Quantum Zeno effect
Encyclopedia
The quantum Zeno effect is a name coined by George Sudarshan
and Baidyanath Misra of the University of Texas
in 1977 in their analysis of the situation in which an unstable particle
, if observed continuously, will never decay. One can nearly "freeze" the evolution of the system by measuring it frequently enough in its (known) initial state. The meaning of the term has since expanded, leading to a more technical definition in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution caused by quantum decoherence
in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, and so on. As an outgrowth of study of the quantum Zeno effect, it has become clear that applying a series of sufficiently strong and fast pulses with appropriate symmetry can also decouple a system from its decohering environment.
The name comes from Zeno's arrow paradox which states that, since an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all.
An earlier theoretical exploration of this effect of measurement was published in 1974 by Degasperis et al. and Alan Turing
described it in 1954:
resulting in the earlier name Turing paradox. The idea is contained in the early work by John von Neumann
, sometimes called the reduction postulate.
According to the reduction postulate, each measurement causes the wavefunction
to "collapse
" to a pure eigenstate of the measurement basis. In the context of this effect, an "observation" can simply be the absorption of a particle, without an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "measurement problem
" in traversing the interface between microscopic and macroscopic.
Closely related (and sometimes not distinguished from the quantum Zeno effect) is the watchdog effect, in which the time evolution of a system is affected by its continuous coupling to the environment.
In quantum mechanics
, the interaction mentioned is called "measurement" because its result can be interpreted in terms of classical mechanics
. Frequent measurement prohibits the transition. It can be a transition of a particle from one half-space to another (which could be used for atomic mirror in an atomic nanoscope
,) a transition of a photon in a waveguide from one mode to another, and it can be a transition of an atom from one quantum state to another.
It can be a transition from the subspace without decoherent loss of a q-bit to a state with a q-bit lost in a quantum computer
.
In this sense, for the q-bit correction, it is sufficient to determine whether the decoherence has already occurred or not.
All these can be considered as applications of the Zeno effect. By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies.
is not limited to the processes of quantum decay. In general, the term Zeno effect is applied to various transitions, and sometimes these transitions may be very different from a mere "decay" (whether exponential or non-exponential).
One realization refers to the observation of an object (Zeno's arrow, or any quantum particle) as it leaves some region of space. In the 20th century, the trapping (confinement) of a particle in some region by its observation outside the region was considered as nonsensical, indicating some non-completeness of quantum mechanics. Even as late as 2001, confinement by absorption was considered as a paradox. Later, similar effects of the suppression of Raman scattering
was considered an expected effect, not a paradox at all. The absorption of a photon at some wavelength, the release of a photon (for example one that has escaped from some mode of a fiber), or even the relaxation of a particle as it enters some region, are all processes that can be interpreted as measurement. Such a measurement suppresses the transition, and is called the Zeno effect in the scientific literature.
In order to cover all of these phenomena (including the original effect of suppression of quantum decay), the
Zeno effect can be defined as a class of phenomena in which some transition is suppressed by an interaction — one that allows the interpretation of the resulting state in the terms transition did not yet happen and transition has already occurred, or The proposition that the evolution of a quantum system is halted if the state of the system is continuously measured by a macroscopic device to check whether the system is still in its initial state.
state of the states A and B. When the superposition state is measured, it will again collapse, either back into state A as in the first measurement, or away into state B. However, its probability of collapsing into state B, after a very short amount of time t, is proportional to t², since probabilities are proportional to squared amplitudes, and amplitudes behave linearly. Thus, in the limit of a large number of short intervals, with a measurement at the end of every interval, the probability of making the transition to B goes to zero.
According to decoherence theory
, the collapse of the wave function is not a discrete, instantaneous event. A "measurement" is equivalent to strongly coupling the quantum system to the noisy thermal environment for a brief period of time, and continuous strong coupling is equivalent to frequent "measurement". The time it takes for the wave function to "collapse" is related to the decoherence time of the system when coupled to the environment. The stronger the coupling is, and the shorter the decoherence time, the faster it will collapse. So in the decoherence picture, a perfect implementation of the quantum Zeno effect corresponds to the limit where a quantum system is continuously coupled to the environment, and where that coupling is infinitely strong, and where the "environment" is an infinitely large source of thermal randomness.
