In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory.
[1][2] The complementarity principle holds that certain pairs of complementary properties cannot all be observed or measured simultaneously.
Bohr considered one of the foundational truths of quantum mechanics to be the fact that setting up an experiment to measure one quantity of a pair, for instance the position of an electron, excludes the possibility of measuring the other, yet understanding both experiments is necessary to characterize the object under study.
Consequently, there is no "single picture" that unifies the results obtained in these different experimental contexts, and only the "totality of the phenomena" together can provide a completely informative description.
[3] Complementarity as a physical model derives from Niels Bohr's 1927 lecture during the Como Conference in Italy, at a scientific celebration of the work of Alessandro Volta 100 years previous.
[4]: 103 Bohr's subject was complementarity, the idea that measurements of quantum events provide complementary information through seemingly contradictory results.
[5] While Bohr's presentation was not well received, it did crystallize the issues ultimately leading to the modern wave-particle duality concept.
The wave theory of light, broadly successful for over a hundred years, had been challenged by Planck's 1901 model of blackbody radiation and Einstein's 1905 interpretation of the photoelectric effect.
These theoretical models use discrete energy, a quantum, to describe the interaction of light with matter.
Despite confirmation by various experimental observations, the photon theory (as it came to be called later) remained controversial until Arthur Compton performed a series of experiments from 1922 to 1924 demonstrating the momentum of light.
[7]: 211 The experimental evidence of particle-like momentum seemingly contradicted other experiments demonstrating the wave-like interference of light.
Many experiments by J. J. Thompson, Robert Millikan, and Charles Wilson, among others, had shown that free electrons had particle properties.
In his Como lecture he says: "our interpretation of the experimental material rests essentially upon the classical concepts.
Niels Bohr apparently conceived of the principle of complementarity during a skiing vacation in Norway in February and March 1927, during which he received a letter from Werner Heisenberg regarding an as-yet-unpublished result, a thought experiment about a microscope using gamma rays.
To Bohr, Heisenberg's paper did not make clear the distinction between a position measurement merely disturbing the momentum value that a particle carried and the more radical idea that momentum was meaningless or undefinable in a context where position was measured instead.
[8] Heisenberg duly appended a note to this effect to his paper, before its publication, stating: Bohr has brought to my attention [that] the uncertainty in our observation does not arise exclusively from the occurrence of discontinuities, but is tied directly to the demand that we ascribe equal validity to the quite different experiments which show up in the [particulate] theory on one hand, and in the wave theory on the other hand.Bohr publicly introduced the principle of complementarity in a lecture he delivered on 16 September 1927 at the International Physics Congress held in Como, Italy, attended by most of the leading physicists of the era, with the notable exceptions of Einstein, Schrödinger, and Dirac.
However, these three were in attendance one month later when Bohr again presented the principle at the Fifth Solvay Congress in Brussels, Belgium.
The lecture was published in the proceedings of both of these conferences, and was republished the following year in Naturwissenschaften (in German) and in Nature (in English).
[9] In his original lecture on the topic, Bohr pointed out that just as 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 capture this new situation in epistemology created by quantum theory.
Frescura and Basil Hiley have summarized the reasons for the introduction of the principle of complementarity in physics as follows:[10] In the traditional view, it is assumed that there exists a reality in space-time and that this reality is a given thing, all of whose aspects can be viewed or articulated at any given moment.
By using one particular piece of apparatus only certain features could be made manifest at the expense of others, while with a different piece of apparatus another complementary aspect could be made manifest in such a way that the original set became non-manifest, that is, the original attributes were no longer well defined.
For Bohr, this was an indication that the principle of complementarity, a principle that he had previously known to appear extensively in other intellectual disciplines but which did not appear in classical physics, should be adopted as a universal principle.Complementarity was a central feature of Bohr's reply to the EPR paradox, an attempt by Albert Einstein, Boris Podolsky and Nathan Rosen to argue that quantum particles must have position and momentum even without being measured and so quantum mechanics must be an incomplete theory.
[11] The thought experiment proposed by Einstein, Podolsky and Rosen involved producing two particles and sending them far apart.
Given that result, they could in principle make a precise prediction of what the corresponding measurement on the other, faraway particle would find.
[12] Later expositions of complementarity by Bohr include a 1938 lecture in Warsaw[13][14] and a 1949 article written for a festschrift honoring Albert Einstein.
[13] This mathematical expression of complementarity builds on the work of Hermann Weyl and Julian Schwinger, starting with Hilbert spaces and unitary transformation, leading to the theorems of mutually unbiased bases.
[24][25] In 1979 Wooters and Zurek introduced an information-theoretic treatment of the double-slit experiment providing on approach to a quantiative model of complementarity.
[26][27] The wave-particle relation, introduced by Daniel Greenberger and Allaine Yasin in 1988, and since then refined by others,[28] quantifies the trade-off between measuring particle path distinguishability,
The detailed definition of the two terms vary among applications,[28] but the relation expresses the verified constraint that efforts to detect particle paths will result in less visible wave interference.
[29]The Consistent histories interpretation of quantum mechanics takes a generalized form of complementarity as a key defining postulate.