ENSEMBLE INTERPRETATION
- + Add to Faves
- + Translate
- + Share
العربية
ä¸å›½
Français
Deutsch
Ελληνική
हिनà¥à¤¦à¥€
Italiano
日本語
Português
РуÑÑкий
Español
The 'Ensemble Interpretation', or 'Statistical Interpretation' of quantum mechanics, is an interpretation that can be viewed as a minimalist interpretation; it is a quantum mechanical interpretation that claims to make the fewest assumptions associated with the standard mathematical formalization. At its heart, it takes the statistical interpretation of Max Born to the fullest extent. The interpretation states that the wave function does not apply to an individual system – or for example, a single particle – but is an abstract mathematical, statistical quantity that only applies to an ensemble of similar prepared systems or particles. Probably the most notable supporter of such an interpretation was Albert Einstein:
To date, probably the most prominent advocate of the Ensemble Interpretation is Leslie E. Ballentine, Professor at Simon Fraser University, and writer of the graduate-level textbook "Quantum Mechanics, A Modern Development".
The ensemble interpretation, unlike other interpretations to the Copenhagen Interpretation , does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process, or make any other statement about the real nature of quantum phenomena; it is simply a statement as to the manner of wave function interpretation. It is identical in all of its predictions as is the standard interpretations.
The attraction of the ensemble interpretation is that it immediately dispenses with the metaphysical issues associated with reduction of the state vector, Schrödinger cat states, and other issues related to the concepts of multiple simultaneous states. As the ensemble interpretation postulates that the wave function only applies to an ensemble of systems, there is no requirement for any single system to exist in more than one state at a time, hence, the wave function is never physically required to be "reduced". This can be illustrated by an example:
Consider a classical die. If this is expressed in Dirac notation, the "state" of the die can be represented by a "wave" function describing the probability of an outcome given by:
:
It is clear that on each throw, only one of the states will be observed, but it is also clear that there is no requirement for any notion of collapse of the wave function/reduction of the state vector, or for the die to physically exist in the summed state. In the ensemble interpretation, wave function collapse would make as much sense as saying that the number of children a couple produced, collapsed to 3 from its average value of 2.4.
The state function is not taken to be physically real, or be a literal summation of states. The wave function, is taken to be an abstract statistical function, only applicable to the statistics of repeated preparation procedures, in much the same way as classical statistical mechanics. It does not directly apply to a single experiment, only the statistical results of many.
David Mermin sees the Ensemble interpretation as being motivated by an adherence ("not always acknowledged") to classical principles.
He also emphasises the importance of ''describing'' single systems, rather than ensembles.
According to proponents of this interpretation, no single system is ever required to be postulated to exist in a physical mixed state so the state vector does not need to collapse.
It can also be argued that this notion is consistent with the standard interpretation in that, in the CI, statements about the exact system state prior to measurement can not be made. That is, if it were possible to absolutely, physically measure say, a particle in two positions at once, then QM would be falsified as QM explicitly postulates that the result of any measurement must be a single eigen value of a single eigenstate.
Like John Gribbin, Alfred Nuemaier find fault with the applicability of the Ensemble Interpretation to small systems.
The claim that the wave functional approach fails ''to apply'' to single particle experiments cannot be taken as a claim that quantum fails in describing single-particle phenomena. In fact, it gives correct results within the limits of a probablistic or stochastic theory.
Probability always require a set of multiple data, and thus single-particle experiments are
really part of an ensemble — an ensemble of individual experiments that are performed one after the other over time. In particular, the interference fringes seen in the double slit experiment require repeated trials to be observed.
One possible criticism is that the procedure described is essentially frequentist. The frequentist approach suffices for ''classical'' probability, but quantum mechanics is a theory of quantum probability, which is more general.[3][4]
Leslie Ballantine promoted the Ensemble Interpretation in his book "Quantum Mechanics, A Modern Development". In it [5], he described what he called the "Watched Pot Experiment". His argument was
that, under certain circmstances, a repeatedly measured system, such as an unstable nucleus, would be prevented from decaying by the act of measurement itself. He initially presented this as a kind of reductio ad absurdum of wave function collapse. [6]
The effect has been shown to be real. (It is more widely known as the quantum Zeno effect). He later wrote papers claiming that it could be explained without wave function collapse.[7]
Early proponents of statistical approaches regarded quantum mechanics as an approximation to
a classical theory. John Gribbin writes:
However, hopes for turning quantum mechanics back into a classical theory were dashed. Gribbin continues:
1. Mermin, N.D. ''The Ithaca interpretation''
2. Alfred Neumaier's FAQ
3. Stanford Encyclopedia of Philosophy
4. Baez, J. ''Bayesian probability Theory and Quantum Mechanics''
5. Ballentine, L. ''Quantum Mechanics, A Modern Development''(p 342)
6. "Like the old
saying "A watched pot never boils", we have been led to the conclusion that a
contineously observed system never changes its state!
