The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wave function is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum measurements are physically realized in different "worlds". The evolution of reality as a whole in MWI is rigidly deterministic and dynamically local. Many-worlds is also called the relative state formulation or the Everett interpretation, after physicist Hugh Everett, who first proposed it in 1957.Hugh Everett Theory of the Universal wavefunction, Thesis, Princeton University, (1956, 1973), pp. 1–140. Bryce DeWitt popularized the formulation and named it many-worlds in the 1970s. See also Cecile M. DeWitt, John A. Wheeler (eds,) The Everett–Wheeler Interpretation of Quantum Mechanics, Battelle Rencontres: 1967 Lectures in Mathematics and Physics (1968).Bryce Seligman DeWitt, The Many-Universes Interpretation of Quantum Mechanics, Proceedings of the International School of Physics "Enrico Fermi" Course IL: Foundations of Quantum Mechanics, Academic Press (1972).
In modern versions of many-worlds, the subjective appearance of wave function collapse is explained by the mechanism of quantum decoherence. Decoherence approaches to interpreting quantum theory have been widely explored and developed since the 1970s.H. Dieter Zeh, On the Interpretation of Measurement in Quantum Theory, Foundations of Physics, vol. 1, pp. 69–76, (1970).Wojciech Hubert Zurek, Decoherence and the transition from quantum to classical, Physics Today, vol. 44, issue 10, pp. 36–44, (1991).Wojciech Hubert Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics, 75, pp. 715–775, (2003). MWI is considered a mainstream interpretation of quantum mechanics, along with the other decoherence interpretations, the Copenhagen interpretation, and hidden variable theories such as Bohmian mechanics.
In the many-worlds interpretation, the universal wave function evolves unitarily without collapse. Interactions lead to decoherence, producing dynamically independent components of the wave function that correspond to different macroscopic outcomes. These components are sometimes called "worlds", though they are emergent, approximate, and not fundamental entities. This is intended to resolve the measurement problem and thus some paradoxes of quantum theory, such as Wigner's friend, the Einstein–Podolsky–Rosen (EPR) paradox and Schrödinger's cat, since the universal wave function contains components corresponding to every possible outcome of a quantum event.
Overview of the interpretation The many-worlds interpretation's key idea is that the linear and unitary dynamics of quantum mechanics applies everywhere and at all times and so describes the whole universe. In particular, it models a measurement as a unitary transformation, a correlation-inducing interaction, between observer and object, without using a collapse postulate, and models observers as ordinary quantum-mechanical systems. This stands in contrast to the Copenhagen interpretation, in which a measurement is a "primitive" concept, not describable by unitary quantum mechanics; using the Copenhagen interpretation the universe is divided into a quantum and a classical domain, and the collapse postulate is central. In MWI, there is no division between classical and quantum: everything is quantum and there is no collapse. MWI's main conclusion is that the universe (or multiverse in this context) is composed of a quantum superposition of an uncountable or undefinable amount or number of increasingly divergent, non-communicating parallel universes or quantum worlds. Sometimes dubbed Everett worlds, each is an internally consistent and actualized alternative history or timeline.
The many-worlds interpretation uses decoherence to explain the measurement process and the emergence of a quasi-classical world. Wojciech H. Zurek, one of decoherence theory's pioneers, said: "Under scrutiny of the environment, only pointer states remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected". Zurek emphasizes that his work does not depend on a particular interpretation.
The many-worlds interpretation shares many similarities with the decoherent histories interpretation, which also uses decoherence to explain the process of measurement or wave function collapse. MWI treats the other histories or worlds as real, since it regards the universal wave function as the "basic physical entity" or "the fundamental entity, obeying at all times a deterministic wave equation". The decoherent histories interpretation, on the other hand, needs only one of the histories (or worlds) to be real.
Several authors, including Everett, John Archibald Wheeler and David Deutsch, call many-worlds a theory or metatheory, rather than just an interpretation. Everett argued that it was the "only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world". Deutsch dismissed the idea that many-worlds is an "interpretation", saying that to call it an interpretation "is like talking about dinosaurs as an 'interpretation' of fossil records".
Formulation In his 1957 doctoral dissertation, Everett proposed that, rather than relying on external observation for analysis of isolated quantum systems, one could mathematically model an object, as well as its observers, as purely physical systems within the mathematical framework developed by Paul Dirac, John von Neumann, and others, discarding altogether the ad hoc mechanism of wave function collapse.