In 1989, David Wineland and his group at NIST observed the quantum Zeno effect for a two-level atomic system that is interrogated during its evolution. Approximately 5000 9Be
+ ions were stored in a cylindrical Penning trap
and laser cooled
to below 250 mK. A resonant RF
pulse was applied which, if applied alone, would cause the entire ground state population to migrate into an excited state. After the pulse was applied, the ions were monitored for photons emitted due to relaxation. The ion trap was then regularly "measured" by applying a sequence of ultraviolet
pulses, during the RF pulse. As expected, the ultraviolet pulses suppressed the evolution of the system into the excited state. The results were in good agreement with theoretical models. A recent review describes subsequent work in this arena.
In 2001, Mark G. Raizen
and his group at the University of Texas at Austin
, observed the quantum Zeno and anti-Zeno effects for an unstable quantum system, as originally proposed by Sudarshan and Misra. Ultracold sodium atoms were trapped in an accelerating optical lattice and the loss due to tunneling was measured. The evolution was interrupted by reducing the acceleration, thereby stopping quantum tunneling. The group observed
suppression or enhancement of the decay rate, depending on the regime of measurement.
The Quantum Zeno Effect is used in commercial atomic magnetometers and naturally by bird's magnetic compass sensory mechanism (magnetoreception).
It is still an open question how closely one can approach the limit of an infinite number of interrogations due to the Heisenberg uncertainty involved in shorter measurement times. In 2006, Streed et al. at MIT observed the dependence of the Zeno effect on measurement pulse characteristics.
The interpretation of experiments in terms of the "Zeno effect" helps describe the origin of a phenomenon.
Nevertheless, such an interpretation does not bring any principally new features not described with the Schrödinger equation
of the quantum system.
Even more, the detailed description of experiments with the "Zeno effect", especially at the limit of high frequency of measurements (high efficiency of suppression of transition, or high reflectivity of a ridged mirror
) usually do not behave as expected for an idealized measurement, and require analysis of the mechanism of the interaction.
It was shown that the Quantum Zeno effect persists in the many-worlds and relative states interpretations of quantum mechanics.
) is becoming a central concept in the exploration of controversial theories of quantum mind
consciousness within the discipline of cognitive science
. In his book, "Mindful Universe" (2007), Henry Stapp
claims that the quantum Zeno effect is the main method by which the mind holds a superposition of the state of the brain in the attention
. He advances that this phenomenon is the principal method by which the conscious will effects change, a possible solution to the mind-body dichotomy
. Stapp and co-workers do not claim finality of their theory, but only:
Needless to say, such conjectures have their opponents, serving perhaps to create more furor, rather than less, for example, see Bourget. A summary of the situation is provided by Davies:
While this last objection may no longer be valid, the significance of the Zeno effect in determining the rate of quantum decoherence in biological systems remains unknown.
uses the effect to explain the construction of a hydrogen-annihilation
-powered rocket in his short story 'Glory', and the Doctor Who
episodes "Blink
", "The Time of Angels
", and "Flesh and Stone
" feature an alien species called the Weeping Angels
who exists in a quantum-locked state, unable to move while observed.
George Sudarshan
Ennackal Chandy George Sudarshan , also E.C.G. Sudarshan, is a prominent Indian American physicist, author, and professor at The University of Texas at Austin.-Early life:...
and Baidyanath Misra of the University of Texas
University of Texas at Austin
The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...
in 1977 in their analysis of the situation in which an unstable particle
Resonance (particle physics)
In particle physics, a resonance is the peak located around a certain energy found in differential cross sections of scattering experiments. These peaks are associated with subatomic particles and their excitations...
, if observed continuously, will never decay. One can nearly "freeze" the evolution of the system by measuring it frequently enough in its (known) initial state. The meaning of the term has since expanded, leading to a more technical definition in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution caused by quantum decoherence
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, and so on. As an outgrowth of study of the quantum Zeno effect, it has become clear that applying a series of sufficiently strong and fast pulses with appropriate symmetry can also decouple a system from its decohering environment.
The name comes from Zeno's arrow paradox which states that, since an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all.
An earlier theoretical exploration of this effect of measurement was published in 1974 by Degasperis et al. and Alan Turing
Alan Turing
Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...
described it in 1954:
resulting in the earlier name Turing paradox. The idea is contained in the early work by John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
, sometimes called the reduction postulate.
According to the reduction postulate, each measurement causes the wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
to "collapse
Wavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...