This conclusion is, of course false. The fallacy clearly results from the
assertion that if an observation indicates no decay, then the state vector must
be |y_u>. Each successive observation in the sequence would then "reduce" the
state back to its initial value |y_u>, and in the limit of continuous
observation there could be no change at all. Here we see that it is disproven by the simple empirical fact that [..] continuous observation does not prevent motion. It is sometimes claimed that the
rival interpretations of quantum mechanics differ only in philosophy, and can
not be experimentally distinguished. That claim is not always true. as this
example proves" ".Ballentine, L. ''Quantum Mechanics, A Modern Development''(p 342)
7. "The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any ‘‘collapse of the wave function,’’ but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of ‘‘wave-function collapse.’’" Physical Review
8. John Gribbin, ''Q for Quantum''
★ Quantum Mechanics as Wim Muynk sees it
★ Einstein's Reply to Criticisms
★ Kevin Aylwards's account of the Ensemble Interpretation
★ Detailed Ensemble Interpretation by Marcel Nooijen
★ Pechenkin, A.A. ''The early statistical interpretations of quantum mechanics''
★ Krüger, T. ''An attempt to close the Einstein–Podolsky–Rosen debate''
To date, probably the most prominent advocate of the Ensemble Interpretation is Leslie E. Ballentine, Professor at Simon Fraser University, and writer of the graduate-level textbook "Quantum Mechanics, A Modern Development".
The ensemble interpretation, unlike other interpretations to the Copenhagen Interpretation , does not attempt to justify, or otherwise derive, or explain quantum mechanics from any deterministic process, or make any other statement about the real nature of quantum phenomena; it is simply a statement as to the manner of wave function interpretation. It is identical in all of its predictions as is the standard interpretations.
| Contents |
| Measurement and Collapse |
| Criticism |
| Single particles |
| Criticism |
| The frequentist probability variation |
| Criticism |
| The quantum Zeno effect |
| Earlier Classical Ensemble Ideas |
| References |
| External links |
Measurement and Collapse
The attraction of the ensemble interpretation is that it immediately dispenses with the metaphysical issues associated with reduction of the state vector, Schrödinger cat states, and other issues related to the concepts of multiple simultaneous states. As the ensemble interpretation postulates that the wave function only applies to an ensemble of systems, there is no requirement for any single system to exist in more than one state at a time, hence, the wave function is never physically required to be "reduced". This can be illustrated by an example:
Consider a classical die. If this is expressed in Dirac notation, the "state" of the die can be represented by a "wave" function describing the probability of an outcome given by:
:
It is clear that on each throw, only one of the states will be observed, but it is also clear that there is no requirement for any notion of collapse of the wave function/reduction of the state vector, or for the die to physically exist in the summed state. In the ensemble interpretation, wave function collapse would make as much sense as saying that the number of children a couple produced, collapsed to 3 from its average value of 2.4.
The state function is not taken to be physically real, or be a literal summation of states. The wave function, is taken to be an abstract statistical function, only applicable to the statistics of repeated preparation procedures, in much the same way as classical statistical mechanics. It does not directly apply to a single experiment, only the statistical results of many.
Criticism
David Mermin sees the Ensemble interpretation as being motivated by an adherence ("not always acknowledged") to classical principles.
"For the notion that probabilistic theories must
be about ensembles implicitly assumes that probability is about ignorance. (The “hidden
variables†are whatever it is that we are ignorant of.) But in a non-determinstic world
probability has nothing to do with incomplete knowledge, and ought not to require an
ensemble of systems for its interpretation".
He also emphasises the importance of ''describing'' single systems, rather than ensembles.
"The second motivation for an ensemble interpretation is the intuition that because
quantum mechanics is inherently probabilistic, it only needs to make sense as a theory of
ensembles. Whether or not probabilities can be given a sensible meaning for individual
systems, this motivation is not compelling. For a theory ought to be able to describe as
well as predict the behavior of the world. The fact that physics cannot make deterministic
predictions about individual systems does not excuse us from pursuing the goal of being
able to describe them as they currently are."[1]
Single particles
According to proponents of this interpretation, no single system is ever required to be postulated to exist in a physical mixed state so the state vector does not need to collapse.
