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 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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Replying to @MathPrinceps @wtgowers and
A profound dichotomy confronts you as a student of this material. Do you mind being frankly Eulerian in your approach to it, or do you have Weierstrassian scruples you feel duty-bound to uphold? If the former, then physicists will (and should) be your preferred expositors.
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Replying to @MathPrinceps @wtgowers and
If the latter, then I suspect you might find Richard Borcherds a helpful guide, especially for orienting yourself in the early going. But the path he lays out is long and intricate, and getting to journey's end is not unlike mastering the content of EGA. http://bit.ly/2E2Zywf
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Replying to @MathPrinceps @ChrisPapavasili and
Thank you for that very interesting answer!
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You are of course most welcome, Professor Gowers. Please let me know if you would like me to expand upon it. In particular, should you wish guidance on which physicists might be best to read (assuming you are of Eulerian disposition), I'd be glad to help.
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Replying to @MathPrinceps @wtgowers and
I'm not
@wtgowers, but I'd still be interested.0 replies 0 retweets 1 likeThanks. Twitter will use this to make your timeline better. UndoUndo
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