" to a pure eigenstate of the measurement basis. In the context of this effect, an "observation" can simply be the absorption of a particle, without an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "measurement problem
Measurement problem
The measurement problem in quantum mechanics is the unresolved problem of how wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer...
" in traversing the interface between microscopic and macroscopic.
Closely related (and sometimes not distinguished from the quantum Zeno effect) is the watchdog effect, in which the time evolution of a system is affected by its continuous coupling to the environment.
Description
Unstable quantum systems are predicted to exhibit a short time deviation from the exponential decay law. This universal phenomenon has led to the prediction that frequent measurements during this nonexponential period could inhibit decay of the system, one form of the quantum Zeno effect. Subsequently, it was predicted that an enhancement of decay due to frequent measurements could be observed under somewhat more general conditions, leading to the so-called anti-Zeno effect.In quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, the interaction mentioned is called "measurement" because its result can be interpreted in terms of classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
. Frequent measurement prohibits the transition. It can be a transition of a particle from one half-space to another (which could be used for atomic mirror in an atomic nanoscope
Atomic nanoscope
The atomic de Broglie microscope is an imaging system which is expected to provide resolution at the nanometer scale....
,) a transition of a photon in a waveguide from one mode to another, and it can be a transition of an atom from one quantum state to another.
It can be a transition from the subspace without decoherent loss of a q-bit to a state with a q-bit lost in a quantum computer
Quantum computer
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...
.
In this sense, for the q-bit correction, it is sufficient to determine whether the decoherence has already occurred or not.
All these can be considered as applications of the Zeno effect. By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies.
Various realizations and general definition
The treatment of the Zeno effect as a paradoxParadox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
is not limited to the processes of quantum decay. In general, the term Zeno effect is applied to various transitions, and sometimes these transitions may be very different from a mere "decay" (whether exponential or non-exponential).
One realization refers to the observation of an object (Zeno's arrow, or any quantum particle) as it leaves some region of space. In the 20th century, the trapping (confinement) of a particle in some region by its observation outside the region was considered as nonsensical, indicating some non-completeness of quantum mechanics. Even as late as 2001, confinement by absorption was considered as a paradox. Later, similar effects of the suppression of Raman scattering
Raman scattering
Raman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa Krishnan in liquids, and by Grigory Landsberg and Leonid Mandelstam in crystals....
was considered an expected effect, not a paradox at all. The absorption of a photon at some wavelength, the release of a photon (for example one that has escaped from some mode of a fiber), or even the relaxation of a particle as it enters some region, are all processes that can be interpreted as measurement. Such a measurement suppresses the transition, and is called the Zeno effect in the scientific literature.
In order to cover all of these phenomena (including the original effect of suppression of quantum decay), the
Zeno effect can be defined as a class of phenomena in which some transition is suppressed by an interaction — one that allows the interpretation of the resulting state in the terms transition did not yet happen and transition has already occurred, or The proposition that the evolution of a quantum system is halted if the state of the system is continuously measured by a macroscopic device to check whether the system is still in its initial state.
Periodic measurement of a quantum system
Consider a system in a state A, which is the eigenstate of some measurement operator. Say the system under free time evolution will decay with a certain probability into state B. If measurements are made periodically, with some finite interval between each one, at each measurement, the wave function collapses to an eigenstate of the measurement operator. Between the measurements, the system evolves away from this eigenstate into a superpositionQuantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...
state of the states A and B. When the superposition state is measured, it will again collapse, either back into state A as in the first measurement, or away into state B. However, its probability of collapsing into state B, after a very short amount of time t, is proportional to t², since probabilities are proportional to squared amplitudes, and amplitudes behave linearly. Thus, in the limit of a large number of short intervals, with a measurement at the end of every interval, the probability of making the transition to B goes to zero.
According to decoherence theory
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
, the collapse of the wave function is not a discrete, instantaneous event. A "measurement" is equivalent to strongly coupling the quantum system to the noisy thermal environment for a brief period of time, and continuous strong coupling is equivalent to frequent "measurement". The time it takes for the wave function to "collapse" is related to the decoherence time of the system when coupled to the environment. The stronger the coupling is, and the shorter the decoherence time, the faster it will collapse. So in the decoherence picture, a perfect implementation of the quantum Zeno effect corresponds to the limit where a quantum system is continuously coupled to the environment, and where that coupling is infinitely strong, and where the "environment" is an infinitely large source of thermal randomness.