It can also be argued that this notion is consistent with the standard interpretation in that, in the CI, statements about the exact system state prior to measurement can not be made. That is, if it were possible to absolutely, physically measure say, a particle in two positions at once, then QM would be falsified as QM explicitly postulates that the result of any measurement must be a single eigen value of a single eigenstate.
Criticism
Like John Gribbin, Alfred Nuemaier find fault with the applicability of the Ensemble Interpretation to small systems.
"Among the traditional interpretations, the statistical interpretation
discussed by Ballentine in Rev. Mod. Phys. 42, 358-381 (1970) is the
least demanding (asssumes less than the Copenhagen interpretation
and the Many Worlds interpretation) and the most consistent one.
It explains almost everything, and only has the disatvantage that
it explicitly excludes the applicability of QM to single systems or very small ensembles (such as the few solar neutrinos or top quarks
actually detected so far), and does not bridge the gulf between
the classical domain (for the description of detectors) and the
quantum domain (for the description of the microscopic system)".
(emphasis added) [2]
The frequentist probability variation
The claim that the wave functional approach fails ''to apply'' to single particle experiments cannot be taken as a claim that quantum fails in describing single-particle phenomena. In fact, it gives correct results within the limits of a probablistic or stochastic theory.
Probability always require a set of multiple data, and thus single-particle experiments are
really part of an ensemble — an ensemble of individual experiments that are performed one after the other over time. In particular, the interference fringes seen in the double slit experiment require repeated trials to be observed.
Criticism
One possible criticism is that the procedure described is essentially frequentist. The frequentist approach suffices for ''classical'' probability, but quantum mechanics is a theory of quantum probability, which is more general.[3][4]
The quantum Zeno effect
Leslie Ballantine promoted the Ensemble Interpretation in his book "Quantum Mechanics, A Modern Development". In it [5], he described what he called the "Watched Pot Experiment". His argument was
that, under certain circmstances, a repeatedly measured system, such as an unstable nucleus, would be prevented from decaying by the act of measurement itself. He initially presented this as a kind of reductio ad absurdum of wave function collapse. [6]
The effect has been shown to be real. (It is more widely known as the quantum Zeno effect). He later wrote papers claiming that it could be explained without wave function collapse.[7]
Earlier Classical Ensemble Ideas
Early proponents of statistical approaches regarded quantum mechanics as an approximation to
a classical theory. John Gribbin writes:
"The basic idea is that each quantum entity (such as an electron or a photon) has precise quantum properties (such as position or momentum) and the quantum wavefunction is related to the probability of getting a particular experimental result when one member (or many members) of the ensemble is selected by an experiment"
However, hopes for turning quantum mechanics back into a classical theory were dashed. Gribbin continues:
[8]
"There are many difficulties with the idea, but the killer blow was struck when individual quantum entities such as photons were observed behaving in experiments in line with the quantum wave function description. The Ensemble interpretation is now only of historical interest"
References
1. Mermin, N.D. ''The Ithaca interpretation''
2. Alfred Neumaier's FAQ
3. Stanford Encyclopedia of Philosophy
4. Baez, J. ''Bayesian probability Theory and Quantum Mechanics''
5. Ballentine, L. ''Quantum Mechanics, A Modern Development''(p 342)
6. "Like the old
saying "A watched pot never boils", we have been led to the conclusion that a
contineously observed system never changes its state!
This conclusion is, of course false. The fallacy clearly results from the
assertion that if an observation indicates no decay, then the state vector must
be |y_u>. Each successive observation in the sequence would then "reduce" the
state back to its initial value |y_u>, and in the limit of continuous
observation there could be no change at all. Here we see that it is disproven by the simple empirical fact that [..] continuous observation does not prevent motion. It is sometimes claimed that the
rival interpretations of quantum mechanics differ only in philosophy, and can
not be experimentally distinguished. That claim is not always true. as this
example proves" ".Ballentine, L. ''Quantum Mechanics, A Modern Development''(p 342)
7. "The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any ‘‘collapse of the wave function,’’ but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of ‘‘wave-function collapse.’’" Physical Review
8. John Gribbin, ''Q for Quantum''
External links
★ Quantum Mechanics as Wim Muynk sees it
★ Einstein's Reply to Criticisms
★ Kevin Aylwards's account of the Ensemble Interpretation
★ Detailed Ensemble Interpretation by Marcel Nooijen
★ Pechenkin, A.A. ''The early statistical interpretations of quantum mechanics''
★ Krüger, T. ''An attempt to close the Einstein–Podolsky–Rosen debate''
This article provided by Wikipedia. To edit the contents of this article, click here for original source.
psst.. try this: add to faves
