More precisely, we begin by noting that Turing machines compute by following a single multiway branch in a completely deterministic fashion. Nondeterministic Turing machines, on the other hand, compute by also following a single multiway branch, but with the choices of which successive branches to take made in accordance with some nondeterministic rule. Therefore, P vs. NP (i.e. the question of whether the set of all problems solvable in polynomial time by a deterministic Turing machine is identical to the set of problems solvable in polynomial time by a nondeterministic Turing machine) is ultimately a question about whether a multiway state obtained by following a predetermined path in the multiway system is always reachable by following a nondeterministic path of approximately the same length. This is trivially true in the case of highly causal-invariant universes (e.g. ones in which all multiway branches eventually converge to a normal form). For a more nontrivial, non-terminating multiway system, the relative rates of branch pair divergence/convergence place constraints on the degree to which P and NP can be related.

]]>More precisely, a formal statement of the ER=EPR conjecture is that the Bekenstein–Hawking entropy of a pair of entangled black holes is equivalent to their entanglement entropy. If Hawking radiation effects occur as a result of branch pairs that fail to reconverge as a consequence of disconnections in the multiway causal graph, the ER=EPR conjecture is really just a rather elementary statement about the geometry of branchtime (in other words, it states that the natural distance metric in branchtime is the entanglement entropy of pairs of microstates, which one can prove directly from the properties of the Fubini–Study metric tensor).

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