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mfb comments on Causal Reference - Less Wrong
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Epiphenominal theories of consciousness are kind of silly, but here's another situation I can wonder about... some cellular automata rules, including the Turing-complete Conway's Game of Life, can have different "pasts" that can lead to the same present. From the point of view of a being living in such a universe (one in which information can be destroyed), is there a fact of the matter as to which "past" actually happened?
The Standard Model of particle physics with MWI is time-symmetric (to be precise: CPT symmetric) and conserves information. If you define the precise state at one point in time, you can calculate the unique past which lead to that state and the unique future which will evolve from that state. Note that for general states, "past" and "future" are arbitrary definitions.
(Which is why I specified a different set of laws of physics.)