Background 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. Bohr's subject was complementarity, the idea that measurements of quantum events provide complementary information through seemingly contradictory results. While Bohr's presentation was not well received, it did crystallize the issues ultimately leading to the modern wave-particle duality concept. The contradictory results that triggered Bohr's ideas had been building up over the previous 20 years. This contradictory evidence came both from light and from electrons. 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. The experimental evidence of particle-like momentum seemingly contradicted other experiments demonstrating the wave-like interference of light. The contradictory evidence from electrons arrived in the opposite order. Many experiments by
J. J. Thompson,
Robert Millikan, and
Charles Wilson, among others, had shown that free electrons had particle properties. However, in 1924,
Louis de Broglie proposed that electrons had an associated wave and
Schrödinger demonstrated that wave equations accurately account for electron properties in atoms. Again some experiments showed particle properties and others wave properties. Bohr's resolution of these contradictions is to accept them. In his Como lecture he says: "our interpretation of the experimental material rests essentially upon the classical concepts." 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). 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. Physicists F.A.M. Frescura and
Basil Hiley have summarized the reasons for the introduction of the principle of complementarity in physics as follows:
Debate following the lectures 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. The
thought experiment proposed by Einstein, Podolsky and Rosen involved producing two particles and sending them far apart. The experimenter could choose to measure either the position or the momentum of one particle. Given that result, they could in principle make a precise prediction of what the corresponding measurement on the other, faraway particle would find. To Einstein, Podolsky and Rosen, this implied that the faraway particle must have precise values of both quantities whether or not that particle is measured in any way. Bohr argued in response that the deduction of a position value could not be transferred over to the situation where a momentum value is measured, and vice versa. Later expositions of complementarity by Bohr include a 1938 lecture in
Warsaw and a 1949 article written for a
festschrift honoring Albert Einstein. It was also covered in a 1953 essay by Bohr's collaborator
Léon Rosenfeld. ==Mathematical formalism==