Experiments and discussion
Experimentally, strong suppression of the evolution of a quantum system due to environmental coupling has been observed in a number of microscopic systems.In 1989, David Wineland and his group at NIST observed the quantum Zeno effect for a two-level atomic system that is interrogated during its evolution. Approximately 5000 9Be
Beryllium
Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...
+ ions were stored in a cylindrical Penning trap
Penning trap
Penning traps are devices for the storage of charged particles using a homogeneous static magnetic field and a spatially inhomogeneous static electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have...
and laser cooled
Laser cooling
Laser cooling refers to the number of techniques in which atomic and molecular samples are cooled through the interaction with one or more laser light fields...
to below 250 mK. A resonant RF
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
pulse was applied which, if applied alone, would cause the entire ground state population to migrate into an excited state. After the pulse was applied, the ions were monitored for photons emitted due to relaxation. The ion trap was then regularly "measured" by applying a sequence of ultraviolet
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...
pulses, during the RF pulse. As expected, the ultraviolet pulses suppressed the evolution of the system into the excited state. The results were in good agreement with theoretical models. A recent review describes subsequent work in this arena.
In 2001, Mark G. Raizen
Mark G. Raizen
Mark George Raizen is a physicist who conducts experiments on quantum optics and atom optics.-Birth and Education:Raizen was born in New York City where generations of his family resided since the 1840s. While he comes from a long line of medical doctors, dating back to the Civil War, Raizen's life...
and his group at the University of Texas at Austin
University of Texas at Austin
The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...
, observed the quantum Zeno and anti-Zeno effects for an unstable quantum system, as originally proposed by Sudarshan and Misra. Ultracold sodium atoms were trapped in an accelerating optical lattice and the loss due to tunneling was measured. The evolution was interrupted by reducing the acceleration, thereby stopping quantum tunneling. The group observed
suppression or enhancement of the decay rate, depending on the regime of measurement.
The Quantum Zeno Effect is used in commercial atomic magnetometers and naturally by bird's magnetic compass sensory mechanism (magnetoreception).
It is still an open question how closely one can approach the limit of an infinite number of interrogations due to the Heisenberg uncertainty involved in shorter measurement times. In 2006, Streed et al. at MIT observed the dependence of the Zeno effect on measurement pulse characteristics.
The interpretation of experiments in terms of the "Zeno effect" helps describe the origin of a phenomenon.
Nevertheless, such an interpretation does not bring any principally new features not described with the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
of the quantum system.
Even more, the detailed description of experiments with the "Zeno effect", especially at the limit of high frequency of measurements (high efficiency of suppression of transition, or high reflectivity of a ridged mirror
Ridged mirror
In atomic physics, a ridged mirror is a kind of atomic mirror, designed for the specular reflection of neutral particles coming at the grazing incidence angle, characterised in the following: in order to reduce the mean attraction of particles to the surface and increase the reflectivity, this...
) usually do not behave as expected for an idealized measurement, and require analysis of the mechanism of the interaction.
It was shown that the Quantum Zeno effect persists in the many-worlds and relative states interpretations of quantum mechanics.
Significance to cognitive science
The quantum Zeno effect (with its own controversies related to measurementMeasurement problem
The measurement problem in quantum mechanics is the unresolved problem of how wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer...
) is becoming a central concept in the exploration of controversial theories of quantum mind
Quantum mind
The quantum mind or quantum consciousness hypothesis proposes that classical mechanics cannot explain consciousness, while quantum mechanical phenomena, such as quantum entanglement and superposition, may play an important part in the brain's function, and could form the basis of an explanation of...
consciousness within the discipline of cognitive science
Cognitive science
Cognitive science is the interdisciplinary scientific study of mind and its processes. It examines what cognition is, what it does and how it works. It includes research on how information is processed , represented, and transformed in behaviour, nervous system or machine...
. In his book, "Mindful Universe" (2007), Henry Stapp
Henry Stapp
Henry Stapp is an American physicist, well-known for his work in quantum mechanics.-Biography:Stapp received his PhD in particle physics at the University of California, Berkeley, under the supervision of Nobel Laureates Emilio Segrè and Owen Chamberlain...
claims that the quantum Zeno effect is the main method by which the mind holds a superposition of the state of the brain in the attention
Attention
Attention is the cognitive process of paying attention to one aspect of the environment while ignoring others. Attention is one of the most intensely studied topics within psychology and cognitive neuroscience....
