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The many-worlds interpretation (or MWI) is an Interpretation Of Quantum Mechanics that rejects the Non-deterministic and Irreversible Wavefunction Collapse associated with Measurement in the Copenhagen Interpretation in favor of the conventional Deterministic and Time-reversible laws of Quantum Physics . The phenomena associated with measurement are explained by Decoherence which occurs when a quantum mechanical system interacts with its environment. MWI reconciles how we perceive non-deterministic events (such as the random decay of a radioactive atom) with the deterministic Equations of quantum physics. An implication of this reconcillation between determinism and non-determinism is that the universe is much larger than we would otherwise think, and that the world we see (including ourselves) is continuously branching into a greater and greater number of divergent copies. History, which prior to MWI had been viewed as a single "world-line", is rather a many-branched tree. Many worlds is also sometimes referred as a Theory , rather than just an interpretation, since it is argued that many worlds can make testable predictions, or that the other non-MWI interpretations are inconsistent, illogical or unscientific in their handling of measurements. Hugh Everett , MWI's originator, argued that his proposal was a Metatheory , since it made statements about other interpretations of quantum theory. OUTLINE Although several versions of MWI have been proposed since or some relativistic Quantum Field Theory or String Theory equivalent, does not alter the content of MWI, and in particular the conclusion that the universe (or Multiverse in this context) is a Quantum Superposition of several, possibly Infinite ly many, states of increasingly divergent, non-communicating parallel universes or quantum worlds. The ideas of MWI originated in Hugh Everett 's Princeton Ph. D. thesis, developed under his thesis advisor John Wheeler , but the phrase "many worlds" is due to Bryce DeWitt , who wrote more on the topic of Everett's original work. DeWitt's formulation has become so popular that many confuse it with Everett's original work. MWI is one of many Multiverse hypotheses in Physics and Philosophy . It is currently considered a mainstream interpretation along with the Copenhagen and Consistent Histories interpretations. MANY WORLDS AND THE PROBLEM OF INTERPRETATION 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 in this experiment, they appear as particles and not as non-localized waves. The Copenhagen Interpretation of quantum mechanics proposed a process of " Collapse " from wave behavior to particle-like behavior to explain this phenomenon of observation. By the time John Von Neumann wrote his famous treatise ''Mathematische Grundlagen der Quantenmechanik'' in 1932 , the phenomenon of "wavefunction collapse" was accommodated into the Mathematical Formulation Of Quantum Mechanics by postulating that there were two processes of wavefunction change: # The discontinuous Probabilistic change brought about by observation and Measurement . # The Deterministic Time Evolution of an isolated system that obeys Schrödinger's Equation . The phenomenon of wavefunction collapse for (1) 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 more fundamental physical principles was considered desirable. Everett's Ph. D. work was intended to provide such an alternative interpretation. Everett proposed that for a composite system (for example that formed by a particle interacting with a measuring apparatus) the statement that a subsystem has a well-defined state is meaningless. This led Everett to derive from the dynamics the notion of a ''relativity of states'' of one subsystem relative to another. Everett's formalism for understanding the process of wavefunction collapse as a result of observation is mathematically equivalent to a quantum superposition of wavefunctions; each element of the superpositon after an observation contains an observer whose relative state contain an associated collapsed object state. Since Everett stopped doing research in theoretical physics shortly after obtaining his Ph. D., much of the elaboration of his ideas was carried out by other researchers. BRIEF OVERVIEW In Everett's formulation, a measuring apparatus M and an object system '''S''' form a composite system, each of which prior to measurement exists in well-defined (but time-dependent) states. Measurement is regarded as causing M and '''S''' to interact. After '''S''' interacts with M, it is no longer possible to describe either system by an independent state. According to Everett, the only meaningful descriptions of each system 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'''. systems.]] In DeWitt's formulation, the state of '''S''' after a sequence of measurements is given by a quantum superposition of states, each one corresponding to an alternative measurement history of '''S'''. For example, consider the smallest possible truly quantum system S, as shown in the illustration. This describes for instance, the spin-state of an electron. Considering a specific axis (say the ''z''-axis) the north pole represents spin "up" and the south pole, spin "down". The superposition states of the system are described by (the surface of) a sphere called the Bloch Sphere . To perform a measurement on S, it is made