# Many-worlds interpretation

The Many Worlds Interpretation ( VWI ; from English many-worlds interpretation , abbr .: MWI ) is an interpretation of quantum mechanics in physics . It originally goes back to the American physicist Hugh Everett III. and in its basic approach it clearly distinguishes itself from the traditional Copenhagen interpretation ( Bohr / Heisenberg ). Other names are Everett interpretation , EWG interpretation (Everett / Wheeler / Graham ), theory of the universal wave function , many-pasts interpretation , many-worlds theory or simply many-worlds . Even today there is still a great deal of interest in this interpretation and also different views as to how its relation to reality is to be understood.

Everett postulated “relative” quantum mechanical states in 1957 . The US physicist Bryce DeWitt then spread this approach in the 1960s and 1970s under many worlds and used it to describe the different possible states of the quantum system after a measurement. The VWI does not contain a collapse of the wave function and explains its subjective appearance with the mechanism of quantum decoherence , which resolves the physical paradoxes of quantum theory, such as the EPR paradox and the Schrödinger's cat paradox , since every possible outcome of every event is in its own "past" or "world" is defined and actually exists.

## Motivation and basic concepts

The Copenhagen interpretation was the predominant doctrine in Everett's time. However, many physicists saw a contradiction between the deterministic time development of a quantum physical state according to the continuous Schrödinger equation and the requirement for a probabilistic and instantaneous collapse of the wave function at the moment of a measurement (see also postulates of quantum mechanics ). The Copenhagen interpretation sees two complementary dynamics: On the one hand, the reversible and deterministic development of the state in an unobserved system, and on the other hand, a sudden, irreversible and non-local change in the state during a measurement. The founders of the Copenhagen interpretation justified this with the need for classical terms, which makes a subdivision of the overall system into classical and quantum mechanical areas inevitable: only if a measurement result can be described with classical terms, the measurement result can be considered a clear and irreversible event (fact) .

Everett's motivation was primarily to derive the collapse postulate and the probability interpretation from the other axioms . His aim was to simplify the axiomatics of quantum mechanics. He also wanted to give a possibility of internal application of quantum mechanics, i.e. an application of the formalism to a purely quantum mechanical system. This is not possible in the Copenhagen interpretation due to the subdivision into classical and quantum mechanical areas. This question was of particular interest for the development of a consistent theory of quantum gravity . An often cited example of such an internal application is the formulation of a wave function of the universe, i.e. the description of a purely quantum mechanical universe without an outside observer.

In his original article Relative State Formulation of Quantum Mechanics from 1957, Everett aims to reconstruct quantum mechanics only from the deterministic development of a state according to the Schrödinger equation, so he dispenses with a collapse postulate and tries to describe the measurement process only using the Schrödinger equation . He attaches importance to the fact that the wave function does not have an a priori interpretation, this must first be obtained from the correspondence with experience. The framework of the interpretation is, however, determined by the theory. Everett emphasizes that a description of the observer is necessary within the framework of the theory.

Everett first developed the concept of the relative states of composite systems: If there are interactions between parts of the system, the states of these parts are no longer independent of one another, but are correlated in a certain way . From this point of view, he also deals with measurements on a quantum system. Everett defines the observer by any object with the ability to remember the result of the measurement. This means that the state of the observer changes as a result of the measurement. The measurement is therefore only treated as a special type of interaction between two quantum systems. In contrast to some other interpretations, it is thus not distinguished from the point of view of the axioms.

By formally analyzing the relative states of the observer to the observed system in terms of the dynamic development of the Schrödinger equation, Everett is able to reproduce some axioms of the Copenhagen interpretation, but without a collapse of the wave function. Instead, the wave function - including the observer - “branches” into different forms that are superimposed on one another and cannot interact with one another. It is these branches that Bryce DeWitt later calls the eponymous many worlds, although the many worlds are not spatially separated worlds, but separate states in the respective state space . Everett himself spoke of relative states; he originally referred to his interpretation as Correlation Interpretation and then as Relative State Formulation . He understood this as a metatheory for quantum mechanics.

