Decoherence

Decoherence is a phenomenon in quantum physics that leads to the incomplete or complete suppression of the coherence properties of quantum mechanical states . Decoherence effects arise when a previously closed system interacts with its environment. This changes both the state of the environment and the state of the system irreversibly . The decoherence concept was introduced around 1970 by the German physicist Dieter Zeh .

The concepts of decoherence are nowadays an important aid for many common interpretations of quantum mechanics to clarify the question of how the classical phenomena of macroscopic quantum systems can be interpreted. However, they are incompatible with the Copenhagen interpretation , which defines measuring devices as “classical” systems that cannot be described in quantum mechanics.

Furthermore, decoherence is a main problem in the construction of quantum computers , in which a quantum mechanical superposition of as many states as possible is to be maintained undisturbed over a sufficiently long period of time.

Basic concepts

Problem

If quantum mechanics is a fundamental theory, since the laws of quantum mechanics are formulated independently of the size of the system under consideration, the transition from the physical properties of microscopic systems to the properties of macroscopic systems must be quantum mechanically describable. However, quantum phenomena such as the double-slit experiment raise the question of how the “classic” behavior of macroscopic systems can be explained in the context of quantum mechanics. In particular, it is by no means immediately obvious what physical meaning a quantum mechanical superposition state should have when applied to a macroscopic system. In 1954 , Albert Einstein, in his correspondence with Max Born, asked how the localization of macroscopic objects can be explained in the context of quantum mechanics. He pointed out that the "smallness" of quantum mechanical effects in macroscopic masses is insufficient to explain the localization:

“ And be two solutions of the same Schrödinger equation . Then there is also a solution of the Schrödinger equation with the same claim to describe a possible real state. If the system is a macro system, and if and are “narrow” in relation to the macro coordinates, then this is no longer the case in the vast majority of possible cases . Narrowness in terms of macro coordinates is a requirement that is not only independent of the principles of quantum mechanics, but also incompatible with these principles. " ${\ displaystyle \ psi _ {1}}$ ${\ displaystyle \ psi _ {2}}$ ${\ displaystyle \ psi = \ psi _ {1} + \ psi _ {2}}$ ${\ displaystyle \ psi _ {1}}$ ${\ displaystyle \ psi _ {2}}$ ${\ displaystyle \ psi}$

Another example of the (apparent) paradoxes when applying quantum mechanical concepts to macroscopic systems is the thought experiment devised by Erwin Schrödinger , now known as " Schrödinger's cat " .

Influence of the environment

It was not until around 1970 (work by Dieter Zeh ) that, based on theoretical and experimental investigations of the measurement process , the realization gradually emerged that the above-mentioned. Considerations and thought experiments on macroscopic states are unrealistic in that they ignore their inevitable interactions with the environment. It turned out that superposition effects such as the above-mentioned interference at the double slit are extremely sensitive to any influence from the environment: collisions with gas molecules or photons , but also the emission or absorption of radiation, impair or destroy the solid phase relationship between the individual states involved of the system under consideration, which is decisive for the occurrence of interference effects. ${\ displaystyle | \ phi _ {n} ^ {\ text {System}} \ rangle}$

In the terminology of quantum mechanics, this phenomenon, known as decoherence, can be traced back to the interaction between the system states and the scattered particles. This can be described by interlinking the individual states with the states of the environment. As a result of this interaction, the phase relationships between the states involved only remain well-defined when considering the overall system (system + environment). If the system states are considered in isolation , however, purely statistical , i.e. H. “Classic” distributions of these states. ${\ displaystyle | \ phi _ {n} ^ {\ text {System}} \ rangle}$ ${\ displaystyle | \ phi _ {m} ^ {\ text {Scattered particles}} \ rangle}$ ${\ displaystyle | \ phi _ {n} ^ {\ text {System}} \ rangle}$

Typical decoherence times

Decoherence times in seconds
Environmental influence	Free electron	Dust particles 10 µm	Bowling ball
300 K, normal pressure	10 ⁻¹²	10 ⁻¹⁸	10 ⁻²⁶
300 K, ultra-high vacuum (laboratory)	10	10 ⁻⁴	10 ⁻¹²
with sunlight (on earth)	10 ⁻⁹	10 ^-10	10 ⁻¹⁸
with thermal radiation (300 K)	10 ⁻⁷	10 ⁻¹²	10 ⁻²⁰
with cosmic background radiation (2.73 K)	10 ⁻⁹	10 ⁻⁷	10 ⁻¹⁸

An idea of the efficiency of this phenomenon is given in Table 1, which lists typical orders of magnitude of the decoherence times (i.e. the time periods within which the coherence is lost) for various objects and environmental influences. Obviously, due to the practically unavoidable influence of the environment, the superimposed states of macroscopic objects disintegrate into a classic ensemble of uncorrelated individual states within a very short time (even the 10 µm dust particle must be referred to as macroscopic in this sense).

