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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Replying to @MathPrinceps @johncarlosbaez and
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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Replying to @MathPrinceps @johncarlosbaez and
Meantime, it remains unclear whether any experiment can ever be done by humans that might reveal some essential predictive inadequacy in either general relativity or quantum theory. Each, supreme in its own domain and haughtily ignoring the other, seems all but invulnerable.
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Replying to @MathPrinceps @johncarlosbaez and
So the situation is perhaps about as discouraging as it could possibly be. We know we're wrong, yet we lack access to phenomena capable of forcing us to correct our errors (and of guiding our guesswork as we struggle to correct them.)
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I'm actually pretty optimistic that we'll solve this; it's hard to combine the insights of quantum theory and general relativity, but that very difficulty is helpful, because it provides a strong constraint in a situation where we don't have enough experiments. (continued)
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Replying to @johncarlosbaez @MathPrinceps and
All attempts to combine quantum theory and general relativity so far suffer from "internal" problems - problems you can detect without doing experiments. But there are also experimental puzzles that want explanations, like "dark matter" (or whatever is). (continued)
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Replying to @johncarlosbaez @MathPrinceps and
So, there are plenty of angles to work. But we may need 2 or 3 new ideas that only work well when combined. So, it could take decades. I quit working on quantum gravity because I wanted to do some things that would succeed in my lifetime. But in the long run I'm optimistic.
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In the long run, I'm cautiously pessimistic. The problems here are now clear enough to identify as fundamental; we'll need something vastly more than ingenuity and optimism to get past them. And, worst of all, it seems very doubtful whether we'll ever know if we've got it right.
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The existing theories of quantum gravity are so bad that it's very easy for me to imagine that someday people will come up with a vastly better one... and we'll all say "Duh! Why didn't anyone think of that sooner?"
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Replying to @johncarlosbaez @MathPrinceps and
We are SO constrained by the scient. authorities of the "fathers" of EM, the quantum, and gravitation, that we don't investigate critically enough the phys-math foundations of their theories. Having so many fundamental questions unanswered, the times are ripe to do it.
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