asking questions like: assuming you could classically control some particle excitations (i.e. control macroscopic variables like position) that have some quantum state, what could you compute?
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Replying to @raeez
extremely interesting to me! sometimes i like thinking about it in other ways, like depending upon the theory and the configuration, what computational constraints are imposed on the universe. e.g. is the complexity of qcd in a nucleon tied to its mass & therefore time (sluggish)
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Replying to @DanielleFong
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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i think there are computational complexity constraints, constraints of dynamics, but maybe not physical constraints, constraints to scale as you'd normally see it.
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