Many-worlds interpretation
The many-worlds interpretation (English many- worlds interpretation or MWI, German abbreviation also VWI) is in physics an interpretation of quantum mechanics, which goes back to Hugh Everett III. It is now next to the traditional Copenhagen interpretation as the most popular interpretation of quantum mechanics. The many-worlds interpretation is also known as the Everett interpretation, frequent stories interpretation, EEC interpretation ( Everett, John Archibald Wheeler and R. Neil Graham) or many-worlds theory, the VWI however, as well as most other interpretation is not an alternative theory, in the experiment because it is not different from the conventional quantum mechanics.
Everett developed in 1957 to approach this interpretation of the observation relative quantum mechanical states. He was anxious to avoid the collapse of the wave function, which had resulted in the Copenhagen interpretation repeatedly to criticism, and thus should be given an unrestricted as possible validity of the Schrödinger equation. Your name goes back to the U.S. physicist Bryce DeWitt, who first suggested to interpret the different states of the quantum system after a measurement as worlds.
Motivation and basic concepts
The Copenhagen interpretation was to Everett times than the prevailing dogma. However, many physicists saw a contradiction between the deterministic time evolution of a quantum physical state after the continuous Schrödinger equation and the demand for a probabilistic and instantaneous collapse of the wave function at the moment of measurement ( see also postulates of quantum mechanics). Thus, the Copenhagen interpretation sees two complementary dynamics: first, the reversible and deterministic evolution of the state in an unobserved system, on the other hand, a sudden, irreversible and non-local change of state in a measurement. The founder of the Copenhagen interpretation justified this with the necessity of classical concepts, which makes a subdivision of the overall system in classical and quantum field inescapable: Only when a measurement result with classical concepts is writable, the measurement result as a clear and irreversible event occurring ( fact ) can apply.
Everett's motivation was primarily to derive the collapse postulate and the probability interpretation of the other axioms. He aimed at a simplification of the axiomatic theory of quantum mechanics. He would thereby also be a possibility of internal application of quantum mechanics, so an application of the formalism to a purely quantum mechanical system. This is in the Copenhagen interpretation is not possible due to the division into classical and quantum mechanical areas. This question was especially for the development of a consistent theory of quantum gravity is of great interest. An often -cited example of such an internal application is the formulation of a wave function of the universe, ie the description of a purely quantum mechanical universe with no outside observer.
In his original article Relative State Formulation of Quantum Mechanics 1957 Everett aims to reconstruct the quantum mechanics only on the deterministic evolution of a state according to the Schrödinger equation, so he waived a collapse postulate and attempt to describe the measurement process only using the Schrödinger equation. He attaches importance to the fact that the wave function plays no a priori interpretation, this must only be obtained from the correspondence with the experience. The frame of interpretation was, however, determined by the theory. Everett points out that a description of the observer within the framework of the theory is necessary.
Everett first developed the concept of relative states of composite systems: If it comes to interactions between parts of the system, the states of these parts are no longer independent but are correlated to a certain way. From this perspective, he also deals with the measurement on a quantum system. The observer defines Everett thereby by any object with the ability to remember the result of the measurement. This means that changes the state of the observer by the result of the measurement. The measurement is thus merely treated as a special kind of interaction between two quantum systems. It is thus, unlike in many other interpretations, not honored by the axioms ago.
By analyzing the relative states of the observer to the observed system formally in terms of the dynamic development of the Schrödinger equation, Everett is able to reproduce some of the axioms of the Copenhagen interpretation, but without a collapse of the wave function. Instead, the wave function branched into different sections, which have each other no coherence, no longer able to interact with each other. These branches are what Bryce DeWitt later than the eponymous many worlds referred to the many worlds but not spatially separate worlds, but separated states in the relevant state space are. Everett himself talked at first only of relative states, his interpretation he called Correlation interpretation, he understood it as a meta-theory to quantum mechanics.
Reception
Under the guidance of his doctor father John Archibald Wheeler Everett published a shortened version of his dissertation (The Theory of the Universal Wave Function) under the title ' Relative State ' Formulation of Quantum Mechanics in the journal Reviews of Modern Physics. It was preceded by, among others, talks with one of the founders of the Copenhagen interpretation, Niels Bohr, dismissive of Everett's work remarked. Then pounded Wheeler, even students of drilling on a new version, which shortened especially the sharp criticism Everett on the Copenhagen interpretation. Although most of the leading physicists was known Everett's work, his formulation was virtually ignored in the next decade. Frustrated and misunderstood to Everett finally withdrew from physics and devoted himself to the military and political advice to the Pentagon on issues of nuclear use.
