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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) are passed through the double slit, a calculation assuming wave-like behavior of light is needed to identify where the particles are likely to be observed. Yet when the particles are observed, they appear as particles and not as non-localized waves. The rival Copenhagen interpretation of quantum mechanics proposed a process of " collapse" from wave behavior to particle-like behavior to explain this phenomenon of observation.
The process of wavefunction collapse proposed by the Copenhagen interpretation was widely regarded as artificial and ad-hoc, and consequently an alternative interpretation in which the behavior of measurement could be understood from a more fundamental physical principles was considered desirable. Everett's Ph. D. work was intended to provide such an alternative. Everett left physics research soon after obtaining his degree so much of the elaboration of his ideas was carried out by others.
The goal of the relative-state formalism, as originally proposed by Everett in his 1957 doctoral dissertation, was to interpret the effect of external observation entirely within the mathematical framework developed by Dirac, von Neumann and others, discarding altogether the ad-hoc mechanism of wave function collapse. Since Everett's original work, there have appeared a number of formalisms in the literature, which use similar terminology and have similar objectives, but which are hard to reconcile with each other. We point out that one way to do away with the language of wave function collapse, based on the idea of partial trace is discussed separately in the next section.
From any of the relative-state formalisms, we can obtain a relative-state interpretation by two assumptions. The first is that the wavefunction is not simply a description of the object's state, but that it actually is entirely equivalent to the object, a claim it has in common with other interpretations. The second is that observation has no special role, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation. In Everett's formulation, any measuring apparatus M that interacts with an object system S forms a composite system; after the interaction, it is no longer possible to describe the state of S or that of M by an independent wave-function. The only meaningful descriptions of each are relative states: for example the relative state of S given the state of M or the relative state of M given the state of S.
The many-worlds interpretation is DeWitt's rendering of the relative state formalism (and interpretation). Everett referred to the system (such as an observer) as being split by an observation, each split corresponding to a possible outcome of an observation. These splits generate a possible observation tree as shown in the graphic below. Subsequently DeWitt introduced the term "world" to describe a complete measurement record of an observer, which corresponds roughly to a path starting at the root of that tree. Note that "splitting" in this sense, is hardly new or even quantum mechanical. The path space interpretation of stochastic processes is in many ways the same idea. The novelty in DeWitt's viewpoint was the various worlds could be superposed to form quantum mechanical states.
Under the many-worlds interpretation, the Schrödinger equation holds all the time everywhere. An observation or measurement of an object by an observer is modelled by applying the Schrödinger wave equation to the entire system comprising the observer and the object. One consequence is that every observation causes the universal wavefunction to decohere into two or more non-interacting branches, or "worlds". Since many observation-like events are constantly happening, there are an enormous number of simultaneously existing states.
If a system is composed of two or more subsystems, the system's state will typically be a superposition of products of the subsystems' states. Once the subsystems interact, their states are no longer independent. Each product of subsystem states in the overall superposition evolves over time independently of other products. The subsystems have become entangled and it is no longer possible to consider them independent of one another. Everett's term for this entanglement of subsystem states was a relative state, since each subsystem must now be considered relative to the other subsystems with which it has interacted.
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