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La condizione classica di non radiazione è la condizione per cui in elettromagnetismo classico una distribuzione di cariche elettriche non emette radiazione elettromagnetica. In elettromagnetismo classico secondo la formula di Larmor, una carica puntiforme accelerata emette radiazione elettromagnetica, ovvero luce. In alcuni modelli classici dell'elettrone una distribuzione di cariche può accelerare senza che ci sia emissione di radiazione. La derivazione moderna di queste condizioni di non radiazione da parte di Hermann A. Haus si basa sulle componenti di Fourier della corrente prodotta da una carica puntiforme in movimento. Essa afferma che una distribuzione di cariche accelerata emette radiazione se e solo se le sue componenti di Fourier sono It states that a distribution of accelerated charges will radiate if and only if it has Fourier components synchronous with waves traveling at the speed of light.

History
Finding a nonradiating model for the electron on an atom dominated the early work on atomic models. In a planetary model of the atom, the orbiting point electron would constantly accelerate towards the nucleus, and thus according to the Larmor formula emit electromagnetic waves. In 1910 Paul Ehrenfest published a short paper on "Irregular electrical movements without magnetic and radiation fields" demonstrating that Maxwell's equations allow for the existence of accelerating charge distributions which emit no radiation. The need for a nonradiating classical electron was however abandoned in 1913 by the Bohr model of the atom, which postulated that electrons orbiting the nucleus in particular circular orbits with fixed angular momentum and energy would not radiate. Modern atomic theory explains these stable quantum states with the help of Schrödinger's equation.

In the meantime, our understanding of classical nonradiation has been considerably advanced since 1925. Beginning as early as 1933, George Adolphus Schott published a surprising discovery that a charged sphere in accelerated motion (such as the electron orbiting the nucleus) may have radiationless orbits. Admitting that such speculation was out of fashion, he suggests that his solution may apply to the structure of the neutron. In 1948, Bohm and Weinstein also found that charge distributions may oscillate without radiation; they suggest that a solution which may apply to mesons. Then in 1964, Goedecke derived, for the first time, the general condition of nonradiation for an extended charge-current distribution, and produced many examples, some of which contained spin and could conceivably be used to describe fundamental particles. Goedecke was led by his discovery to speculate: Naturally, it is very tempting to hypothesize from this that the existence of Planck's constant is implied by classical electromagnetic theory augmented by the conditions of no radiation. Such a hypothesis would be essentially equivalent to suggesting a 'theory of nature' in which all stable particles (or aggregates) are merely nonradiating charge-current distributions whose mechanical properties are electromagnetic in origin.

The nonradiation condition went largely ignored for many years. Philip Pearle reviews the subject in his 1982 article Classical Electron Models. A Reed College undergraduate thesis on nonradiation in infinite planes and solenoids appears in 1984. An important advance occurred in 1986, when Hermann Haus derived Goedecke's condition in a new way. Haus finds that all radiation is caused by Fourier components of the charge/current distribution that are lightlike (i.e. components that are synchronous with light speed). When a distribution has no lightlike Fourier components, such as a point charge in uniform motion, then there is no radiation. Haus uses his formulation to explain Cherenkov radiation in which the speed of light of the surrounding medium is less than c.

Collegamenti esterni

 * Invisibility Physics: Acceleration without radiation, part I