Copenhagen interpretation
From Wikipedia, the free encyclopedia
| Quantum physics |
 |
| Quantum mechanics |
| Fundamental concepts |
|
Decoherence · Interference |
| Experiments |
|
Double-slit experiment |
| Equations |
|
Schrödinger equation |
| Advanced theories |
|
Quantum field theory |
| Interpretations |
|
Copenhagen · Quantum logic |
| Scientists |
|
Planck · Schrödinger |
|
|
The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. Bohr and Heisenberg extended the probabilistic interpretation of the wave function, proposed by Max Born. Their interpretation attempts to answer some perplexing questions which arise as a result of the quantum mechanics, such as wave-particle duality and the measurement problem.
Contents |
[edit] Overview
There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.
- -- Aage Petersen paraphrasing Niels Bohr, Quantum Reality by Nick Herbert
There is no definitive statement of the Copenhagen Interpretation [1]since it consists of the views developed by a number of scientists and philosophers at the turn of the 20th Century. The following have been associated with the Copenhagen interpretation
[edit] Principles
- A system is completely described by a wave function ψ, which represents an observer's knowledge of the system. (Heisenberg)
- The description of nature is essentially probabilistic. The probability of an event is related to the square of the amplitude of the wave function. (Max Born)
- Heisenberg's uncertainty principle ensures that it is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities.
- (Complementary Principle) Matter exhibits a wave-particle duality. An experiment can show the particle like properties of matter, or wave-like properties, but not both at the same time.(Niels Bohr)
- Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.
- The Correspondence Principle of Bohr and Heisenberg, saying that the quantum mechanical description of large systems should closely approximate to the classical description.
[edit] The meaning of the wave function
The Copenhagen Interpretation denies that the wave function is real, or is at least non-committal about its reality.
There are some who say that there are objective variants of the Copenhagen Interpretation that allow for a "real" wave function, but it is questionable whether that view is really consistent with Positivism and some of Bohr's statements. Niels Bohr emphasized that Science is concerned with the predictions of experiments, additional questions are not scientific but rather meta-physical. Bohr was heavily influenced by Positivism. On the other hand, Bohr and Heisenberg were not in complete agreement, and took different views at different times. Heisenberg in particular was prompted to move towards realism.[2]
Even if the wave function is not regarded as real, there is still a divide between those who treat it as definitely and entirely subjective, and those who are non-committal or agnostic about the subject.
An example of the agnostic view is given by von Weiszacker, who, while participating in a colloquium at Cambridge, denied that the CI asserted: "What cannot be observed does not exist". He suggested instead that the CI follows the principle: "What is observed certainly exists; about what is not observed we are still free to make suitable assumptions. We use that freedom to avoid paradoxes."'[3];
The subjective view, that the wave function is merely a mathematical tool for calculating probabilities of specific experiment, is a similar approach to the Ensemble interpretation. Both approaches are tantamount to hidden variable theories, and are therefore jeopardized by the Aspect experiment as discussed below.
[edit] The nature of collapse
All versions of the Copenhagen interpretation include at least a formal or methodological version of wave function collapse.[4], in which unobserved eigenvalues are removed from further consideration. (In other words, Copenhagenists have never rejected collapse, even in the early days of quantum physics, in the way that many worlds adherents do).
An adherent of the subjective view, that the wave function represents nothing but knowledge, would take an equally subjective view of "collapse", as nothing more than an observer becoming informed about something that was previously ambiguous. The existence of collapse as an objective process, with obvious implications about the reality of the wave function, is more contentious.
It is maintained by some[5] that the concept of collapse of a "real" wave function was introduced by John Von Neumann and was not part of the original formulation of the Copenhagen Interpretation[citation needed]).
[edit] Acceptance among physicists
According to a poll at a Quantum Mechanics workshop in 1997, the Copenhagen interpretation is the most widely-accepted specific interpretation of quantum mechanics, followed by the Many-worlds interpretation.[6] Although current trends show substantial competition from alternative interpretations, throughout much of the twentieth century the Copenhagen interpretation had strong acceptance among physicists. John Gribbin [7] describes it as having fallen from primacy after the 1980's.
[edit] Consequences
The nature of the Copenhagen Interpretation is exposed by considering a number of experiments and paradoxes.
1. Schrödinger's Cat - A cat is put in a box with a radioactive source and a radiation detector. There is a 50-50 chance that a particle will be emitted and detected by the detector. If a particle is detected, a poisonous gas will be released and the cat killed. The wave function is in a 50-50 mixture of alive cat and dead cat. How can the cat be both alive and dead?
