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Derek Potter

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Everett created the Relative State Formulation in order to resolve the contradictions, as he saw it, of QM. He introduced his doctoral thesis by stating that conventional QM works perfectly well - it predicts quantum statistics. However, interpreting conventional QM realistically leads to paradoxes. These are largely associated with the collapse of the wavefunction.

Everett's solution was to remove the collapse. The system evolves under linear wave mechanics and nothing else. Everett developed a primitive theory of measurement which predicted the appearence of collapse. He thus replaced the

Everett showed that the appearence of wavefunction collapse follows from wave mechanics. To do this he considered the interaction of two subsystems, the system under observation, S, and the observer system O. He modeled the observation as a simple interaction that creates a state of O that is strongly correlated with the state of S. This is fairly trivial if S is in an eigenstate of the interaction

Given that the states of S correlate with the states of O, what happens when S is a superposition? Interaction leaves the states entangled - neither subsystem has a state of its own, the state can only be specified by reference to the state of the rest of the system. The total system is in a superposition of states which can be labelled by the observed outcome, x

∑ a

S is said to be in the state |x

There is considerable justification for calling the states "worlds". An observer experiences the world. In this case, O's experience is the state he/she

However, MWI has been criticised for making assumptions. Can someone please tell me what assumptions other than wave mechanics are implicit in the RSF? Or in calling the relative states "worlds" given the caveats above?

Thanks,

Derek

Everett's solution was to remove the collapse. The system evolves under linear wave mechanics and nothing else. Everett developed a primitive theory of measurement which predicted the appearence of collapse. He thus replaced the

*of collapse with a result that is***axiom***from wave mechanics alone. It is now generally believed that Everett's theory does not provide the quantitative predictions of collapse theory but needs the addition of decoherence. (This is an important criticism of the original theory but I do not want to discuss whether Everett's treatment of the measurement problem was complete, suffice it to say that it can be made so or at least that any remaining problems are common to all interpretations.)***derived**Everett showed that the appearence of wavefunction collapse follows from wave mechanics. To do this he considered the interaction of two subsystems, the system under observation, S, and the observer system O. He modeled the observation as a simple interaction that creates a state of O that is strongly correlated with the state of S. This is fairly trivial if S is in an eigenstate of the interaction

*O enters a pointer state. (Again, the reasons why this is even possible let alone normal are part of the measurement problem.)***and**Given that the states of S correlate with the states of O, what happens when S is a superposition? Interaction leaves the states entangled - neither subsystem has a state of its own, the state can only be specified by reference to the state of the rest of the system. The total system is in a superposition of states which can be labelled by the observed outcome, x

_{i}, thus∑ a

_{i}|x_{i}>_{(S)}|x_{i}>_{(O)}S is said to be in the state |x

_{i}> relative to the state of O, |x_{i}>, and vice versa. The states of the total system are popularly described as worlds though Everett did not like the term. As there are typically many of them, the treatment is usually called the Many Worlds Interpretation.There is considerable justification for calling the states "worlds". An observer experiences the world. In this case, O's experience is the state he/she

**or it**enters as a result of observing S. Thus the different x_{i}s characterise different phenomenal states. Each state of S evolves independently in the superposition so the picture of separate worlds coexisting is natural - as long as no new physics like "universe splitting" is added.However, MWI has been criticised for making assumptions. Can someone please tell me what assumptions other than wave mechanics are implicit in the RSF? Or in calling the relative states "worlds" given the caveats above?

Thanks,

Derek

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