## reception

Under the guidance of his PhD supervisor John Archibald Wheeler , Everett published an abbreviated version of his dissertation ( The Theory of the Universal Wave Function ) under the title 'Relative State' Formulation of Quantum Mechanics in Reviews of Modern Physics . This was preceded, among other things, by discussions with one of the founders of the Copenhagen interpretation, Niels Bohr , who expressed his disapproval of Everett's work. Then Wheeler, himself a student of Bohr, insisted on a new version that abbreviated Everett's harsh criticism of the Copenhagen interpretation. Although Everett's work was known to most of the leading physicists, his formulation was all but ignored for the next decade. Frustrated and misunderstood, Everett finally withdrew from physics and devoted himself to advising the Pentagon on military policy on nuclear issues.

In 1970, the American physicist Bryce DeWitt published an article in Physics Today entitled Quantum mechanics and reality , which took up Everett's interpretation and put it up for discussion. In this essay he also introduced the term many worlds interpretation . In the following years, the many-worlds interpretation grew in popularity, which is also due to the development of the theory of decoherence . This also assumes that the Schrödinger equation is as valid as possible, which runs counter to the concept of the Copenhagen interpretation.

Everett's approach was also enjoying growing popularity in the field of quantum cosmology and quantum gravity , as it was the only interpretation so far in which it made sense to speak of a quantum universe. The idea of ​​the universal wave function was also taken up and further developed by a number of physicists, including Wheeler and DeWitt in the development of the Wheeler-DeWitt equation for quantum gravity as well as James Hartle and Stephen W. Hawking (Hartle-Hawking boundary condition for a universal wave function ). The Many Worlds Interpretation evolved from a niche existence into a popular interpretation, the basic approach of which was known by many of the leading physicists of the late 20th century (including Murray Gell-Mann , Stephen W. Hawking, Steven Weinberg ). Attempts have also been made to further develop the concept of the many-worlds interpretation. This gave rise to the consistent histories interpretation , for example , which attempted to continue the basic concept of Everett's approach, the universal validity of the Schrödinger equation, but without the existence of many worlds.

In addition to the traditional Copenhagen interpretation, there is still strong interest in the many-worlds interpretation, although objections continue to be controversial. There are many proponents, especially in the field of quantum cosmology and the quantum information developed in the 1980s and 1990s . The best-known proponents of the many-worlds interpretation are currently the Israeli physicist David Deutsch and the German physicist Dieter Zeh , one of the founders of the decoherence theory. According to Zeh, from an empirical point of view, one advantage of the VWI is that it can plausibly explain the a priori very unlikely "fine-tuning" of the natural constants that made life in the universe possible without having to resort to a strong, targeted anthropic principle , reminiscent of the plan of an intelligent creator god and thus colored religious and not scientific ( intelligent design ). According to the VWI, the fact that our branch of the multiverse made intelligent life possible despite the extremely low probability is simply due to the fact that no intelligent living beings exist in the countless other branches of the Everettian multiverse that do not meet these requirements. who can even ask this question. So we live in a life-friendly world because we could not have developed in the many hostile worlds that also exist (weak anthropic principle).

Resistance to the VWI comes mainly from physicists who see quantum mechanics only as a calculation guide in the microscopic area and who emphasize the fundamental incomprehensibility of quantum mechanics (“ shut-up and calculate ”). A well-known representative of this position is the German Nobel Prize winner Theodor Hänsch .

## Formal access

### Basic remarks

The many-worlds interpretation essentially refers to one postulate:

Every isolated system develops according to the Schrödinger equation  ${\ displaystyle \ mathrm {i} \ hbar {\ frac {\ partial} {\ partial t}} | \ psi \ rangle = {\ hat {H}} | \ psi \ rangle \ ,.}$

With the omission of the reduction of the state vector in particular, two important conclusions result from this postulate:

1. Since the universe as a whole is by definition an isolated system, this also develops according to the Schrödinger equation.
2. Measurements cannot have clear results. Instead, the different measurement results are also implemented in different branches of reality (“worlds”) (see example).

