Complementarity

In physics, complementarity is a basic principle of quantum theory proposed by Niels Bohr, closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality.

Simultaneous Coexistence in Reality

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 electron as either a particle or a wave, 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.

The Impossibility of a Sharp Separation

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 mechanics, while others consider it to be a discovery that is as important as the formal aspects of quantum theory. For instance, Leon Rosenfeld 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 waves, 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 microscope’, 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

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.

The emergence of complementarity

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.“[3] 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 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 5 cm 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.