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quantum theory, modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles; the quantum theory and the theory of relativity together form the theoretical basis of modern physics. Just as the theory of relativity assumes importance in the special situation where very large speeds are involved, so the quantum theory is necessary for the special situation where very small quantities are involved, i.e., on the scale of molecules, atoms, and elementary particles. Aspects of the quantum theory have provoked vigorous philosophical debates concerning, for example, the uncertainty principle and the statistical nature of all the predictions of the theory.## Relationship of Energy and Matter

## Dual Nature of Waves and Particles

## Evolution of Quantum Theory

**Early Developments****Quantum Mechanics and Later Developments**## Bibliography

According to the older theories of classical physics, energy is treated solely as a continuous phenomenon, while matter is assumed to occupy a very specific region of space and to move in a continuous manner. According to the quantum theory, energy is held to be emitted and absorbed in tiny, discrete amounts. An individual bundle or packet of energy, called a quantum (pl. quanta), thus behaves in some situations much like particles of matter; particles are found to exhibit certain wavelike properties when in motion and are no longer viewed as localized in a given region but rather as spread out to some degree.

For example, the light or other radiation given off or absorbed by an atom has only certain frequencies (or wavelengths), as can be seen from the line spectrum associated with the chemical element represented by that atom. The quantum theory shows that those frequencies correspond to definite energies of the light quanta, or photons, and result from the fact that the electrons of the atom can have only certain allowed energy values, or levels; when an electron changes from one allowed level to another, a quantum of energy is emitted or absorbed whose frequency is directly proportional to the energy difference between the two levels.

The restriction of the energy levels of the electrons is explained in terms of the wavelike properties of their motions: electrons occupy only those orbits for which their associated wave is a standing wave (i.e., the circumference of the orbit is exactly equal to a whole number of wavelengths) and thus can have only those energies that correspond to such orbits. Moreover, the electrons are no longer thought of as being at a particular point in the orbit but rather as being spread out over the entire orbit. Just as the results of relativity approximate those of Newtonian physics when ordinary speeds are involved, the results of the quantum theory agree with those of classical physics when very large "quantum numbers" are involved, i.e., on the ordinary large scale of events; this agreement in the classical limit is required by the correspondence principle of Niels Bohr. The quantum theory thus proposes a dual nature for both waves and particles, one aspect predominating in some situations, the other predominating in other situations.

While the theory of relativity was largely the work of one man, Albert Einstein, the quantum theory was developed principally over a period of thirty years through the efforts of many scientists. The first contribution was the explanation of black body radiation in 1900 by Max Planck, who proposed that the energies of any harmonic oscillator (see harmonic motion), such as the atoms of a black body radiator, are restricted to certain values, each of which is an integral (whole number) multiple of a basic, minimum value. The energy *E* of this basic quantum is directly proportional to the frequency ν of the oscillator, or *E*=*h*ν, where *h* is a constant, now called Planck's constant, having the value 6.63×10^{-34} joule-second. In 1905, Einstein proposed that the radiation itself is also quantized according to this same formula, and he used the new theory to explain the photoelectric effect. Following the discovery of the nuclear atom by Rutherford (1911), Bohr used the quantum theory in 1913 to explain both atomic structure and atomic spectra, showing the connection between the electrons' energy levels and the frequencies of light given off and absorbed.

Quantum mechanics, the final mathematical formulation of the quantum theory, was developed during the 1920s. In 1924, Louis de Broglie proposed that not only do light waves sometimes exhibit particlelike properties, as in the photoelectric effect and atomic spectra, but particles may also exhibit wavelike properties. This hypothesis was confirmed experimentally in 1927 by C. J. Davisson and L. H. Germer, who observed diffraction of a beam of electrons analogous to the diffraction of a beam of light. Two different formulations of quantum mechanics were presented following de Broglie's suggestion. The wave mechanics of Erwin Schrödinger (1926) involves the use of a mathematical entity, the wave function, which is related to the probability of finding a particle at a given point in space. The matrix mechanics of Werner Heisenberg (1925) makes no mention of wave functions or similar concepts but was shown to be mathematically equivalent to Schrödinger's theory.

