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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Replying to @ChrisPapavasili @johncarlosbaez and
I wonder about that too. Is there an account of the standard model suitable for a mathematically trained non-expert that doesn't just say what it is but also gives you a good idea of why it was inevitable, given the experimental data, that we would come up with it?
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I doubt any single volume can do all this for the audience you posit. It's like asking for an account of arithmetic geometry suitable for graph theorists that reveals how the historical influences and heuristics that drove its creators resulted inevitably in the current subject.
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Replying to @MathPrinceps @wtgowers and
Of course an account of the sort you want can indeed be cobbled together from multiple sources. But making one's way through it is going to be a very ambitious undertaking. And certain steps in the journey will have to be taken on faith; they still lack a rigorous foundation.
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Replying to @MathPrinceps @wtgowers and
A further key question is: how much detail do you want, and how careful do you prefer to be? If, for example, you insist on knowing why a quantum field should be an operator-valued (tempered) distribution, then you're going to need to consult various somewhat obscure sources.
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