An important advantage of the VWI is that, in contrast to the Copenhagen interpretation, it does not distinguish a priori between classical and quantum mechanical states. This only results from the calculation of decoherence times; if the decoherence time is very short, a system can be regarded as quasi-classical . In purely formal terms, however, every system at VWI is initially a quantum system.

### Relative states

Everett first developed his approach from a concept of relative states, which he introduced as follows:

An overall system consists of two subsystems and the Hilbert space of the overall system is the tensor product of the Hilbert spaces of the two subsystems. be in a pure state , then for every state of there is a relative state of . The state of the overall system can thus be viewed as ${\ displaystyle S}$${\ displaystyle S_ {1}}$${\ displaystyle S_ {2}}$${\ displaystyle {\ mathcal {H}}}$${\ displaystyle S}$ ${\ displaystyle | \ Psi \ rangle}$${\ displaystyle | X \ rangle}$${\ displaystyle S_ {1}}$${\ displaystyle | Y \ rangle}$${\ displaystyle S_ {2}}$

${\ displaystyle | \ Psi \ rangle = \ sum _ {i, j} \ alpha _ {ij} | X_ {i} \ rangle | Y_ {j} \ rangle}$

write, where and are bases of the subsystems. A relative state in relation to the overall system can now be constructed as follows for any : ${\ displaystyle | X_ {i} \ rangle}$${\ displaystyle | Y_ {j} \ rangle}$ ${\ displaystyle | X_ {k} \ rangle}$

${\ displaystyle | \ Psi; X_ {k, \ mathrm {rel}} \ rangle = N_ {k} \ sum _ {j} \ alpha _ {kj} | Y_ {j} \ rangle}$,

where is a normalization constant. This state of the system is independent of the choice of base . It also applies: ${\ displaystyle N_ {k}}$${\ displaystyle \ {| X_ {k} \ rangle \}}$

${\ displaystyle | \ Psi \ rangle = \ sum _ {k} {\ frac {1} {N_ {k}}} | X_ {k} \ rangle | \ Psi; X_ {k, rel} \ rangle = \ sum _ {k} \ sum _ {j} \ alpha _ {kj} | X_ {k} \ rangle | Y_ {j} \ rangle}$

It is therefore obviously pointless to assign certain (independent) states to the subsystems. It is only possible to assign a relative status to a subsystem with respect to a certain status of the other subsystem. The states of the subsystems are thus correlated. From this follows a fundamental relativity of the states when considering composite systems.

Simple composite systems are, for example, entangled systems as in experiments to violate Bell's inequality : In this case, both spin components come into question as a basis. It is only possible to make a meaningful statement about the state of a subsystem when the state of the other system is certain. As a result, it does not make sense to speak of an absolute decomposition of the state of the overall system according to the states of the two subsystems, but only of a relative decomposition with regard to a specific state of the two subsystems.

### The observation process

The observer with the above Properties is described by a state vector , which are the events that the observer has registered so far. ${\ displaystyle \ Psi _ {[a, b, c, \ dots]} ^ {B}}$${\ displaystyle a, b, c, \ dots}$

Everett examined several cases of observation. The quantum system to be examined can always be described by the state . The states of the observer can be classically differentiated for different measurement data, there is no coherence between individual states of the observer. ${\ displaystyle \ sum _ {n} a_ {n} | S_ {n} \ rangle}$

Everett first looked at multiple observations of a system:

