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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Replying to @wtgowers @ChrisPapavasili and
Best way to get to the standard model for the mathematically inclined I'd say is follow the path of works by Weinberg and 't Hooft. Unfortunately, I don't know of a compilation that actually contains equations. But this books may be a good starting point: https://www.amazon.com/Search-Ultimate-Building-Blocks-Hooft/dp/0521578833 …
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Weinberg's three volumes (Quantum Theory of Fields, CUP) are probably optimal for theoretical physicists, but they fall far short of the level of rigor and explicitness which most modern mathematicians expect. For that, first there's Glimm-Jaffe, and then Deligne-Kazhdan et. al.
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Replying to @MathPrinceps @skdh and
Again, it really depends on what you want. If you must know is why everything is as it is, you can't expect standard sources to help much; most give short shrift to first principles, and focus instead on getting efficiently to and through the procedures and their applications.
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Replying to @MathPrinceps @skdh and
I think the main thing to know, though, is that understanding the standard model means understanding both quantum field theory in general, and the quantization of gauge fields in particular -- and neither is easy to learn. Even brilliant people need to budget some years for this.
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I'm tempted to say that the demands of the project are in direct proportion to the mathematical scruples that one brings to it, too. If you insist on understanding everything from first principles, the task is at present impossible. And impossible things always take a while.
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