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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Replying to @wtgowers @ChrisPapavasili and
I doubt it's possible to make a case that it was inevitable. I suspect there are other mathematical formulations which would give the exact same measurement predictions that we simply don't use for historical reasons.
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Mathematicians like uniqueness theorems; they seek axioms so exquisitely coherent that they completely and perfectly characterize just one thing that they can then prove must exist. Some quantum field theorists share this passion, and strive to satisfy it (mostly, alas, in vain.)
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Replying to @MathPrinceps @skdh and
The great thing about a mathematical uniqueness theorem is that it promises to remove all historical contingency. Things must be a certain way, not in obedience to tradition, but because otherwise one or more of these utterly transparent foundational principles would be violated.
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Replying to @MathPrinceps @skdh and
The yearning for this sort of understanding of quantum field theory drove Arthur Wightman and his various colleagues and disciples to seek axioms for the discipline that might simultaneously free it of all dependence on historical accident and expose its absolute essentials.
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Replying to @MathPrinceps @skdh and
The program of the axiomatic quantum field theorists remains incomplete (and indeed one can win a million dollars merely by proving that it can be completed), but that doesn't mean it was entirely without successes. We do now know why some things must be so, and not otherwise.
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Of course the few things we understand in this way fall far short of what we'd need to remove all contingency from the formulation of the standard model. But it's not just by historical accident that we are where we are; not everything is up for grabs. And it's nice to know that.
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