. He advances that this phenomenon is the principal method by which the conscious will effects change, a possible solution to the mind-body dichotomy
Mind-body dichotomy
The mind-body problem is a philosophical problem arising in the fields of metaphysics and philosophy of mind. The problem arises because mental phenomena appear to be qualitatively and substantially different from the physical bodies on which they appear to depend. There are a few major theories on...
. Stapp and co-workers do not claim finality of their theory, but only:
- The new framework, unlike its classic-physics-based predecessor, is erected directly upon, and is compatible with, the prevailing principles of physics.
Needless to say, such conjectures have their opponents, serving perhaps to create more furor, rather than less, for example, see Bourget. A summary of the situation is provided by Davies:
- There have been many claims that quantum mechanics plays a key role in the origin and/or operation of biological organisms, beyond merely providing the basis for the shapes and sizes of biological molecules and their chemical affinities.…The case for quantum biologyQuantum biologyQuantum biology refers to applications of quantum mechanics to biological objects and problems. Usually, it is taken to refer to applications of the "non-trivial" quantum features such as superposition, nonlocality, entanglement and tunneling, as opposed to the "trivial" applications such as...
remains one of “not proven.” There are many suggestive experiments and lines of argument indicating that some biological functions operate close to, or within, the quantum regime, but as yet no clear-cut example has been presented of non-trivial quantum effects at work in a key biological process.
While this last objection may no longer be valid, the significance of the Zeno effect in determining the rate of quantum decoherence in biological systems remains unknown.
In popular culture
Greg EganGreg Egan
Greg Egan is an Australian science fiction author.Egan published his first work in 1983. He specialises in hard science fiction stories with mathematical and quantum ontology themes, including the nature of consciousness...
uses the effect to explain the construction of a hydrogen-annihilation
Annihilation
Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....
-powered rocket in his short story 'Glory', and the Doctor Who
Doctor Who
Doctor Who is a British science fiction television programme produced by the BBC. The programme depicts the adventures of a time-travelling humanoid alien known as the Doctor who explores the universe in a sentient time machine called the TARDIS that flies through time and space, whose exterior...
episodes "Blink
Blink (Doctor Who)
"Blink" is the 10th episode of the third series of the new production of the British science fiction television series Doctor Who. It was first broadcast on 9 June 2007, and is the only episode in the 2007 series written by Steven Moffat; the episode is based on a previous short story written by...
", "The Time of Angels
The Time of Angels
"The Time of Angels" is the fourth episode in the fifth series of British science fiction television series Doctor Who, first broadcast on 24 April 2010 on BBC One. It is the first episode of a two-part story written by showrunner Steven Moffat and directed by Adam Smith; the second episode was...
", and "Flesh and Stone
Flesh and Stone
"Flesh and Stone" is the fifth episode of the fifth series of British science fiction television series Doctor Who. Written by showrunner Steven Moffat and directed by Adam Smith, the episode was first broadcast on 1 May 2010 on BBC One...
" feature an alien species called the Weeping Angels
Weeping Angels
The Weeping Angels are a fictional ancient race of aliens from the Doctor Who television series, featured in the Tenth Doctor episode "Blink", and the Eleventh Doctor episodes "The Time of Angels", "Flesh and Stone" and in a cameo appearance in Series 6's "The God Complex"...
who exists in a quantum-locked state, unable to move while observed.
See also
- EinselectionEinselectionEinselection is short for environment - induced superselection, a nickname coined by Wojciech H. Zurek. Classicality is an emergent property induced in open quantum systems by their environments...
- Interference (wave propagation)
- Measurement problemMeasurement problemThe measurement problem in quantum mechanics is the unresolved problem of how wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer...
- Quantum decoherenceQuantum decoherenceIn quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
- Quantum DarwinismQuantum darwinismQuantum Darwinism is a theory explaining the emergence of the classical world from the quantum world as due to a process of Darwinian natural selection; where the many possible quantum states are selected against in favor of a stable pointer state. It is proposed by Wojciech Zurek and a group of...
- Reality tunnelReality tunnelReality tunnel is a term coined by Timothy Leary and popularised by Robert Anton Wilson , akin to the idea of representative realism....
- Wavefunction collapseWavefunction collapseIn quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...
- Zeno's paradoxesZeno's paradoxesZeno's paradoxes are a set of problems generally thought to have been devised by Greek philosopher Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is...
External links
- Zeno.qcl A computer program written in QCL which demonstrates the Quantum Zeno effect