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Interpretation of quantum mechanics

The many worlds interpretation (MWI) is a philosophical position about how the mathematics used in quantum mechanics relates to physical reality. It asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe. In contrast to some other interpretations, the evolution of reality as a whole in MWI is rigidly deterministic Many worlds is also called the relative state formulation or the Everett interpretation, after physicist Hugh Everett, who first proposed it in 1957. Bryce DeWitt popularized the formulation and named it many worlds in the 1970s. In modern versions of many worlds, the subjective appearance of wave function collapse is explained by the mechanism of quantum decoherence. 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. It is one of a number of multiverse hypotheses in physics and philosophy. MWI views time as a many branched tree, wherein every possible quantum outcome is realized. This is intended to resolve the measurement problem and thus some paradoxes of quantum theory, such as Wigner's friend, Zurek emphasizes that his work does not depend on a particular interpretation.

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. MWI is a realist, deterministic and 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 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 wavefunctions, then many worlds is invalid.

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) pass through the double slit, a calculation assuming wavelike behavior of light can be used to identify where the particles are likely to be observed. Yet when the particles are observed in this experiment, they appear as particles (i. e., at definite places) and not as non localized waves. Some versions of the Copenhagen interpretation of quantum mechanics proposed a process of "collapse" in which an indeterminate quantum system would probabilistically collapse onto, or select, just one determinate outcome to "explain" this phenomenon of observation. Wave function collapse was widely regarded as artificial and ad hoc, so an alternative interpretation in which the behavior of measurement could be understood from more fundamental physical principles was considered desirable. Everett's PhD work provided such an interpretation. He argued that for a composite system—such as a subject (the "observer" or measuring apparatus) observing an object (the "observed" system, such as a particle)—the claim that either the observer or the observed has a well defined state is meaningless; in modern parlance, the observer and the observed have become entangled: we can only specify the state of one relative to the other, i. e., the state of the observer and the observed are correlated after the observation is made. This led Everett to derive from the unitary, deterministic dynamics alone (i. e., without assuming wave function collapse) the notion of a relativity of states. Everett noticed that the unitary, deterministic dynamics alone entailed that after an observation is made each element of the quantum superposition of the combined subject–object wave function contains two "relative states": a "collapsed" object state and an associated observer who has observed the same collapsed outcome; what the observer sees and the state of the object have become correlated by the act of measurement or observation. The subsequent evolution of each pair of relative subject–object states proceeds with complete indifference as to the presence or absence of the other elements, as if wave function collapse has occurred, Since the wave function appears to have collapsed then, Everett reasoned, there was no need to actually assume that it had collapsed. And so, invoking Occam's razor, he removed the postulate of wave function collapse from the theory. It consists of an experimenter (Wigner's friend) making a measurement on a quantum system in an isolated laboratory, and another experimenter (Wigner) who would make a measurement on the first one. According to the many worlds theory, the first experimenter would end up in a macroscopic superposition of seeing one result of the measurement in one branch, and another result in another branch. The second experimenter could then interfere these two branches in order to test whether it is in fact in a macroscopic superposition or has collapsed into a single branch, as predicted by the Copenhagen interpretation. Since then Lockwood, Vaidman, and others have made similar proposals, which require placing macroscopic objects in a coherent superposition and interfering them, a task currently beyond experimental capability.

Since the many worlds interpretation's inception, physicists have been puzzled about the role of probability in it. As put by Wallace, there are two facets to the question: Since then several other derivations of the Born rule in the many worlds framework have been proposed. There is no consensus on whether this has been successful.

DeWitt and Graham among others, have proposed derivations of the Born rule based on a frequentist interpretation of probability. They try to show that in the limit of uncountably many measurements, no worlds would have relative frequencies that didn't match the probabilities given by the Born rule, but these derivations have been shown to be mathematically incorrect.

A decision theoretic derivation of the Born rule was produced by David Deutsch (1999) and refined by Wallace and Saunders. They consider an agent who takes part in a quantum gamble: the agent makes a measurement on a quantum system, branches as a consequence, and each of the agent's future selves receives a reward that depends on the measurement result. The agent uses decision theory to evaluate the price they would pay to take part in such a gamble, and concludes that the price is given by the utility of the rewards weighted according to the Born rule. Some reviews have been positive, although these arguments remain highly controversial; some theoretical physicists have taken them as supporting the case for parallel universes. For example, a New Scientist story on a 2007 conference about Everettian interpretations quoted physicist Andy Albrecht as saying, "This work will go down as one of the most important developments in the history of science."

