Meaning

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 the narrow orthodox form, it is stated that a single quantum mechanical entity can either behave as a particle or as wave, but never simultaneously as both; that a stronger manifestation of the particle nature leads to a weaker manifestation of the wave nature and vice versa. This article needs additional references or sources for verification. ... Fig. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ... Niels (Henrik David) Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... Copenhagen (IPA: or ; Danish: IPA: ) is the capital of Denmark and the countrys largest city. ... Werner Heisenberg Werner Karl Heisenberg (December 5, 1901 – February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics. ... Fig. ... In quantum physics, the Heisenberg uncertainty principle, sometimes called the Heisenberg indeterminacy principle, expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle. ... Separate articles treat Eastern Orthodox Christianity and Orthodox Judaism. ...

Nature

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. In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ... In quantum physics, the Heisenberg uncertainty principle is a mathematical property of a pair of canonical conjugate quantities - usually stated in a form of reciprocity of spans of their spectra. ... In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units. ...

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. In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ... Hannes Alfvén (1908-1995), winning the Nobel Prizing for his work on magnetohydrodynamics [1]. List of Nobel Prize laureates in Physics from 1901 to the present day. ... “Einstein” redirects here. ... Niels (Henrik David) Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in 1922. ... Werner Karl Heisenberg (December 5, 1901 – February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ...

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.) In quantum physics, the Heisenberg uncertainty principle is a mathematical property of a pair of canonical conjugate quantities - usually stated in a form of reciprocity of spans of their spectra. ...

Experiments

Various neutron interferometry experiments demonstrate the subtleness of the notions of duality and complementarity in an interesting way. By passing through the interferometer, the neutron appears to act as a wave. Yet upon passage, the neutron is subject to gravitation, which one might think only particles, and not waves, are subject to. 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 a photon (or an electron) of corresponding wavelength. In physics, a neutron interferometer is an interferometer capable of diffracting neutrons, allowing the wave-like nature of neutrons, and other related phenomena, to be explored. ... Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, to form a greater picture based on the combination of the two sources. ... This article or section does not adequately cite its references or sources. ... “Gravity” redirects here. ... A gravitational field is a model used within physics to explain how gravity exists in the universe. ... A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ...

See also

• Afshar experiment
• Copenhagen interpretation
• Englert-Greenberger duality relation
• Ehrenfest's theorem
• Interpretation of quantum mechanics
• Wave-particle duality
• Quantum entanglement
• Quantum indeterminacy

In physics, and more specifically, quantum mechanics, the Afshar experiment is an optical experiment, devised by Shahriar S. Afshar in 2004, that its proponents claim disproves Niels Bohrs principle of complementarity. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... The Englert-Greenberger duality relation relates the visibility, , of interference fringes with the definiteness, or distinguishability, , of the photons paths in quantum optics. ... The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ... It has been suggested that Quantum mechanics, philosophy and controversy be merged into this article or section. ... In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ... It has been suggested that Quantum coherence be merged into this article or section. ... Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. ...

External links

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

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.

Marlan Scully is a theoretical physicist best known for his work in quantum optics. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... Quantum decoherence is the general term for the consequences of irreversible quantum entanglement. ... Irreversibility is that property of an event which makes reverting back to the state before the occurrence of the event impossible. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ... In quantum physics, the Heisenberg uncertainty principle is a mathematical property of a pair of canonical conjugate quantities - usually stated in a form of reciprocity of spans of their spectra. ...

References and notes