complementarity

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In physics, complementarity is a basic principle of quantum theory closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality, in which different measurements made on a system reveal it to have either particle-like or wave-like properties. Niels Bohr is usually associated with this concept, which he developed at Copenhagen with Heisenberg, as a philosophical adjunct to the recently developed mathematics of quantum mechanics and in particular the Heisenberg uncertainty principle. In its narrow orthodox form, complementarity is the notion that a single quantum mechanical entity can behave either as a particle or as wave, but never simultaneously as both; a stronger manifestation of the particle nature leads to a weaker manifestation of the wave nature and vice versa.

Nature

The principle states that sometimes an object can have several (apparently) contradictory properties. Sometimes we can switch back and forth between the different views, but we can never see both at the same time. But in reality, the figure exists as BOTH at the same time, but we can only perceive or view it one at a time, and never together. For example, we can think of electrons as both a particle or a wave or stream of particles depending on the situation. An object being a particle AND a wave is seemingly mutually exclusive and not possible. But an electron, in some sense, is both at once.

A profound aspect of complementarity is that it not only applies to measurability or knowability of some property of a physical entity, but more importantly it applies to the limitations of that physical entity’s very manifestation of the property in the physical world. All properties of physical entities exist only in pairs, which Bohr described as complementary or conjugate pairs (-which are also Fourier transform pairs). Physical reality is determined and defined by manifestations of properties which are limited by trade-offs between these complementary pairs. For example, an electron can manifest a greater and greater accuracy of its position only in even trade for a complementary loss in accuracy of manifesting its momentum. This means that there is a limitation on the precision with which an electron can possess (i.e., manifest) position, since an infinitely precise position would dictate that its manifested momentum would be infinitely imprecise, or undefined (i.e., non-manifest or not possessed), which is not possible. The ultimate limitations in precision of property manifestations are quantified by the Heisenberg uncertainty principle and Planck units. Complementarity and Uncertainty dictate that all properties and actions in the physical world are therefore non-deterministic to some degree.

Complementarity or wave–particle duality is considered to be one of the distinguishing characteristics of quantum mechanics, whose theoretical and experimental development has been honoured by more than a few Nobel Prizes for Physics. It has been discussed by prominent physicists for the last 100 years, from the time of Albert Einstein, Niels Bohr and Werner Heisenberg, onwards.

The emergence of complementarity in a system occurs when one considers the circumstances under which one attempts to measure its properties; as Bohr noted, the principle of complementarity "implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear." It is important to distinguish, as did Bohr in his original statements, the principle of complementarity from a statement of the uncertainty principle. For a technical discussion of contemporary issues surrounding complementarity in physics, see, e.g., [1] (from which parts of this discussion were drawn.)

Experiments

The quintessential example of wave–particle complementarity in the laboratory is the double slit. The crux of the complementary behavior is the question, "What can be said about the particles in the experiment?" or "What information exists – embedded in the constituents of the universe – that can reveal the history of the signal particles as they pass through the double slit?". If information exists (even if it is not measured by a conscious observer) that reveals "which slit" each particle traversed, then each particle will exhibit no wave interference with the other slit. This is the particle-like behavior. But if no information exists about which slit – so that no conscious observer, no matter how well equipped, will ever be able to determine which slit each particle traverses – then the signal particles will interfere with themselves as if they traveled through both slits at the same time, as a wave. This is the wave-like behavior. These behaviors are complementary, according to the Englert-Greenberger duality relation, because when one behavior is observed the other is absent. Both behaviors can be observed at the same time, but each only as lesser manifestations of their full behavior (as determined by the duality relation). This superposition of complementary behaviors exists whenever there is partial "which slit" information. While there is some contention to the duality relation, and thus complementarity itself, the contrary position is not accepted by mainstream physics.

Various neutron interferometry experiments demonstrate the subtlety of the notions of duality and complementarity. By passing through the interferometer, the neutron appears to act as a wave. Yet upon passage, the neutron is subject to gravitation. As the neutron interferometer is rotated through Earth's gravitational field a phase change between the two arms of the interferometer can be observed, accompanied by a change in the constructive and destructive interference of the neutron waves on exit from the interferometer. Some interpretations claim that understanding the interference effect requires one to concede that a single neutron takes both paths through the interferometer at the same time; a single neutron would "be in two places at once", as it were. Since the two paths through a neutron interferometer can be as far as five to 15 cm apart, the effect is hardly microscopic. This is similar to traditional double-slit and mirror interferometer experiments where the slits (or mirrors) can be arbitrarily far apart. So, in interference and diffraction experiments, neutrons behave the same way as photons (or electrons) of corresponding wavelength.

See also

• Afshar experiment
• Bohr–Einstein debates
• Copenhagen interpretation
• Englert–Greenberger duality relation
• Ehrenfest's theorem
• Interpretation of quantum mechanics
• Quantum entanglement
• Quantum indeterminacy
• Transactional interpretation

References

Further reading

• Berthold-Georg Englert, Marlan O. Scully & Herbert Walther, Quantum Optical Tests of Complementarity , Nature, Vol 351, pp 111–116 (9 May 1991) and (same authors) The Duality in Matter and Light Scientific American, pg 56-61, (December 1994). Demonstrates that complementarity is enforced, and quantum interference effects destroyed, by decoherence (irreversible object-apparatus correlations), and not, as was previously popularly believed, by Heisenberg's uncertainty principle itself.

External links

• Niels Bohr's report of conversations with Einstein about complementarity and Einstein's reply.[2]