In

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

,

**complementarity** is a basic principle of

quantum theoryQuantum 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...

proposed by

Niels BohrNiels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

, closely identified with the

Copenhagen interpretationThe Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

, and refers to effects such as the

wave–particle dualityWave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects...

. Just like the finitude of the speed of light implies the impossibility of a sharp separation between space and time (relativity), the finitude of the quantum of action implies the impossibility of a sharp separation between the behavior of a system and its interaction with the measuring instruments and leads to the well known difficulties with the concept of 'state' in quantum theory; the notion of complementarity is intended to symbolize this new situation in epistemology created by quantum theory. Some people consider it a philosophical adjunct to

quantum mechanicsQuantum 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...

, while others consider it to be a discovery that is as important as the formal aspects of quantum theory. For instance,

Leon RosenfeldLéon Rosenfeld was a Belgian physicist. He obtained a PhD at the University of Liège in 1926, and he was a collaborator of the physicist Niels Bohr. He did early work in quantum electrodynamics that predates by two decades the work by Dirac and Bergmann. He coined the name lepton...

has stated that "[...] complementarity is not a philosophical superstructure invented by Bohr to be placed as a decoration on top of the quantal formalism, it is the bedrock of the quantal description."

In a restricted sense, complementarity is the idea that classical concepts such as space-time location and energy-momentum, which in classical physics were always combined into a single picture, cannot be so combined in quantum mechanics. In any given situation, the use of certain classical concepts excludes the simultaneous meaningful application of other classical concepts. For example, if an apparatus of screens and shutters is used to localize a particle in space-time, momentum-energy concepts become inapplicable. This is reflected in the formalism in the fact that a localized wave-packet is a superposition of

plane waveIn the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....

s, and therefore does not have a definite energy-momentum. This reciprocal limitation in the possibilities of definition of complementary concepts corresponds exactly to the limitations of the classical picture, where any attempt at the localization of a particle through objects such as slits in diaphragms introduces the possibility of an exchange of momentum with those objects, which is in principle uncontrollable if those objects are to serve their intended purpose of defining a space-time frame. Another famous example is '

Heisenberg's microscopeHeisenberg's microscope exists only as a thought experiment, one that was proposed by Werner Heisenberg, criticized by his mentor Niels Bohr, and subsequently served as the nucleus of some commonly held ideas, and misunderstandings, about Quantum Mechanics...

', which Heisenberg first discovered using his uncertainty relations.

The notion of complementarity was first introduced in a paper by Bohr published in Nature called "The Quantum Postulate and the Recent Development of Atomic Theory". An article written by Bohr called "Discussions with Einstein on Epistemological Problems in Atomic Physics" is considered to be a definitive description of the notion of complementarity.

## Nature

The complementarity principle states that some objects have multiple properties that appear to be contradictory. Sometimes it is possible to switch back and forth between different views of an object to observe these properties, but in principle, it is impossible to view both at the same time, despite their simultaneous coexistence in reality. For example, we can think of an

electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

as either a

particleA point particle is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space...

or a

waveIn physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

, depending on the situation. An object that's both a particle

*and* a wave would seem to be impossible because, normally, such things are mutually exclusive. Nonetheless, an electron is truly 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 transformIn mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

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 principleIn quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

and

Planck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...

. Complementarity and Uncertainty dictate that all properties and actions in the physical world are therefore non-deterministic to some degree.

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 that 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., Bandyopadhyay (2000), 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 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 positionThe Afshar experiment is an optical experiment, devised and carried out by Shahriar Afshar in 2001, which investigates the principle of complementarity in quantum mechanics...

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

neutronThe neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

appears to act as a wave. Yet upon passage, the neutron is subject to

gravitationGravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

. As the neutron interferometer is rotated through Earth's

gravitational fieldThe gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

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 to 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
The Afshar experiment is an optical experiment, devised and carried out by Shahriar Afshar in 2001, which investigates the principle of complementarity in quantum mechanics...

- Bohr–Einstein debates
The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr, who were two of its founders. Their debates are remembered because of their importance to the philosophy of science. An account of them has been written by Bohr in an article...

- Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

- Englert–Greenberger duality relation
- Ehrenfest's theorem
- Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...

- Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...

- Quantum indeterminacy
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...

- Transactional interpretation
The transactional interpretation of quantum mechanics describes quantum interactions in terms of a standing wave formed by retarded and advanced waves. It was first proposed in 1986 by John G...

## Further reading

- Berthold-Georg Englert
Berthold-Georg Englert is Provost's Chair Professor at the National University of Singapore, and Principal Investigator at the Centre for Quantum Technologies. In 2006, he was recognized for outstanding contributions to theoretical research on quantum coherence. B.-G...

, Marlan O. Scully & Herbert WaltherProf. Dr. Dr. Herbert Walther was an internationally acclaimed leader in the fields of quantum optics and laser physics. He was born in Ludwigshafen/Rhein in 1935 and died near Munich in 2006. He was a founding director of the Max Planck Institute of Quantum Optics in Garching, Germany. He also...

, *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 interferenceIn physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater or lower amplitude. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have...

effects destroyed, by decoherence (irreversibleIn science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....

object-apparatus correlationsThe framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....

), and not, as was previously popularly believed, by Heisenberg's uncertainty principleIn quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

itself.
- Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

, *Causality and Complementarity: Supplementary papers edited by Jan Faye and Henry J. Folse. The Philosophical Writings of Niels Bohr, Volume IV*. Ox Bow Press. 1998.

## External links