number plus infinity (many types of infinities arise).

String theory is the only known reconciliation of general relativity and quantum mechanics and chances are high that this status won't ever change.

There's of course no contradiction between "appropriately reduced in reach" general relativity and "appropriately tamed" quantum mechanics – after all, to a certain extent, both of these frameworks have been established so there has to exist a more accurate theory that agrees with all the established insights.

However, there are contradictions between quantum mechanics (which seems perfectly exact and valid) and classical general relativity believed literally. For example, classical general relativity paints a black hole as a perfectly determined, unique state of the spacetime. It carries no entropy because it has "no hair" according to classical general relativity. According to quantum mechanics, this can't be the case. A black hole has to carry and does carry a huge entropy – in fact, a greater entropy than any other localized object of the same mass – which is needed for the second law of thermodynamics to hold (entropy has to increase in time) and which is needed to "preserve the information" about the initial state, something that is required by "unitarity" in quantum mechanics. So some "tunneling" of the information from the interior has to be possible.

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So these contradictions are all about black holes and entropy, infinite versus no entropy, and the information and whichever details thereof? –  Tom J Nowell Jul 19 '13 at 13:45
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Maybe but I don't have any theorem of this sort. When the gravitational fields are weak, some perturbative expansions and n-loop approximations of quantized GR may be OK. The discrepancies only get highlighted in strong gravitational fields and in that case, one also gets the horizons - coordinate singularities, to say the least. Note that if there's a disagreement about the information, there's a disagreement about everything. –  Luboš Motl Jul 20 '13 at 15:22
    
see absolutely no incompatibility. Both theories are incomplete at extremes and the structures of string theory fill that in. Only string theory can extend them at this high energy limit and remain consistent with a quantized gravity. –  user12811 Jul 23 '13 at 21:46

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