Quantum mechanics was combined with the theory of relativity in the formulation of P. A. M. Dirac (1928), which, in addition, predicted the existence of antiparticles. A particularly important discovery of the quantum theory is the uncertainty principle, enunciated by Heisenberg in 1927, which places an absolute theoretical limit on the accuracy of certain measurements; as a result, the assumption by earlier scientists that the physical state of a system could be measured exactly and used to predict future states had to be abandoned. Other developments of the theory include quantum statistics, presented in one form by Einstein and S. N. Bose (the Bose-Einstein statistics) and in another by Dirac and Enrico Fermi (the Fermi-Dirac statistics); quantum electrodynamics, concerned with interactions between charged particles and electromagnetic fields; its generalization, quantum field theory; and quantum electronics.

See W. Heisenberg, *The Physical Principles of the Quantum Theory* (1930) and *Physics and Philosophy* (1958); G. Gamow, *Thirty Years that Shook Physics* (1966); J. Gribbin, *In Search of Schrödinger's Cat* (1984).

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Licensed from Columbia University Press

Licensed from Columbia University Press

Branch of mathematical physics that deals with atomic and subatomic systems. It is concerned with phenomena that are so small-scale that they cannot be described in classical terms, and it is formulated entirely in terms of statistical probabilities. Considered one of the great ideas of the 20th century, quantum mechanics was developed mainly by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, and Max Born and led to a drastic reappraisal of the concept of objective reality. It explained the structure of atoms, atomic nuclei (*see* nucleus), and molecules; the behaviour of subatomic particles; the nature of chemical bonds (*see* bonding); the properties of crystalline solids (*see* crystal); nuclear energy; and the forces that stabilize collapsed stars. It also led directly to the development of the laser, the electron microscope, and the transistor.

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Theory that brings quantum mechanics and special relativity together to account for subatomic phenomena. In particular, the interactions of subatomic particles are described in terms of their interactions with fields, such as the electromagnetic field. However, the fields are quantized and represented by particles, such as photons for the electromagnetic field. Quantum electrodynamics is the quantum field theory that describes the interaction of electrically charged particles via electromagnetic fields. Quantum chromodynamics describes the action of the strong force. The electroweak theory, a unified theory of electromagnetic and weak forces, has considerable experimental support, and can likely be extended to include the strong force. Theories that include the gravitational force (*see* gravitation) are more speculative. *Seealso* grand unified theory, unified field theory.

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Quantum theory of the interactions of charged particles with the electromagnetic field. It describes the interactions of light with matter as well as those of charged particles with each other. Its foundations were laid by P. A. M. Dirac when he discovered an equation describing the motion and spin of electrons that incorporated both quantum mechanics and the theory of special relativity. The theory, as refined and developed in the late 1940s, rests on the idea that charged particles interact by emitting and absorbing photons. It has become a model for other quantum field theories.

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Experimental method of computing that makes use of quantum-mechanical phenomena. It incorporates quantum theory and the uncertainty principle. Quantum computers would allow a bit to store a value of 0 and 1 simultaneously. They could pursue multiple lines of inquiry simultaneously, with the final output dependent on the interference pattern generated by the various calculations. *Seealso* DNA computing, quantum mechanics.

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Theory that describes the action of the strong force. The strong force acts only on certain particles, principally quarks that are bound together in the protons and neutrons of the atomic nucleus, as well as in less stable, more exotic forms of matter. Quantum chromodynamics has been built on the concept that quarks interact via the strong force because they carry a form of “strong charge,” which has been given the name “colour.” The three types of charge are called red, green, and blue, in analogy to the primary colours of light, though there is no connection with the usual sense of colour.

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In physics, a discrete natural unit, or packet, of energy, charge, angular momentum, or other physical property. Light, for example, which appears in some respects as a continuous electromagnetic wave, on the submicroscopic level is emitted and absorbed in discrete amounts, or quanta; for light of a given wavelength, the magnitude of all the quanta emitted or absorbed is the same in both energy and momentum. These particlelike packets of light are called photons, a term also applicable to quanta of other forms of electromagnetic energy such as X rays and gamma rays. Submicroscopic mechanical vibrations in the layers of atoms comprising crystals also give up or take on energy and momentum in quanta called phonons. *Seealso* quantum mechanics.

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Quantum theory may mean:## See also

In science:

- Old quantum theory under the Bohr model
- Quantum mechanics, an umbrella term sometimes for all of quantum physics, but sometimes for just non-relativistic theories
- Quantum field theory, a generic type of relativistic quantum theory, which includes:
- Quantum gravity, a general term for theories intended to quantize general relativity
- Quantum optics

In popular culture:

- "Quantum Theory", the final song from Jarvis, by Jarvis Cocker

- Introduction to quantum mechanics
- Continuum theories, roughly opposite to quantum theories

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