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roywiggins said >you have a universe that is infinite from "inside", but "from the outside", there's an outer boundary. and you say >specifying the state of
by kerenua 8y ago
roywiggins said
>you have a universe that is infinite from "inside", but "from the outside", there's an outer boundary.
and you say
>specifying the state of the universe on the boundary of a manifold is sufficient to completely specify the state inside
this would be similar to me viewing a Mandelbrot set and being able to tell its infinitely deep?
- tbabb 8y agoMaybe a better analogy would be: If you know the complete state of the universe at one moment in time, you know the state at all moments in time, because you can run the laws of physics (forward or backward) and compute the state at some other time without adding information. (In physics, this arises from a property called "unitarity"). The holographic principle says you can do the same thing, but by knowing the state of the universe on a boundary that encompasses the whole system (when you parameterize spacetime in a convenient way), as opposed to by knowing the state everywhere at one moment.
- roywiggins 8y agoYou still have to know the state of the whole boundary (which is huge) but the important part is that the boundary is one fewer dimension than the interior, which (apparently) makes the math easier.