The ergodic hypothesis supposes that for an ensemble all possible states can occur over a sufficiently long period of time (which can be very long). Everett’s many worlds hypothesis supposes that difficulties in theory related to quantum mechanics might be mathematically resolved if all possibilities actually occur contemporaneously. Has anyone related to the two hypotheses? What are the sources? If not, are they related? If not, why not?
The similarity is obvious, but it is not the same.
In Everett's case one has superposition of states, in ergodic case one has mixed states. For macroscopically different states superposition and mixture are indistinguishable. I am not sure, are ergodic states are different enough.
No. Everett's many worlds interpretation tries to interpret the probabilities of assigned to states by describing all of them. This doesn't have anything to do with the ergodic hypothesis in classical mechanics, already, since the probabilities aren't those of the microcanonical enemble; nor does it have anything to do with the ergodic hypothesis of quantum states, since the many worlds interpretation, by construction, doesn't describe superpositions, since it describes only classical states. However, without the superpositions, the description is inconsistent.
Dear Dr. Shour: The Many World Interpretation makes no new assumption. Rather, it states that the full quantum state of the (system+apparatus+observer+environment) evolves unitarily according to the Schrodinger equation, so that each of the branches in the entangled state are actually happening. MWI does away with the state-vector collapse postulate. Of course, it is not clear how the Born Rule for probabilities (i.e. indeterminism of QM) emerges from MWI.
On the other hand, Ergodic Hypothesis is an assumption (a good one though) in order to equate ensemble averages to time averages.
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