The most fruitful approach I've found to answering these questions is to realize the particles as objects in some representation category of some symmetry (group, quantum group etc.).
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Replying to @raeez
right, I see how a lot of things can collapse to that approximately, classical dynamics even can collapse to this (e.g. noether's theorem)
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Replying to @raeez
we still end up with weirdness on branch cuts between symmetries/ 3-manifold. wondering if this is where a lot of quantum weirdness comes from. e.g. free will theorem for, as
@EricRWeinstein says, questions we ask of quantum particles the classical theory says are not well posed.3 replies 1 retweet 1 like -
Replying to @DanielleFong @EricRWeinstein
Then you're led to ask what non-commutative deformations correspond to 3-fold topology... and the waters get pretty deep quite fast
There's a pretty deep connection, happy to explain it as I see it some time1 reply 1 retweet 1 like -
Replying to @raeez @EricRWeinstein
yeah so that's a fascinating question, right? it's not clear there are limits. following from the free will theorem, it's possible that an extremely willful and intelligent electron could play a sort of... extremely intelligent game of quantum go at the boundaries




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i mean there's a singularity in there. anything can happen, anything could be hidden and is just behnd the renormalization
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Replying to @DanielleFong @EricRWeinstein
A precise way of making sense of the question I'm most interested in right now is: given a geometric description of a singularity... how do you describe the dynamics that emerge from the presence of that singularity? In ideal cases, the answer is an explicit quantum field theory
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if the explicit description of the QFT corresponding to that singularity is "good" enough (say has a lot of symmetry), one can concretely answer all of the questions we've been posing: what computations are possible, what dynamics are possible etc.
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yeah I think, I think there's really room for a kind of 'statistical mechanics' that blurs out the kind of extreme cases I've been describing and draw some nice boundaries that will work for almost all practical purposes, but maybe not at the event horizon of a black hole
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