Relative state Everett's original work introduced the concept of a relative state. Two (or more) subsystems, after a general interaction, become correlated, or as is now said, entangled. Everett noted that such entangled systems can be expressed as the sum of products of states, where the two or more subsystems are each in a state relative to each other. After a measurement or observation one of the pair (or triple, etc.) is the measured, object or observed system, and one other member is the measuring apparatus (which may include an observer) having recorded the state of the measured system. Each product of subsystem states in the overall superposition evolves over time independently of other products. Once the subsystems interact, their states have become correlated or entangled and can no longer be considered independent. In Everett's terminology, each subsystem state was now correlated with its relative state, since each subsystem must now be considered relative to the other subsystems with which it has interacted.
In the example of Schrödinger's cat, after the box is opened, the entangled system is the cat, the poison vial and the observer. One relative triple of states would be the alive cat, the unbroken vial and the observer seeing an alive cat. Another relative triple of states would be the dead cat, the broken vial and the observer seeing a dead cat.
In the example of a measurement of a continuous variable (e.g., position q), the object-observer system decomposes into a continuum of pairs of relative states: the object system's relative state becomes a Dirac delta function each centered on a particular value of q and the corresponding observer relative state representing an observer having recorded the value of q. The states of the pairs of relative states are, post measurement, correlated with each other.
In Everett's scheme, there is no collapse; instead, the Schrödinger equation, or its quantum field theory, relativistic analog, holds all the time, everywhere. An observation or measurement is modeled by applying the wave equation to the entire system, comprising the object being observed and the observer. One consequence is that every observation causes the combined observer–object's wave function to change into a quantum superposition of two or more non-interacting branches.
Thus the process of measurement or observation, or any correlation-inducing interaction, splits the system into sets of relative states, where each set of relative states, forming a branch of the universal wave function, is consistent within itself, and all future measurements (including by multiple observers) will confirm this consistency.
Renamed many-worlds Everett had referred to the combined observer–object system as split by an observation, each split corresponding to the different or multiple possible outcomes of an observation. These splits generate a branching tree, where each branch is a set of all the states relative to each other. Bryce DeWitt popularized Everett's work with a series of publications calling it the Many Worlds Interpretation. Focusing on the splitting process, DeWitt introduced the term "world" to describe a single branch of that tree, which is a consistent history. All observations or measurements within any branch are consistent within themselves.
Since many observation-like events have happened and are constantly happening, Everett's model implies that there are an enormous and growing number of simultaneously existing states or "worlds".
Properties
MWI removes the observer-dependent role in the quantum measurement process by replacing wave function collapse with the established mechanism of quantum decoherence. As the observer's role lies at the heart of all "quantum paradoxes" such as the EPR paradox and von Neumann's "boundary problem", this provides a clearer and easier approach to their resolution.
Since the Copenhagen interpretation requires the existence of a classical domain beyond the one described by quantum mechanics, it has been criticized as inadequate for the study of cosmology. While there is no evidence that Everett was inspired by issues of cosmology, he developed his theory with the explicit goal of allowing quantum mechanics to be applied to the universe as a whole, hoping to stimulate the discovery of new phenomena. This hope has been realized in the later development of quantum cosmology.
MWI is a realist, deterministic and dynamically local theory. It achieves this by removing wave function collapse, which is indeterministic and nonlocal, from the deterministic and local equations of quantum theory.
MWI (like other, broader multiverse theories) provides a context for the anthropic principle, which may provide an explanation for the fine-tuned universe.Paul C. W. Davies, Other Worlds, chapters 8 & 9 The Anthropic Principle & Is the Universe an accident?, (1980) .Paul C. W. Davies, The Accidental Universe, (1982) .
MWI depends crucially on the linearity of quantum mechanics, which underpins the superposition principle. If the final theory of everything is non-linear with respect to wave functions, then many-worlds is invalid. All quantum field theories are linear and compatible with the MWI, a point Everett emphasized as a motivation for the MWI. While quantum gravity or string theory may be non-linear in this respect, there is as yet no evidence of this.Steven Weinberg, Dreams of a Final Theory: The Search for the Fundamental Laws of Nature (1993), , pp. 68–69.Steven Weinberg. Testing Quantum Mechanics, Annals of Physics Vol. 194, #2 (1989), pp. 336–386.
Weingarten and Taylor & McCulloch have made separate proposals for how to define wave function branches in terms of quantum circuit complexity.
Alternative to wave function collapse