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Many-Worlds Interpretation of Quantum Mechanics:
The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

1. Introduction
The fundamental idea of the MWI, going back to Everett 1957, is that there are myriads of worlds in the Universe in addition to the world we are aware of. In particular, every time a quantum experiment with different possible outcomes is performed, all outcomes are obtained, each in a different world, even if we are only aware of the world with the outcome we have seen. In fact, quantum experiments take place everywhere and very often, not just in physics laboratories: even the irregular blinking of an old fluorescent bulb is a quantum experiment.

There are numerous variations and reinterpretations of the original Everett proposal, most of which are briefly discussed in the entry on Everett's relative state formulation of quantum mechanics. Here, a particular approach to the MWI (which differs from the popular “actual splitting worlds” approach in De Witt 1970) will be presented in detail, followed by a discussion relevant for many variants of the MWI.

The MWI consists of two parts:

i.A mathematical theory which yields the time evolution of the quantum state of the (single) Universe.
ii.A prescription which sets up a correspondence between the quantum state of the Universe and our experiences.
Part (i) is essentially summarized by the Schrödinger equation or its relativistic generalization. It is a rigorous mathematical theory and is not problematic philosophically. Part (ii) involves “our experiences” which do not have a rigorous definition. An additional difficulty in setting up (ii) follows from the fact that human languages were developed at a time when people did not suspect the existence of parallel worlds.

The mathematical part of the MWI, (i), yields less than mathematical parts of some other theories such as, e.g., Bohmian mechanics. The Schrödinger equation itself does not explain why we experience definite results in quantum measurements. In contrast, in Bohmian mechanics the mathematical part yields almost everything, and the analog of (ii) is very simple: it is the postulate according to which only the “Bohmian positions” (and not the quantum wave) correspond to our experience. The Bohmian positions of all particles yield the familiar picture of the (single) world we are aware of. Thus, philosophically, a theory like Bohmian mechanics achieves more than the MWI, but at the price of adding the non-local dynamics of Bohmian particle positions.



2. Definitions
2.1 What is “A World”?
A world is the totality of macroscopic objects: stars, cities, people, grains of sand, etc. in a definite classically described state.
The concept of a “world” in the MWI belongs to part (ii) of the theory, i.e., it is not a rigorously defined mathematical entity, but a term defined by us (sentient beings) in describing our experience. When we refer to the “definite classically described state” of, say, a cat, it means that the position and the state (alive, dead, smiling, etc.) of the cat is maximally specified according to our ability to distinguish between the alternatives, and that this specification corresponds to a classical picture, e.g., no superpositions of dead and alive cats are allowed in a single world.

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