Superselection in measurements

In the above explanations, it was implicitly assumed that macroscopic systems, at the latest after the end of the decoherence processes, assume states that have the familiar “classical” properties. However, it is not immediately clear which of the many conceivable basic systems represent the preferred basis for macroscopic systems. Why do z. For example, in macroscopic systems, localized spatial states usually play a preferred role, while microscopic systems are often found in delocalized states (e.g. energy eigenstates )?

This question can also be traced back to the influence of the environment on the system under consideration. According to this, only a "robust" basis, which is not immediately destroyed by decoherence mechanisms, defines the actually realizable observables (various concrete examples including a justification for the preferred occurrence of spatially localized states can be found e.g. in Erich Joos and Maximilian Schlosshauer ) . This preference for certain macroscopic states is a super selection or einselection referred (for environmentally-induced super selection).

Decoherence and measurement problem

In the literature one often finds the statement that decoherence and superselection represent a solution to the measurement problem , one of the fundamental unanswered questions in quantum mechanics. However, this statement is very controversial.

When it is said that the decoherence produces “classical” properties, then this means that the quantum system approximately ( “for all practical purposes” ) no longer shows any interference or superposition. Measurements on decoherent systems show a classic statistical distribution of the measured values; this also makes contradictions to classical physics such as the Einstein-Podolsky-Rosen paradox disappear .

However, decoherence theory cannot explain individual measurements, but only makes statistical statements about ensembles made up of several measurement processes. In order to explain why only a single, specific result is perceived in a single measurement, a more extensive interpretation is still necessary, as is attempted, for example, with the collapse of the wave function of the Copenhagen interpretation of quantum theory or in the context of the many worlds interpretation . The dynamic collapse theories are also compatible with the decoherence theory.

literature

Mario Castagnino, Sebastian Fortin, Roberto Laura and Olimpia Lombardi, A general theoretical framework for decoherence in open and closed systems , Classical and Quantum Gravity, 25, pp. 154002-154013, (2008).
Bertrand Duplantier: Quantum decoherence. Birkhäuser, Basel 2007, ISBN 3-7643-7807-7
Vladimir M. Akulin: Decoherence, entanglement and information protection in complex quantum systems. Springer, Dordrecht 2005, ISBN 1-4020-3282-X .
Maximilian A. Schlosshauer: Decoherence and the quantum-to-classical transition. Springer, Berlin 2008, ISBN 3-540-35773-4 .
Erich Joos: Elements of Environmental Decoherence, in: D. Giulini u. a. (Ed.): Decoherence and the Appearance of a Classical World in Quantum Theory , Springer 2003, arxiv : quant-ph / 9908008
Dieter Zeh: Decoherence: Basic Concepts and Their Interpretation , in: P. Blanchard, D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu (Ed.): Bielefeld conference on Decoherence: Theoretical, Experimental, and Conceptual Problems , Springer 1999, arxiv : quant-ph / 9506020

Web links

Decoherence.de
Entry in Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy . (by Guido Bacciagaluppi 2012)
Zeh: Decoherence and other quantum misunderstandings , Didactics workshop Universität Karlsruhe 2009, (PDF; 180 kB)
Franz Embacher, Basic Idea of Decoherence, University of Vienna

Individual evidence

↑ ^a ^b ^c ^d ^e Schlosshauer, Maximilian: "Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics", Reviews of Modern Physics 76 (2004), 1267-1305. arxiv : quant-ph / 0312059v4 .
^ A. Einstein, M. Born: Briefwechsel 1916-1955 , Langen / Müller 2005, ISBN 3-7844-2997-1
↑ ^a ^b ^c E. Joos et al .: Decoherence and the Appearance of a Classical World in Quantum Theory , Springer 2003, ISBN 3-540-00390-8
↑ Horst Völz: Basics and contents of the four types of information: How the information came about and what types there are . Ed .: Springer-Verlag. Springer-Verlag, Berlin, ISBN 978-3-658-06406-8 , pp. 143 .
↑ See e.g. B. "Against the 'measurement'". In JS Bell: Quantum Mechanics, Six Possible Worlds and other articles , de Gruyter, Berlin 2015, ISBN 978-3-11-044790-3 , pp. 241-259.

[Schlosshauer2004-1] Schlosshauer, Maximilian: "Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics", Reviews of Modern Physics 76 (2004), 1267-1305. arxiv : quant-ph / 0312059v4 .

[Born1969-2] A. Einstein, M. Born: Briefwechsel 1916-1955 , Langen / Müller 2005, ISBN 3-7844-2997-1

[Joos2003-3] E. Joos et al .: Decoherence and the Appearance of a Classical World in Quantum Theory , Springer 2003, ISBN 3-540-00390-8

[4] Horst Völz: Basics and contents of the four types of information: How the information came about and what types there are . Ed .: Springer-Verlag. Springer-Verlag, Berlin, ISBN 978-3-658-06406-8 , pp. 143 .

[5] See e.g. B. "Against the 'measurement'". In JS Bell: Quantum Mechanics, Six Possible Worlds and other articles , de Gruyter, Berlin 2015, ISBN 978-3-11-044790-3 , pp. 241-259.