${\ displaystyle \ sum _ {n} a_ {n} | S_ {n} \ rangle \ otimes \ Psi _ {[\ dots]} ^ {B} \ longrightarrow \ sum _ {n} a_ {n} | S_ { n} \ rangle \ otimes \ Psi _ {[\ dots, S_ {n}]} ^ {B} \ longrightarrow \ sum _ {n} a_ {n} | S_ {n} \ rangle \ otimes \ Psi _ {[ \ dots, S_ {n}, S_ {n}]} ^ {B}}$

Once the observer registers the result , the measurement will always give the same result, so repeating the experiment on the same system leads to the same result. Analogous observations show that carrying out the same measurement on different, identically prepared systems generally leads to different measurement results and that several observers always measure the same thing on the same system. ${\ displaystyle S_ {n}}$

The next goal is to assign a measure to a sequence of measurements , which represents the probability of observing a certain sequence for an observer within the system. To this end, Everett first considered a superposition of orthonormal states that was carried out by ${\ displaystyle [S_ {n_ {1}} ^ {1}, S_ {n_ {2}} ^ {2}, \ dots, S_ {n_ {N}} ^ {N}]}$${\ displaystyle \ phi _ {i}}$

${\ displaystyle \ alpha \ phi '= \ sum _ {i} a_ {i} \ phi _ {i}}$

is given, whereby should already be normalized . It can thus be seen directly that applies. Everett now demanded that the measure of the state , which can only depend on, is equal to the sum of the measures , so that: ${\ displaystyle \ phi '}$${\ displaystyle | \ alpha | ^ {2} = \ sum _ {i} a_ {i} ^ {*} a_ {i}}$${\ displaystyle \ phi '}$${\ displaystyle | \ alpha |}$${\ displaystyle \ phi _ {i}}$

${\ displaystyle m (\ alpha) = m \ left ({\ sqrt {\ sum _ {i} a_ {i} ^ {*} a_ {i}}} \ right) = \ sum _ {i} a_ {i } ^ {*} a_ {i}}$

This equation has the only solution , so an event chain of the above has Shape the measure ${\ displaystyle m (a_ {i}) = ca_ {i} ^ {*} a_ {i}}$

${\ displaystyle m \ left [S_ {n_ {1}} ^ {1}, S_ {n_ {2}} ^ {2}, \ dots, S_ {n_ {N}} ^ {N} \ right] = \ prod _ {i} a_ {i} ^ {*} a_ {i}}$

If this is factored, then the probability for the event can be understood, which corresponds to Born's rule . ${\ displaystyle a_ {i} ^ {*} a_ {i}}$${\ displaystyle S_ {i}}$

There are also other derivations of Born's rule from the reduced set of axioms. a. those of Deutsch and Hartle.

## example

As an example, a double-slit experiment with a single particle (e.g. an electron ) can be used. An observer measures which hole the particle has passed through. The double-slit observer system is approximately isolated. The particle can be registered at gap 1 or gap 2, these are the ( orthogonal ) states and . Furthermore, the observer bets an amount of money that the particle will be registered at gap 1, so his expectations will be transformed into joy or disappointment during the measurement . ${\ displaystyle | 1 \ rangle}$${\ displaystyle | 2 \ rangle}$${\ displaystyle | {\ ddot {-}} \ rangle}$${\ displaystyle | {\ ddot {\ smile}} \ rangle}$${\ displaystyle | {\ ddot {\ frown}} \ rangle}$

Now a unitary time evolution operator can be defined according to the Schrödinger equation . This must have the shape accordingly . In relation to the experiment, the following requirements are placed on the operator: ${\ displaystyle U}$${\ displaystyle U = e ^ {- iH \ tau / \ hbar}}$

• ${\ displaystyle U \ left (| 1 \ rangle \ otimes | {\ ddot {-}} \ rangle \ right) = | 1 \ rangle \ otimes | {\ ddot {\ smile}} \ rangle}$ (The observer is happy when the particle is registered at gap 1.)
• ${\ displaystyle U (| 2 \ rangle \ otimes | {\ ddot {-}} \ rangle) = | 2 \ rangle \ otimes | {\ ddot {\ frown}} \ rangle}$ (The observer is disappointed when the particle is registered at gap 2.)

