Magnetic Monopole(redirected from Dirac-Zwanziger-Schwinger quantization condition)
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magnetic monopole[mag′ned·ik ′män·ə‚pōl]
the laws of nature reveal a high degree of similarity between electric and magnetic fields, and the field equations established by J. Maxwell are the same for both. There is, however, a major difference: whereas particles with electric charges, positive and negative, are seen constantly in nature and create a Coulomb electric field in the surrounding space, neither positive nor negative magnetic charges have ever been found alone. A magnet always has two poles, one at each end—positive and negative and equal in magnitude. The magnetic field around the magnet is the field produced by both poles.
The laws of classical electrodynamics admit the existence of particles with a single magnetic pole—magnetic monopoles— and give specific equations for their field and motion. The laws contain no prohibitions that would rule out the existence of magnetic monopoles.
The situation is somewhat different in quantum mechanics. Consistent equations of motion can be constructed for a charged particle moving in the field of a magnetic monopole and for a magnetic monopole moving in the field of a particle only if the electric charge e of the particle and the magnetic charge jut of the magnetic monopole are related by the equation
Where ħ is Planck’s constant, c is the speed of light, and n is a positive or negative integer. This condition comes about because particles are represented in quantum mechanics as waves, and interference effects appear in the motion of particles of one type under the influence of particles of another type. If a magnetic monopole with magnetic charge μ exists, then formula (1) requires that all charged particles in its vicinity have a charge e equal to an integral multiple of the quantity ħc/2μ. Thus, electric charges must be quantized.
However, it is precisely the phenomenon that all observed charges are multiples of the electron charge that is one of the fundamental laws of nature. If a magnetic monopole existed, this law would have a natural explanation. No other explanation of the quantization of electric charge is known.
Taking e as the charge of an electron, the value of which is determined by the equation e2/ħc = 1/137, one may obtain from formula (1) the least magnetic charge μo of a monopole, defined by the equation Thus, μo is much greater than e. It follows that the track of a fast magnetic monopole in a cloud chamber or bubble chamber should stand out against a background of the tracks of other particles. Although painstaking searches have been made for these tracks, no magnetic mono-poles have as yet been detected.
The magnetic monopole is a stable particle and cannot disappear until it encounters another monopole that has a magnetic charge equal in magnitude and opposite in sign. If magnetic monopoles are generated by the high-energy cosmic rays that continuously strike the earth, then they should be encountered everywhere on the earth’s surface. They have been sought, but they have not been found. It is not known whether this is because magnetic monopoles are generated only very infrequently or because they do not exist at all.
P. A. M. DIRAC
[Editor’s note: The hypothesis of the existence of the magnetic monopole—a particle that has a positive or a negative magnetic charge—was first advanced by P. A. M. Dirac in 1931. The magnetic monopole is therefore also known as Dirac’s mono-pole.]
REFERENCESDirac, P. A. M. “Quantised Singularities in the Magnetic Field.” Proceedings of the Royal Society, series A, 1931, vol. 133, no. 821.
Devons, S. “Poiski magnitnogo monoplia.” Uspekhi fizicheskikh nauk, 1965, vol. 85, fasc. 4, pp. 755-60. (With a supplement by B. M. Bolotovskii, pp. 761-62.)
Shvinger, Iu. “Magnitnaia model’ materii.” Uspekhi fizicheskikh nauk, 1971, vol. 103, fasc. 2, pp. 355-65.
MonopoV Diraka. Moscow, 1970. (Collection of articles, translated from English; edited by B. M. Bolotovskii and Iu. D. Usachev.)