In
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
, einselections, short for "environment-induced
superselection
In quantum mechanics, superselection extends the concept of selection rules.
Superselection rules are postulated rules forbidding the preparation of quantum states that exhibit coherence between eigenstates of certain observables.
It was origina ...
", is a name coined by
Wojciech H. Zurek
for a process which is claimed to explain the appearance of
wavefunction collapse
In quantum mechanics, wave function collapse occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an ''observa ...
and the
emergence of
classical descriptions of reality from
quantum descriptions. In this approach, classicality is described as an emergent property induced in
open quantum systems by their environments. Due to the
interaction
Interaction is action that occurs between two or more objects, with broad use in philosophy and the sciences. It may refer to:
Science
* Interaction hypothesis, a theory of second language acquisition
* Interaction (statistics)
* Interactions o ...
with the environment, the vast majority of states in the
Hilbert space of a quantum open system become highly unstable due to entangling interaction with the environment, which in effect monitors selected observables of the system. After a
decoherence
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...
time, which for macroscopic objects is typically many orders of magnitude shorter than any other dynamical timescale,
a generic quantum state decays into an
uncertain state which can be expressed as a mixture of simple
pointer states In quantum Darwinism and similar theories, pointer states are quantum states, sometimes of a measuring apparatus, if present, that are less perturbed by decoherence than other states, and are the quantum equivalents of the classical states of the sy ...
. In this way the environment induces effective superselection rules. Thus, einselection precludes stable existence of pure superpositions of pointer states. These '
pointer states In quantum Darwinism and similar theories, pointer states are quantum states, sometimes of a measuring apparatus, if present, that are less perturbed by decoherence than other states, and are the quantum equivalents of the classical states of the sy ...
' are stable despite environmental interaction. The einselected states lack coherence, and therefore do not exhibit the quantum behaviours of
entanglement and
superposition.
Advocates of this approach argue that since only quasi-local, essentially classical states survive the decoherence process, einselection can in many ways explain the emergence of a (seemingly) classical reality in a fundamentally quantum universe (at least to local observers). However, the basic program has been criticized as relying on a circular argument (e.g.
R. E. Kastner).
So the question of whether the 'einselection' account can really explain the phenomenon of wave function collapse remains unsettled.
Definition
Zurek has defined einselection as follows: "
Decoherence
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...
leads to einselection when the
states of the
environment
Environment most often refers to:
__NOTOC__
* Natural environment, all living and non-living things occurring naturally
* Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
corresponding to different pointer states become orthogonal:
",
Details
Einselected pointer states are distinguished by their ability to persist in spite of the environmental monitoring and therefore are the ones in which quantum open systems are observed. Understanding the nature of these states and the process of their dynamical selection is of fundamental importance. This process has been studied first in a measurement situation: When the system is an apparatus whose intrinsic dynamics can be neglected, pointer states turn out to be
eigenstates
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution i ...
of the interaction
Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
between the apparatus and its environment.
[
*
*] In more general situations, when the system's dynamics is relevant, einselection is more complicated. Pointer states result from the interplay between self-evolution and environmental monitoring.
To study einselection, an operational definition of pointer states has been introduced.
This is the "predictability sieve" criterion, based on an intuitive idea: ''Pointer states'' can be defined as the ones which become minimally entangled with the environment in the course of their evolution. The predictability sieve criterion is a way to quantify this idea by using the following algorithmic procedure: For every initial pure state
, one measures the
entanglement generated dynamically between the system and the environment by computing the entropy:
::
or some other measure of predictability
[
*
*
*
*
*] from the reduced
density matrix
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using ...
of the system
(which is initially
).
The entropy is a function of time and a functional of the initial state
. Pointer states are obtained by minimizing
over
and demanding that the answer be robust when varying the time
.
The nature of pointer states has been investigated using the predictability sieve criterion only for a limited number of examples.
Apart from the already mentioned case of the measurement situation (where pointer states are simply eigenstates of the interaction Hamiltonian) the most notable example is that of a quantum
Brownian particle coupled through its position with a bath of independent
harmonic oscillators
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force ''F'' proportional to the displacement ''x'':
\vec F = -k \vec x,
where ''k'' is a positive consta ...
. In such case pointer states are localized in
phase space, even though the interaction Hamiltonian involves the position of the particle.
Pointer states are the result of the interplay between self-evolution and interaction with the environment and turn out to be coherent states.
There is also a
quantum limit A quantum limit in physics is a limit on measurement accuracy at quantum scales.
Depending on the context, the limit may be absolute (such as the Heisenberg limit), or it may only apply when the experiment is conducted with naturally occurring qu ...
of decoherence: When the spacing between
energy levels
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The t ...
of the system is large compared to the
frequencies present in the environment,
energy eigenstates
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat ...
are einselected nearly independently of the nature of the system-environment coupling.
Collisional decoherence
There has been significant work on correctly identifying the pointer states in the case of a massive particle decohered by collisions with a fluid environment, often known as ''collisional decoherence''. In particular, Busse and Hornberger have identified certain solitonic wavepackets as being unusually stable in the presence of such decoherence.
See also
Mott problem
References
{{reflist
Quantum mechanics
Emergence