The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of probability. This is the first of two reviews of the Everett interpretation, and focuses on structure, with particular attention to the role of decoherence theory. Written in terms of the quantum histories formalism, decoherence theory just is the theory of branching structure, in Everett's sense.

We study whether the probabilistic postulate could be derived from basic principles. Through the analysis of the Strong Law of Large Numbers and its formulation in quantum mechanics, we show, contrary to the claim of the many-worlds interpretation defenders and the arguments of some other authors, the impossibility of obtaining the probabilistic postulate by means of the frequency analysis of an ensemble of infinite copies of a single system. It is shown, though, how the standard form of the probability as (...) the square of the scalar product follows from Gleason's theorem. (shrink)

The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. 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.

We review the decoherent histories approach to the interpretation of quantum mechanics. The Everett relative-state theory is reformulated in terms of decoherent histories. A model of evolutionary adaptation is shown to imply decoherence. A general interpretative framework is proposed: probability and value-definiteness are to have a similar status to the attribution of tense in classical spacetime theory.

Pour résoudre les paradoxes bien connus de la mécanique quantique, on propose une interprétation par ramification (ou univers parallèles) analogue à celle d?Everett, mais avec des différences: (i) on propose une infinité continue de branches, dont les poids (o[ugrave] probabilités) se calculent par intégrale; (ii) les branches sont séparées par des ramifieurs qui se propagent à la vitesse de la lumière. Lorsqu?est négligeable la composante d?énergie négative de la fonction d?onde, le poids de chaque branche en un point donné u (...) est égal au flux du quadrivecteur (courant-densité de présence), soit à travers l'élément d?écran antérieur à u sur lequel l'impact est perçu, soit à travers le cône passé de u si aucun impact n?est perçu. In order to solve well-known paradoxes in quantum mechanics, we propose a reworking of Everett's interpretation with ramified branches (or many worlds), yet somewhat different: (i) branches form an infinity continuum and each weight (probability) is defined by an integral; (ii) branches are separated by ramifiers which propagate themselves with the velocity of light. Assuming we can neglect the negative-energy component in the wave function, then the weight of each branch at a given point u is equal to the flux of the quadrivector (current-presence density), either through the screen element where the impact occurs, or through the past light-cone of u if no impact occurs. (shrink)

This is a self-contained introduction to the Everett interpretation of quantum mechanics. It is the introductory chapter of Many Worlds? Everett, quantum theory, and reality, S. Saunders, J. Barrett, A. Kent, and D. Wallace, Oxford University Press.