In 2005, Zurek produced a derivation of the Born rule based on the symmetries of entangled states; Schlosshauer and Fine argue that Zurek's derivation is not rigorous, as it does not define what probability is and has several unstated assumptions about how it should behave. In 2016, Charles Sebens and Sean M. Carroll, building on work by Lev Vaidman, proposed a similar approach based on self locating uncertainty. In this approach, decoherence creates multiple identical copies of observers, who can assign credences to being on different branches using the Born rule. The Sebens–Carroll approach has been criticized by Adrian Kent, and Vaidman does not find it satisfactory.

In 2021, Simon Saunders produced a branch counting derivation of the Born rule. The crucial feature of this approach is to define the branches so that they all have the same magnitude or 2 norm. The ratios of the numbers of branches thus defined give the probabilities of the various outcomes of a measurement, in accordance with the Born rule.

As originally formulated by Everett and DeWitt, the many worlds interpretation had a privileged role for measurements: they determined which basis of a quantum system would give rise to the eponymous worlds. Without this the theory was ambiguous, as a quantum state can equally well be described (e. g.) as having a well defined position or as being a superposition of two delocalized states. The assumption is that the preferred basis to use is the one which assigns a unique measurement outcome to each world. This special role for measurements is problematic for the theory, as it contradicts Everett and DeWitt's goal of having a reductionist theory and undermines their criticism of the ill defined measurement postulate of the Copenhagen interpretation. by incorporating decoherence into the many worlds theory. In this approach, the preferred basis does not have to be postulated, but rather is identified as the basis stable under environmental decoherence. In this way measurements no longer play a special role; rather, any interaction that causes decoherence causes the world to split. Since decoherence is never complete, there will always remain some infinitesimal overlap between two worlds, making it arbitrary whether a pair of worlds has split or not. Wallace argues that this is not problematic: it only shows that worlds are not a part of the fundamental ontology, but rather of the emergent ontology, where these approximate, effective descriptions are routine in the physical sciences. Since in this approach the worlds are derived, it follows that they must be present in any other interpretation of quantum mechanics that does not have a collapse mechanism, such as Bohmian mechanics. This approach to deriving the preferred basis has been criticized as creating circularity with derivations of probability in the many worlds interpretation, as decoherence theory depends on probability and probability depends on the ontology derived from decoherence. Wallace contends that decoherence theory depends not on probability but only on the notion that one is allowed to do approximations in physics. Everett originally called his approach the "Correlation Interpretation", where "correlation" refers to quantum entanglement). The phrase "many worlds" is due to Bryce DeWitt, Schrödinger's writings from the period also contain elements resembling the modal interpretation originated by Bas van Fraassen. Because Schrödinger subscribed to a kind of post Machian neutral monism, in which "matter" and "mind" are only different aspects or arrangements of the same common elements, treating the wave function as physical and treating it as information became interchangeable. Leon Cooper and Deborah Van Vechten developed a very similar approach before reading Everett's work. Zeh also came to the same conclusions as Everett before reading his work, then built a new theory of quantum decoherence based on these ideas. According to people who knew him, Everett believed in the literal reality of the other quantum worlds. His son and wife reported that he "never wavered in his belief over his many worlds theory". In their detailed review of Everett's work, Osnaghi, Freitas, and Freire Jr. note that Everett consistently used quotes around "real" to indicate a meaning within scientific practice.

One of MWI's strongest longtime advocates is David Deutsch. According to him, the single photon interference pattern observed in the double slit experiment can be explained by interference of photons in multiple universes. Viewed this way, the single photon interference experiment is indistinguishable from the multiple photon interference experiment. In a more practical vein, in one of the earliest papers on quantum computing, Deutsch suggested that parallelism that results from MWI could lead to "a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it". He also proposed that MWI will be testable (at least against "naive" Copenhagenism) when reversible computers become conscious via the reversible observation of spin.