Before the measurement, the particle is in superposition of two states,, the observer is in expectation , so the state of the entire system is . If the measurement is now carried out, this is described mathematically by applying the operator to the state of the overall system : ${\ displaystyle | \ psi ^ {T} \ rangle = | 1 \ rangle + | 2 \ rangle}$${\ displaystyle | \ psi ^ {B} \ rangle = | {\ ddot {-}} \ rangle}$${\ displaystyle | \ psi _ {\ mathrm {ges}} \ rangle = | \ psi ^ {T} \ rangle \ otimes | \ psi ^ {B} \ rangle = (| 1 \ rangle + | 2 \ rangle) \ otimes | {\ ddot {-}} \ rangle}$${\ displaystyle U}$${\ displaystyle | \ psi _ {\ mathrm {ges}} \ rangle}$

${\ displaystyle | \ psi _ {\ mathrm {ges}} \ rangle \ longrightarrow U | \ psi _ {\ mathrm {ges}} \ rangle = U \ left [(| 1 \ rangle + | 2 \ rangle) \ otimes | {\ ddot {-}} \ rangle \ right] = | 1 \ rangle \ otimes | {\ ddot {\ smile}} \ rangle + | 2 \ rangle \ otimes | {\ ddot {\ frown}} \ rangle}$

The result is a superposition of the composite system particles at the double slit and observer. Obviously, this is not a clear result, instead there is a superposition of the two possible results. This result is interpreted in the VWI in such a way that at the moment of the measurement the universe branches and the two mathematically required results are realized in different worlds. This is consistent because the happy observer formally has no way of interacting with the unhappy observer: the two states are completely orthogonal to one another in the configuration space . Thus, due to the mathematical structure of this result, any interaction is excluded.

This example can also be used to illustrate another important fact: At no point is there a split that is not induced by the formalism. The branching that takes place is fully described by the dynamics of the states of the observer and the system. So it is not another, independent postulate. This means that the measurement process does not have an excellent role in VWI - it is just treated as a subclass of ordinary interactions.

## criticism

### ontology

Illustration of the separation of the universe due to two superimposed and entangled quantum mechanical states using Schrödinger's cat

Probably the best-known and most frequent criticism of the VWI concerns its ontology : it is accused of violating the principle of simplicity ( Ockham's razor ), because although it predicts the existence of myriads of different worlds, it itself provides evidence that these cannot be observed are. VWI representatives counter this by stating that the many worlds are not an independent postulate, but rather follow from the universal validity of the Schrödinger equation , i.e. from the consistent application of an empirically supported theory. This shortens and simplifies the axiomatics of quantum mechanics. As a result, Occam's razor prefers the VWI over the Copenhagen interpretation . Occam's razor should not be applied to mere existential postulates, but to the theoretical assumptions behind them. In the end, one also assumes that the theory of relativity retains its validity even inside black holes , even if this cannot be observed directly. The Copenhagen interpretation is based on v. a. on the suggestive effect of everyday human perceptions, but make unnecessary additional assumptions just so as not to conflict with them. According to the VWI, the fact that humans cannot perceive macroscopic superpositions trivially results from the decoherence of the neurons in our brains and from the nature of human consciousness. Therefore, there is no need at all to attribute more than just a subjective character to the collapse of the wave function observed in the experiment . The Copenhagen interpretation, however, unnecessarily interprets this collapse in an "objective", absolute sense and even accepts that it can neither be described mathematically nor plausibly justified theoretically. In doing so, it violates the principle of simplicity, while the VWI does not in fact contain any additional assumptions that go beyond the mere, experimentally supported theory.