to interact with another similar system '''M'''. After the interaction, the combined system is described by a state that ranges over a six-dimensional space (the reason for the number six is explained in the article on the Bloch sphere). This six-dimensional object can also be regarded as a quantum superposition of two "alternative histories" of the original system S, one in which "up" was observed and the other in which "down" was observed. Each subsequent binary measurement (that is interaction with a system '''M''') causes a similar split in the history tree. Thus after three measurements, the system can be regarded as a quantum superposition of 8= 2 × 2 × 2 copies of the original system S. The accepted terminology is somewhat misleading because it is incorrect to regard the universe as splitting at certain times; at any given instant there is one state in one universe. RELATIVE STATE 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 similar formalisms in the literature. One such idea is discussed in the next section. From the relative-state formalism, 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. 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 tree as shown in the graphic below. Subsequently DeWitt introduced the term "world" to describe a complete measurement history 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 idea of a space of complete alternative histories had already been used in the theory of probability since the mid 1930s for instance to model Brownian Motion . Under the many-worlds interpretation, the Schrödinger Equation holds all the time everywhere. An observation or measurement of an object by an observer is modeled by applying the Schrödinger wave equation to the entire system comprising the observer ''and'' the object. One consequence is that every observation can be thought of as causing the universal wavefunction to change into a quantum superposition of 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 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. COMPARATIVE PROPERTIES AND EXPERIMENTAL SUPPORT One of the salient properties of the many-worlds interpretation is that observation does not require an exceptional construct (such as wave function collapse) to explain it. Many physicists, however, dislike the implication that there are infinitely many non-observable alternate universes. 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 area of research is devising experiments which could distinguish between various interpretations of quantum mechanics, although there is some skepticism whether it is even meaningful to ask such a question. Indeed, it can be argued that there is a mathematical equivalence between Copenhagen (as expressed for instance in a set of algorithms for manipulating density states) and many-worlds (which gives the same answers as Copenhagen using a more elaborate mathematical picture) which would seem to make such an endeavor impossible. However, this algorithmic equivalence may not be true on a cosmological scale. It has been proposed that in a world with infinite alternate universes, the 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. In the Copenhagen interpretation, the mathematics of quantum mechanics allows one to predict Probabilities for the occurrence of various events. In the many-worlds interpretation, all these events occur simultaneously. What meaning should be given to these probability calculations? And why do we observe, in our history, that the events with a higher computed probability seem to have occurred more often? One answer to these questions is to say that there is a Probability Measure on the space of all possible universes, where a possible universe is a complete path in the tree of branching universes. This is indeed what the calculations give. Then we should expect to find ourselves in a universe with a relatively high probability rather than a relatively low probability: even though all outcomes of an experiment occur, they do not occur in an equal way. As an interpretation which (like other interpretations) is consistent with the equations, it is hard to find testable predictions of MWI. There is a rather more dramatic test than the one outlined above for people prepared to put their lives on the line: use a machine which kills them if a random quantum decay happens. If MWI is true, they will still be alive in the world where the decay didn't happen and would feel no interruption in their stream of conciousness. By repeating this process a number of times, their continued conciousness would be arbitrarily unlikely unless MWI was true, when they would be alive in all the worlds where the random decay was on their side. From their viewpoint they would be immune to this death process. Clearly, if MWI does not hold, they would be dead in the one world. Other people would generally just see them die and would not be able to benefit from the result of this experiment. 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. EVERETT'S MANY-WORLDS INTERPRETATION AND AXIOMATICS The existence of many worlds in superposition is not accomplished by introducing some new . (Such a superposition of consistent state combinations of different systems is called an Entangled State .) Hartle (1968) showed that in Everett's relative-state theory, Born's probability law |
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