Philosophers of science James Ladyman and Don Ross say that MWI could be true, but do not embrace it. They note that no quantum theory is yet empirically adequate for describing all of reality, given its lack of unification with general relativity, and so do not see a reason to regard any interpretation of quantum mechanics as the final word in metaphysics. They also suggest that the multiple branches may be an artifact of incomplete descriptions and of using quantum mechanics to represent the states of macroscopic objects. They argue that macroscopic objects are significantly different from microscopic objects in not being isolated from the environment, and that using quantum formalism to describe them lacks explanatory and descriptive power and accuracy.

Some scientists consider some aspects of MWI to be unfalsifiable and hence unscientific because the multiple parallel universes are non communicating, in the sense that no information can be passed between them. Victor J. Stenger remarked that Murray Gell Mann's published work explicitly rejects the existence of simultaneous parallel universes. Collaborating with James Hartle, Gell Mann worked toward the development a more "palatable" post Everett quantum mechanics. Stenger thought it fair to say that most physicists find MWI too extreme, though it "has merit in finding a place for the observer inside the system being analyzed and doing away with the troublesome notion of wave function collapse". efn|"Gell Mann and Hartle, along with a score of others, have been working to develop a more palatable interpretation of quantum mechanics that is free of the problems that plague all the interpretations we have considered so far. This new interpretation is called, in its various incarnations, post Everett quantum mechanics, alternate histories, consistent histories, or decoherent histories. I will not be overly concerned with the detailed differences between these characterizations and will use the terms more or less interchangeably." According to Penrose, "the rules must change when gravity is involved". He further asserts that gravity helps anchor reality and "blurry" events have only one allowable outcome: "electrons, atoms, molecules, etc., are so minute that they require almost no amount of energy to maintain their gravity, and therefore their overlapping states. They can stay in that state forever, as described in standard quantum theory". On the other hand, "in the case of large objects, the duplicate states disappear in an instant due to the fact that these objects create a large gravitational field". Philosopher of science Robert P. Crease says that MWI is "one of the most implausible and unrealistic ideas in the history of science" because it means that everything conceivable happens. Asher Peres was an outspoken critic of MWI. A section of his 1993 textbook had the title Everett's interpretation and other bizarre theories. Peres argued that the various many worlds interpretations merely shift the arbitrariness or vagueness of the collapse postulate to the question of when "worlds" can be regarded as separate, and that no objective criterion for that separation can actually be formulated.

A poll of 72 "leading quantum cosmologists and other quantum field theorists" conducted before 1991 by L. David Raub showed 58% agreement with "Yes, I think MWI is true". Max Tegmark reports the result of a "highly unscientific" poll taken at a 1997 quantum mechanics workshop. According to Tegmark, "The many worlds interpretation (MWI) scored second, comfortably ahead of the consistent histories and Bohm interpretations." In response to Sean M. Carroll's statement "As crazy as it sounds, most working physicists buy into the many worlds theory", Michael Nielsen counters: "at a quantum computing conference at Cambridge in 1998, a many worlder surveyed the audience of approximately 200 people Many worlds did just fine, garnering support on a level comparable to, but somewhat below, Copenhagen and decoherence." But Nielsen notes that it seemed most attendees found it to be a waste of time: Peres "got a huge and sustained round of applause when he got up at the end of the polling and asked 'And who here believes the laws of physics are decided by a democratic vote? A 2005 poll of fewer than 40 students and researchers taken after a course on the Interpretation of Quantum Mechanics at the Institute for Quantum Computing University of Waterloo found "Many Worlds (and decoherence)" to be the least favored. A 2011 poll of 33 participants at an Austrian conference found 6 endorsed MWI, 8 "Information based/information theoretical", and 14 Copenhagen; the authors remark that MWI received a similar percentage of votes as in Tegmark's 1997 poll. David Deutsch speculates in his book The Beginning of Infinity that some fiction, such as alternate history, could occur somewhere in the multiverse, as long as it is consistent with the laws of physics. According to Ladyman and Ross, many seemingly physically plausible but unrealized possibilities, such as those discussed in other scientific fields, generally have no counterparts in other branches, because they are in fact incompatible with the universal wave function. Most experts believe the experiment would not work in the real world, because the world with the surviving experimenter has a lower "measure" than the world before the experiment, making it less likely that the experimenter will experience their survival.