The Copenhagen Interpretation: The wave function reflects our knowledge of the system. The wave function 
simply means that there is a 50-50 chance that the cat is alive or dead.
2. Wigner's Friend - Wigner puts his friend in with the cat. The external observer believes the system is in the state . His friend however is convinced that cat is alive. I.e. for him, the cat is in the state | alive > . How can Wigner and his friend see different wave functions?
The Copenhagen Interpretation: Wigner's friend highlights the subject nature of probability. Each observer (Wigner and his friend) have different information and therefore different wave functions. The distinction between the "objective" nature of reality and the subjective nature of probability has lead to a great deal of controversy. C.f. Bayesian versus Frequentist interpretations of probability.
3. Double Slit Diffraction - Light passes through double slits and onto a screen resulting in a diffraction pattern. Is light a particle or a wave?
The Copenhagen Interpretation: Light is neither. A particular experiment can demonstrate particle (photon) or wave properties, but not both at the same time (Bohr's Complementary Principle).
The same experiment can in theory be performed with electrons, protons, atoms, molecules, viruses, bacteria, cats, humans, elephants and planets. In practice it has been performed for light, electrons, buckminsterfullerene, and some atoms. Matter in general exhibits both particle and wave behaviors.
4. EPR paradox. Entangled "particles" are emitted by a common source. Conservation laws ensure that the measured spin of one particle is the opposite of the measured spin of the other, so that if the spin of one particle is measured, the spin of the other particle is now instantaneously known.
The Copenhagen Interpretation: Assuming wave functions are not real, wave function collapse is interpreted subjectively. The moment one observer measures the spin of one particle, he knows the spin of the other. However another observer cannot benefit until the results of that measurement have been relayed to him, at less than or equal to the speed of light.
Copenhagenists claim that interpretations of quantum mechanics where the wave function is regarded as real have problems with EPR-type effects, since they imply that the laws of physics allow for influences to propagate at speeds greater than the speed of light. However, proponents of Many worlds [8] and the Transactional interpretation [9] [10] dispute that their theories are fatally non-local.
The claim that EPR effects violate the principle that information cannot travel faster than the speed of light can be avoided by noting that they cannot be used for signaling because neither observer can control, or predetermine what she observes, and therefore can not manipulate what the other observer measures. Relativistic difficulties about establishing which measurement occurred first also undermine the idea that one observer is causing the other's measurement.
In fact, it can be argued that the Subjective variant of the Copenhagen interpretation, where the wave function is taken to represent only the observer's knowledge of the situation, is severely undermined by these effects. Suppose that the spins of a pair of entangled particles are fixed (but unknown) at the time of emission. Then the subjective interpretation is straightfoward: the superposition of the wave function just represents lack of information on the part of the observers, and collapse represents their becoming aware. But this is a hidden variable approach; The information is ontologically present, but unknown. Moreover, it is a local hidden-variable approach, since the information is fixed at a precise space-time point, the event that creates the entangled pair. But such local hidden variables are ruled out by the Aspect experiment. Perhaps there are non-local hidden variables? But such non-local, yet ontologically real, phenomena are just what the Subjective Copenhagenism is trying to rule out. A subjective approach is left with the claim that the observers have subjective knowledge that isn't knowledge of anything. But the knowledge of the observers is still correlated. It is just that without either an ontologically real wave function, or local hidden variables, the correlation cannot be explained.
[edit] Criticisms
The completeness of quantum mechanics (thesis 1) was attacked by the Einstein-Podolsky-Rosen thought experiment which was intended to show that quantum physics could not be a complete theory.
Experimental tests of Bell's inequality using entangled particles have supported the predictions of quantum mechanics.
The Copenhagen Interpretation gives special status to measurement processes without cleanly defining them or explaining their peculiar effects. In his article entitled "Criticism and Counterproposals to the Copenhagen Interpretation of Quantum Theory," countering the view of Alexandrov that (in Heisenberg's paraphrase) "the wave function in configuration space characterizes the objective state of the electron." Heisenberg says,
Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory.
- -- Heisenberg, Physics and Philosophy, p. 137
Many physicists and philosophers have objected to the Copenhagen interpretation, both on the grounds that it is non-deterministic and that it includes an undefined measurement process that converts probability functions into non-probabilistic measurements. Einstein's comments "I, at any rate, am convinced that He (God) does not throw dice."[11] and "Do you really think the moon isn't there if you aren't looking at it?" exemplify this. Bohr, in response, said "Einstein, don't tell God what to do". Erwin Schrödinger devised the Schrödinger's cat experiment.
