Generally good, but this seems weak to me: "quantum field theory and general relativity are victims of their own success. For we need to go beyond them, since they face various technical and conceptual problems: such as the hierarchy and cosmological constant problems."
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Replying to @johncarlosbaez @skdh
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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The Standard Model, taken seriously at large scales, predicts that there is no gravity. General relativity, taken seriously at small scales, says that atoms don't have quantized energy levels. So, nobody takes them seriously in these realms they weren't designed for.
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The fundamental problem is that general relativity and quantum mechanics are not just physical theories; each is a comprehensive conceptual framework that imposes constraints on all possible physical theories -- and each ignores the constraints of the other.
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Quantum mechanics presumes a classical theory of spacetime. One cannot even enunciate its basic structural laws without one. But the classical theory of spacetime it presumes is obviously the wrong one; its empirical inadequacies are spectacular. So what to do?
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Replying to @MathPrinceps @johncarlosbaez and
Should one "quantize general relativity," or "general-relativize" quantum theory? Or perhaps do neither? Or both? Some argue that "quantizing" space and time is wrong-headed -- like replacing thermodynamic temperature by a self-adjoint operator on some Hilbert space of states.
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Replying to @MathPrinceps @johncarlosbaez and
And as for "general-relativizing" quantum theory, this seems at best a distant dream beset by formidable obstacles both technical and conceptual. Indeed, one can still win a million dollars, and lasting global fame, merely by "special-relativizing" quantum theory.
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