In 1970 the American physicist Bryce DeWitt published in Physics Today an essay titled Quantum mechanics and reality, which conceived the Everett'sche interpretation and re- presented for discussion. In this paper, he also introduced the term Many- Worlds Interpretation. In subsequent years, the many-worlds interpretation gained greatly in popularity, due to the development of Dekohärenztheorie. This also starts from a far-reaching as possible validity of the Schrödinger equation, which is contrary to the concept of the Copenhagen interpretation.
In the field of quantum cosmology and quantum gravity, the Everett'sche approach a growing popular was because it was the only interpretation to date in which it was at all meaningful to speak of a quantum universe. The idea of the universal wave function has also been taken up by a number of physicists and developed, among other Wheeler and DeWitt in the development of the Wheeler - DeWitt equation of quantum gravity, and James Hartle and Stephen W. Hawking ( Hartle - Hawking boundary condition for a universal wave function ). The many-worlds interpretation has evolved from a niche to a popular interpretation to its basic approach to many of the leading physicists of the late 20th century known (among Murray Gell-Mann, Stephen W. Hawking, Steven Weinberg ). The concept of many-worlds interpretation has also tried to develop, resulting, for example, was the consistent- histories interpretation that tried the basic concept of Everett's approach, the universality of the Schrödinger equation to continue, but without the existence of many worlds.
Today, the many-worlds interpretation is in addition to the traditional Copenhagen interpretation, the most popular interpretation of quantum mechanics. There are many representatives, particularly in the area of quantum cosmology and developed in the 80s and 90s quantum information. Among the most popular advocates of the many-worlds interpretation currently include the Israeli physicist David German and the German physicist Dieter Zeh, one of the founders of the Dekohärenztheorie. Resistance comes mainly from physicists, who only see quantum mechanics as a practical computation at the microscopic level and the fundamental incomprehensibility of quantum mechanics emphasize ( "Shut -up-and -calculate "). A well-known representatives of this position is the German Nobel Laureate Theodor Hänsch.
Formal access
Basic considerations
The many-worlds interpretation relates primarily to a postulate:
- Every isolated system evolves according to the Schrödinger equation
In particular, with the omission of the reduction of the state vector resulting from this postulate two important conclusions:
An important advantage of the VWI is thus, in contrast to the Copenhagen interpretation a priori that it knows no distinction between classical and quantum states. This arises only from the calculation of Dekohärenzzeiten; at a very small decoherence time, a system can be regarded as quasi-classical. However, a purely formal is in the VWI each system first a quantum system.
Relative states
Everett developed his approach first of a concept of relative states, which he introduced as follows:
A complete system consists of two subsystems and the Hilbert space of the total system is the tensor product of Hilbert spaces of the two subsystems. is in a pure state, then there exists for every state of a relative state of. Thus, the state of the entire system can be as
Write, where and bases of the subsystems are. For arbitrary can now be a relative state with respect to the overall system design as follows:
Being a normalization constant. This state of the system is independent of the choice of the base. It also applies:
Thus, it is obviously pointless to assign certain subsystems (independent) states. It is only possible to assign a subsystem a relative state with respect to a certain state of the other subsystem, the states of the sub-systems are thus correlated, it follows a fundamental relativity of states when viewing the composite systems.
Simple composite systems are for example entangled systems as experiments on the violation of Bell 's inequality: In this case, both spin components are used as the base in question, it is only possible to make a meaningful statement about the status of a subsystem, if the state of the other system is established. Thus, it is not sensible to speak of an absolute separation of the state of the overall system by states of the two subsystems, only a relative decomposition with respect to a certain state of the two subsystems.
The observation process
The observer with the above-mentioned properties is described by a state vector, said the events, which so far has registered the observer.
Everett examined several cases of observations. In this case, the quantum system under investigation can always be described by the state. The states of the observer are in the process classically distinguishable on various metrics, there is no coherence between individual states of the observer.
Everett now considered first multiple observations of a system:
Join the observer once the result, the measurement will always yield the same result, and a repetition of the experiment on the same system leads to the same result. Analogous considerations show that performing the same measurement at different, identically prepared systems, in general, to different measurement results leads and that several observers also measure always the same on the same system.
