Shower idea of the day: instead of thinking of light as some weird thing that just happens to make the universe stay consistent under relativity and satisfying arbitrary things like “no information moves faster than light,” think of the universe as a giant computer where 1/
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a thought i keep coming back to related to this is that applying the CLT to a random walk on a grid and zooming out reproduces the euclidean metric which otherwise strikes me as extremely mysterious. suggests to me that space is discrete at the planck length or w/e
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Yeah maybe something like the perceived movement of “light moves at shortest metric path” is a derived property from local random walk stuff. LMK if you have references. (I’ve heard of the thing you said before, but didn’t dig)
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that particular thing is well-understood in path integral terms which ought to have some kind of random walk formulation but i haven’t looked for it or seen it. no idea how to incorporate relativistic invariance this way
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the “speed of light” here is the speed at which this random walk propagates *on average*; analogously, in the feynman path integral formulation of QFT, you integrate over paths where photons travel faster than light
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