The many-worlds interpretation is an interpretation of quantum mechanics, based on Everett's relative-state formulation. The phrase "many worlds" is due to Bryce DeWitt, who wrote more on the topic of Hugh Everett's original work, and this particular version has become so popular that many confuse it with Everett's own work.
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 that the light is behaving as a wave 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. In some interpretations of quantum mechanics, when the position of a particle is measured it appears to "collapse" from wave behavior to particle-like behavior.
The relative-state view argues that this apparent collapse is an illusion. The interpretation has two assumptions. The first is that the wavefunction is not simply a description of the object's state, but that it actually is 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 to collapse upon observation.
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.
Mathematically and physically, the many-worlds interpretation is simpler than the Copenhagen interpretation. The act of observation or measurement is not magical, and the interpretation of probabilities as the squared amplitude of the wave function is a direct consequence of the theory rather than a necessary axiom. However, many physicists dislike the implication that there are an infinite number of non-observable alternate universes. Some physicists have noted that there appears to be an increase in support for the many-worlds interpretation largely because many-worlds seems to allow for predictions on the process of quantum decoherence in a natural way rather than adding it in an ad-hoc manner.
Nevertheless, as of 2002, there were no practical experiments that would distinguish between many-worlds and Copenhagen, and in the absence of observational data, the choice is one of personal taste. However, one active area of research is devising experiments which could distinguish between various interpretations of quantum mechanics. It has been proposed that in a world with infinite alternate universes that universes which collapse would exist for a shorter time than universes which expand, and that would cause detectable probability differences between many-worlds and the Copenhagen interpretation.
It has been controversially claimed that an interesting but dangerous experiment which would also clearly distinguish between the Many Worlds interpretation and all other interpretations involves a quantum suicide machine and a physicist who cares enough about the issue to risk his own life. At best, this would only decide the issue for the brave physicist; bystanders would learn nothing.
The many-worlds interpretation should not be confused with the many-minds interpretation which postulates that it is only the observers' minds that split instead of the whole world.
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References:- The Many-Worlds Interpretation of Quantum Mechanics by Bryce S. DeWitt, R. Neill Graham, eds, Princeton Series in Physics, Princeton University Press (1973)