### Determinism problem

A problem of the many-worlds interpretation that is often highlighted by critics is the question of how it can explain the randomness of quantum events. According to the VWI, every result is actually achieved with a measurement. This raises the question to what extent it makes sense to speak of a probability when all results actually occur. The critics emphasize that the VWI requires a “supernatural observer” in order to make the probability interpretation of measurements plausible at all. Even then, the experiences of real observers would not be explained. VWI representatives insist on a strict distinction between external and internal perspectives and argue that for an observer from the internal perspective, an event can have a random effect despite the deterministic development of a state according to the Schrödinger equation.

### Basic problem

Another point of criticism that is often expressed about the VWI is the so-called basic problem ( problem of preferred basis ). Since the formalism does not specify a preferred basis from the axioms, there is always an infinite number of possibilities for the division of a quantum state into different worlds, apart from the intuitively chosen splitting into the classical basic states. In 1998, however, Wojciech Zurek succeeded in using methods of decoherence theory to show that the classical bases are mathematically preferred by the structure of the Hamilton operator and the value of Planck's quantum of action insofar as they are stable over a longer period of time. As a result, the objects exist in these states long enough to be perceived by quasi-classical measuring devices. Various physicists also point out that the question of the preferred basis or the fact that one perceives well-defined objects in classical, macroscopic states is probably also related to the evolution of humans in this universe.

### Metaphysical objection

Carl Friedrich von Weizsäcker points out that there is no noteworthy difference between the VWI and the Copenhagen interpretation in the context of a modal logic of temporal statements if, purely semantically, “real worlds” are replaced by “possible worlds”: the many worlds describe the one by the Possibility space developing Schrödinger equation; the observation made by a real observer is the realization of one of the formally possible worlds. Weizsäcker recognizes that Everett's approach is the only one among the usual alternatives that “does not go back behind the understanding already achieved by quantum theory, but strives forward beyond it”. However, Everett remained "conservative" in equating reality and factuality. His real - philosophical - objection to the VWI is that the existence of a set of events (“worlds”) is required which “cannot become phenomena ”. Quantum physics, however, is precisely the result of an attempt to describe and predict phenomena consistently.

Even Werner Heisenberg wrote in The physical principles of quantum theory : "One must here remember that human language generally allowed to form sentences that make no consequences can be drawn which are therefore actually completely devoid of content, despite being a kind of For example, the assertion that there is a second world in addition to our world, with which in principle no connection is possible, leads to no conclusion at all; nevertheless, a kind of image arises in our imagination with this assertion. " Anton Zeilinger comments on this sentence in his preface to the cited edition of Heisenberg's book: "A reflection on statements of this kind would considerably shorten some of today's interpretative discussions."