Steven Weinberg in "Einstein's Mistakes", Physics Today, November 2005, page 31, said:
- All this familiar story is true, but it leaves out an irony. Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?
- Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus.
The problem of thinking in terms of classical measurements of a quantum system becomes particularly acute in the field of quantum cosmology, where the quantum system is the universe.[12]
[edit] Alternatives
The Ensemble Interpretation is similar; it offers an interpretation of the wave function, but not for single particles. The consistent histories interpretation advertises itself as "Copenhagen done right". Consciousness causes collapse is often confused with the Copenhagen interpretation.
If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results. If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained. Dropping the principle that the wave function is a complete description results in a hidden variable theory.
Many physicists have subscribed to the null interpretation of quantum mechanics summarized by Paul Dirac's famous dictum "Shut up and calculate!" (often attributed to Richard Feynman).[13]
A list of alternatives can be found at Interpretation of quantum mechanics.
[edit] Notes
- ^ 'In fact Bohr and Heisenberg never totally agreed on how to understand the mathematical formalism of quantum mechanics, and none of them ever used the term “the Copenhagen interpretation” as a joint name for their ideas. In fact, Bohr once distanced himself from what he considered to be Heisenberg's more subjective interpretation Stanford Encyclopedia of Philosophy
- ^ "Historically, Heisenberg wanted to base quantum theory solely on observable quantities such as the intensity of spectral lines, getting rid of all intuitive (anschauliche) concepts such as particle trajectories in space-time [2]. This attitude changed drastically with his paper [3] in which he introduced the uncertainty relations – there he put forward the point of view that it is the theory which decides what can be observed. His move from positivism to operationalism can be clearly understood as a reaction on the advent of Schr¨odinger’s wave mechanics [1] which, in particular due to its intuitiveness, became soon very popular among physicists. In fact, the word anschaulich (intuitive) is contained in the title of Heisenberg’s paper [3]."Kiefer, C. On the interpretation of quantum theory – from Copenhagen to the present day
- ^ John Cramer on the Copenhagen Interpretation
- ^ "To summarise, one can identify the following ingredients as being characteristic for the Copenhagen interpretation(s)[...]Reduction of the wave packet as a formal rule without dynamical significance"Kiefer, C. On the interpretation of quantum theory – from Copenhagen to the present day
- ^ "the “collapse” or “reduction” of the wave function. This was introduced by Heisenberg in his uncertainty paper [3] and later postulated by von Neumann as a dynamical process independent of the Schrodinger equation"Kiefer, C. On the interpretation of quantum theory – from Copenhagen to the present day
- ^ The Many Worlds Interpretation of Quantum Mechanics
- ^ Gribbin, J. Q for Quantum
- ^ Michael price on nonlocality in Many Worlds
- ^ Relativity and Causality in the Transactional Interpretation
- ^ Collapse and Nonlocality in the Transactional Interpretation
- ^ "God does not throw dice" quote
- ^ 'Since the Universe naturally contains all of its observers, the problem arises to come up with an interpretation of quantum theory that contains no classical realms on the fundamental level.'Kiefer, C. On the interpretation of quantum theory from Copenhagen to the present day
- ^ "Shut up and calculate" quote.
[edit] See also
- Afshar experiment
- Bohr-Einstein debates
- Consciousness causes collapse
- Consistent Histories
- Ensemble Interpretation
- Interpretation of quantum mechanics
- Philosophical interpretation of classical physics
[edit] Further reading
- G. Weihs et al., Phys. Rev. Lett. 81 (1998) 5039
- M. Rowe et al., Nature 409 (2001) 791.
- J.A. Wheeler & W.H. Zurek (eds) , Quantum Theory and Measurement, Princeton University Press 1983
- A. Petersen, Quantum Physics and the Philosophical Tradition, MIT Press 1968
- H. Margeneau, The Nature of Physical Reality, McGraw-Hill 1950
- M. Chown, Forever Quantum, New Scientist No. 2595 (2007) 37.
[edit] Video Demonstration
[edit] External links
- Copenhagen Interpretation (Stanford Encyclopedia of Philosophy)
- Physics FAQ section about Bell's inequality
- The Copenhagen Interpretation of Quantum Mechanics
- Preprint of Afshar Experiment
- This Quantum World What is quantum mechanics trying to tell us about the nature of Nature?
