User:Johnjbarton/sandbox/many-worlds-interpretation

Alternative to wavefunction collapse

As with the other interpretations of quantum mechanics, the many-worlds interpretation is motivated by behavior that can be illustrated by the double-slit experiment. When particles of light (or anything else) pass through the double slit, a calculation assuming wavelike behavior of light can be used to identify where the particles are likely to be observed. Yet when the particles are observed in this experiment, they appear as particles (i.e., at definite places) and not as non-localized waves.

In Everett's time the theory, as formalized by John von Neumann, contained two postulated processes. The first was a discontinuous change brought about by observation and known as wave function collapse; the second was a continuous, deterministic change due to the wave equation known as unitary evolution. Everett showed that these are inconsistent by considering an observer A of a system S both being observed by a second observer B. During discontinuous change observed by A, B sees A+S as a continuous deterministic system. To avoid this inconsistency Everett proposes observation using only the second postulate and quantum state 'correlation', now known as entanglement. Thus A becomes entangled with S and B becomes entangled with A+S.

In the von Neumann model the discontinuous change was introduced to explain the random probabilistic results of observations; in Everett's model the probabilities appear to the observers as a consequence of the entanglement. If the state S has two equally possible observable values, the von Neumann model says each happens 50% of the time; Everett's model says A is only ever entangled with the wavefunction for one of the two, but A can recall previous observations which resulted in entanglement with the wavefunction for other value. Reflecting, subjectively, A will conclude the two values each appear 50% of the time. By abandoning the collapse process and adding entanglement, "the formal theory is objectively continuous and causal, while subjectively discontinuous and probabilistic".

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Connection between external observation and complementarity

"The conventional formalism admits no other way of interpreting the wave amplitude; it is logically self-consistent; and it rightly rules out any classical description of the internal dynamics of the system. With the help of the principle of complementarity the "external observation" formulation nevertheless keeps all it consistently can of classical concepts." Wheeler Assessment RMP