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Building on my previous thread, I was recently thinking about how energy and time are related by Noether's theorem (and stress-energy tensor <-> spacetime) and was wondering what symmetry would have information as a conserved quantity?
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I've been recently thinking about how the current base quantities of our unit system (mass, length, time) aren't really fundamental and was wondering what aspects of the world would be highlighted with a different set: •energy •spacetime interval •information
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Credit: Emilio Pisanty
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https://en.wikipedia.org/wiki/SI_base_unit#/media/File:Unit_relations_in_the_new_SI.svg
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This thread reads a bit like Carlo Rovelli’s Order of Time I don’t get most of it, but sounds like you think E, “L”, and some tweak on action are it? If the symmetry associated with E is “L”, that leaves information kinda hanging… is there a symmetry there?
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In short, there's a mathematical duality between a mathematical theory of quantum gravity in 3+1D and a quantum field theory on its boundary in 2+1D. QFT is a hologram of 3D spacetime. Also, complex states of QFT (thermal state) is simple black hole in 3D bulk and vice versa.
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I’ve heard of this black hole surface info before, but don’t really appreciate its significance. What does it *mean* that the info on a volume is proportional to surface area? Also does it apply to higher dimensional models? Are we in a 11d universe with 10d worth of info in it?