Classical nonradiation conditions define the conditions according toclassical electromagnetism under which a distribution of acceleratingcharges will not emitelectromagnetic radiation. According to theLarmor formula in classical electromagnetism, a singlepoint charge underacceleration will emit electromagnetic radiation. In some classical electron models a distribution of charges can however be accelerated so that no radiation is emitted.[1] The modern derivation of these nonradiation conditions byHermann A. Haus is based on the Fourier components of the current produced by a moving point charge. It states that a distribution of accelerated charges will radiateif and only if it hasFourier components synchronous with waves traveling at thespeed of light.[2]
Finding a nonradiating model for theelectron on an atom dominated the early work onatomic models. In aplanetary model of the atom, the orbiting point electron would constantly accelerate towards thenucleus, and thus according to theLarmor formula emitelectromagnetic waves. In 1910Paul Ehrenfest published a short paper on "Irregular electrical movements without magnetic and radiation fields" demonstrating thatMaxwell's equations allow for the existence of accelerating charge distributions which emit no radiation.[3] In 1913, theBohr model of the atom abandoned the efforts to explain why its bound electrons do not radiate bypostulating that they did not radiate. This was later subsumed by a postulate of quantum theory called theSchrödinger 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 theelectron orbiting the nucleus) may have radiationless orbits.[4] Admitting that such speculation was out of fashion, he suggests that his solution may apply to the structure of theneutron. In 1948, Bohm and Weinstein also found that charge distributions may oscillate without radiation; they suggest that a solution which may apply tomesons.[5] 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 containedspin and could conceivably be used to describefundamental particles. Goedecke was led by his discovery to speculate:[6]
Naturally, it is very tempting to hypothesize from this that the existence ofPlanck'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 articleClassical Electron Models.[7] A Reed College undergraduate thesis on nonradiation ininfinite planes andsolenoids appears in 1984.[8] An important advance occurred in 1986, whenHermann Haus derived Goedecke's condition in a new way.[2] Haus finds that all radiation is caused byFourier components of the charge/current distribution that are lightlike (i.e. components that are synchronous withlight speed). When adistribution has no lightlike Fourier components, such as apoint charge in uniform motion, then there is no radiation. Haus uses his formulation to explainCherenkov radiation in which the speed of light in the surrounding medium is less thanc.