The next goal is now to assign a sequence of measurements, a measure which represents the probability of observing a particular sequence for an observer within the system. These Everett initially regarded a superposition of orthonormal states which by
Is given, which is supposed to be already normalized. This is directly seen that applies. Now called Everett, that the measure of the state which can only depend on the sum of the measurements is, therefore the following applies:
This equation has the only solution therefore has a chain of events of the above Form of the measure
This is factored so can be regarded as the probability of the event that corresponds to the Born rule.
There are other derivations of the Born rule from the reduced set of axioms that are known, inter alia, of German and Hartle.
Example
As an example, a double-slit experiment with a single particle (e.g., an electron ) can be used. An observer measures the process by which hole the particle is gone. The system double-slit observer is approximately isolated. The particle may be registered at slit 1 or slit 2, these are the ( orthogonal ) states and. Furthermore, the observer is betting a sum of money that the particle is registered with gap 1, his expectations will therefore transform in the measurement in joy or disappointment.
Now a unitary time evolution operator can be defined according to the Schrödinger equation. This must take the form accordingly. Based on the experiment, the following requirements apply to the operator:
- ( The observer is happy when the particle is registered with gap 1. )
- ( The observer is disappointed when the particle is registered with gap 2. )
Before the measurement, the particle is in a superposition of two states, the observer is located in expectation, the state of the entire system is so. The measurement is now carried out, this is described mathematically by the operator is applied to the state of the overall system:
So the result is a superposition of the composite system particles at a double slit and observers. This is obviously no clear result, instead there is a superposition of the two possible outcomes. This result is interpreted in the VWI so that at the moment of measurement branches the universe and the two mathematically required results are achieved in different worlds. This is consistent because the lucky observer formally has no way to interact with the unfortunate observers: the two states are related to each other in configuration space completely orthogonal, thus is excluded by the mathematical structure of this result, any interaction.
Based on this example can also be another important fact to be illustrated: There is not one splitting induced by the formalism at any point instead. The branching takes place is completely described by the dynamics of the states of the observer and the system, so it is no more independent postulate. This means that the measurement process in the VWI has no special significance - it is simply treated as a subclass of ordinary interactions.
Criticism
Probably the best known and most common criticism of the VWI is its ontology: She is accused of, the principle of simplicity to hurt ( Occam's razor ), since although they predict the existence of a myriad of different worlds, but itself provides the proof that these are not are observable. Representatives of the VWI keep countered that the many worlds are not an independent postulate, but follow from the universality of the Schrödinger equation. This shortens and simplifies the axioms of quantum mechanics, according to which " preferred " Occam's Razor, the VWI before the Copenhagen interpretation.
An often highlighted by critics problem of many-worlds interpretation is the question of how they can explain the randomness of quantum events. According to the VWI, each result is actually realized in a measurement. This raises the question of whether it makes sense to speak of a probability, if it does actually happen all the results. Critics emphasize that the VWI a " supernatural observer " would require to make the probability interpretation of measurements at all plausible. Even then, the experiences of real observers would not explain. Representatives of the VWI rap here on a strict distinction between external and internal perspective and argue that for an observer from the internal perspective an event despite the deterministic evolution of a state according to the Schrödinger equation can act randomly.
One also frequently expressed criticism of the VWI is the so- called basic problem ( " problem of preferred basis "). Since the formalism of the axioms ago does not specify a preferred basis, there are apart from the splitting intuitively selected in the classical basis states always endless possibilities for the splitting of a quantum state in different worlds. 1998 succeeded, however, Wojciech Zurek to show with methods of Dekohärenztheorie that classical mathematical bases are preferred in the structure of the Hamiltonian and the value of Plank 's constant, in that they are stable over a longer period. This means that the objects in those states exist long enough to be perceived by the quasi-classical measuring instruments. Various physicists also point out that the question of the preferred base or the fact that one perceives well-defined objects in classical, macroscopic states, probably also related to the evolution of man in the universe.
Carl Friedrich von Weizsäcker points out that there is no appreciable difference between the VWI and the Copenhagen interpretation in the context of a modal logic of temporal statements there, if purely semantic " real world " would be replaced by " possible worlds ": the many worlds describe by the Inger Schröder equation evolving space of possibilities; by a real observer observation made is the realization of one of the formally possible worlds. V. Weizsäcker acknowledges that the approach Everett'sche the only one among the usual alternatives is that " not back, but forward also aims behind the achieved already by the quantum theory understanding of them." Everett is, however, remained "conservative" in the equation of reality and factuality. His real - philosophical - objection to the VWI is that the existence of a set of events ( "worlds" ) would be asked, "that could not be phenomena ". Quantum physics is but just inferred from the attempt to describe and predict phenomena consistent.