## Individual evidence

1. ^ A b c Hugh Everett III : "Relative State" Formulation of Quantum Mechanics . In: Reviews of modern physics . Vol. 29, 1957, pp. 454-462 , doi : 10.1103 / RevModPhys.29.454 .
2. ^ A b Max Tegmark : Many Worlds in Context . Massachusetts Institute of Technology ( Cambridge / USA) 2009, arxiv : 0905.2182v2 .
3. ^ A b Bryce S. DeWitt : Quantum mechanics and reality . In: physicstoday . Vol. 23, No. 9 , 1970, pp. 30 , doi : 10.1063 / 1.3022331 .
4. Peter Byrne: Many Worlds. Hugh Everett III . a family drama between cold war and quantum physics. Springer, Heidelberg 2012, ISBN 978-3-642-25179-5 (English: The many worlds of Hugh Everett III . Translated by Anita Ehlers).
5. H. Dieter Zeh: Decoherence and other quantum misunderstandings. (PDF 180 kB) May 2011, accessed on April 28, 2014 .
6. ^ A b Bryce DeWitt: Quantum Theory of Gravity. I. The Canonical Theory . In: Physical Review . tape 160 , no. 12 , 1967, p. 1113–1148 , doi : 10.1103 / PhysRev.160.1113 .
7. James Hartle, Stephen W. Hawking: The Wave function of the Universe . In: Physical Review D . tape 28 , no. 5 , 1983, pp. 2960-2975 , doi : 10.1103 / PhysRevD.28.2960 .
8. ^ Murray Gell-Mann: The Quark and the Jaguar: Adventures in the Simple and the Complex . Owl Books, 2002, ISBN 0-7167-2725-0 .
9. Stephen W. Hawking: Black Holes and Thermodynamic . In: Physical Review D . tape 13 , no. 2 , 1976, p. 191-197 , doi : 10.1103 / PhysRevD.13.191 .
10. ^ Steven Weinberg: Dreams of a Final Theory . Vintage, 1994, ISBN 0-679-74408-8 .
11. ^ Frank J Tipler: The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead . Anchor, 1997, ISBN 0-385-46799-0 .
12. a b H. Dieter Zeh: Why do you need “many worlds” in quantum theory? (PDF; 235 kB) September 2012, accessed April 30, 2014 .
13. Interpretations of Quantum Mechanics - Interview Theodor Hänsch. drillingsraum.de, August 29, 2011, accessed May 5, 2012 .
14. ^ A b Max Tegmark: The Interpretation of Quantum Mechanics: Many Worlds or many words? 1997, arxiv : quant-ph / 9709032v1 .
15. ^ David Deutsch: Quantum Theory of Probability and Decisions . In: Proceedings of the Royal Society of London A . tape 455 , 1999, p. 3129-3137 .
16. ^ JB Harte: Quantum Mechanics of Individual Systems . In: American Journal of Physics . tape 36 , 1968, pp. 704-712 .
17. ^ Adrian Kent: Against Many-Worlds Interpretations . In: International Journal of Modern Physics A . tape 5 , no. 9 , 1990, ISSN  0217-751X , pp. 1745–1762 , doi : 10.1142 / S0217751X90000805 , arxiv : gr-qc / 9703089v1 .
18. ^ HP Stapp: The basis problem in many-worlds theories . In: Canadian Journal of Physics . tape 80 , no. 9 , 2002, p. 1043-1052 , doi : 10.1139 / p02-068 .
19. ^ Wojciech H. Zurek: Decoherence, Einselection and the Existential Interpretation (the Rough Guide) . In: Philosophical Transactions of the Royal Society of London A . tape 356 , no. 1743 , August 1998, p. 1793-1821 , doi : 10.1098 / rsta.1998.0250 .
20. ^ Murray Gell-Mann, James Hartle: Quantum Mechanics in the Light of Quantum Cosmology . In: Wojciech H. Zurek (Ed.): Complexity, Entropy and the Physics of Information . Westview Press, 1990, ISBN 0-201-51506-7 , pp. 425-459 .
21. ^ David Deutsch: The Fabric of Reality: Towards a Theory of Everything . New edition. Penguin, 2011, ISBN 0-14-014690-3 .
22. ^ Roger Penrose: Shadows of the Mind: A Search for the Missing Science of Consciousness . New edition. Vintage Books, 1995, ISBN 0-09-958211-2 .
23. Carl-Friedrich von Weizsäcker: Structure of the physics . Carl Hanser, Munich / Vienna 1985, ISBN 3-446-14142-1 , Eleventh Chapter: The Interpretation Problem of Quantum Theory / Thirteenth Chapter: Beyond Quantum Theory, p. 563 ff., 605 f .
24. Carl-Friedrich von Weizsäcker: Structure of the physics . Carl Hanser, Munich / Vienna 1985, ISBN 3-446-14142-1 , Chapter 11: The interpretation problem of quantum theory, p. 564 .
25. Carl-Friedrich von Weizsäcker: Structure of the physics . Carl Hanser, Munich / Vienna 1985, ISBN 3-446-14142-1 , thirteenth chapter: Beyond the quantum theory, p. 606 .
26. a b W. Heisenberg: The physical principles of quantum theory . 5th edition, S. Hirzel Verlag Stuttgart, 2008, ISBN 978-3-7776-1616-2