Those dubious problems aren't the main reasons we need to go beyond QFT and GR. We need to go beyond them because they are inconsistent with each other. We need to find a consistent framework for physics.
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Replying to @johncarlosbaez @skdh
The way I interpreted that remark was that because QFT and GR apply to great accuracy way beyond the domains that they were originally designed for, they feel more universal, and therefore their inconsistency is all the more puzzling.
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But that was just the "victims of their own success" part, and not the bits you describe as dubious problems, where I'm not qualified to comment.
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The "cosmological constant problem" is that the cosmological constant is 10^{-120}, which some people consider oddly small. The "hierarchy problem" is that the Higgs boson mass is a lot smaller than the Planck mass.
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Both these problems are precisely the kind that
@skdh argues we should pay less attention to. They're called "naturalness problems": situations where people worry that a dimensionless constant is suspiciously large or small. They are not inconsistencies between GR and QFT.2 replies 0 retweets 9 likes -
Thus, it's odd that Butterfield listed these two problems and not the vastly more important problem that the Standard Model and GR can't both be correct. We know we need to tweak one or both of these theories to get a consistent framework that fits the data we have!
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Replying to @johncarlosbaez @skdh
To understand this more precisely, can we say something stronger, such as that GR is actually wrong at small scales -- that is, conflicts with experiment rather than just with the Standard Model? And is there any large-scale phenomenon that the Standard Model gets wrong?
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Professor Gowers, I regret not responding earlier to this question, because it's absolutely crucial. No experiment probing the microworld has ever revealed a defect in GR. But the logic of propositions referring to denizens of the microworld is inconsistent with GR.
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Replying to @MathPrinceps @wtgowers and
This, I would argue, is the key point: I want particularly to stress that this logic is mandated not by QM, but by observation. Its validity in its domain of application is unambiguously affirmed not indirectly, via the successes of QM, but directly, by the phenomena themselves.
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Replying to @MathPrinceps @wtgowers and
I cannot emphasize this strongly enough: we observe directly phenomena in the microworld that are irreconcilable with the most primitive assumptions of GR. It's not the overwhelming empirical success of QM that obliges us to accept a non-classical logic. It's direct observation.
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I have long been profoundly grateful to the late great Itamar Pitowsky for making this point exquisitely clear to me at last, and I wish his brilliant expositions of the essential ideas here were vastly better known. In particular, I strongly recommend:http://bit.ly/2GCzU31
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