nonradiation condition

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.

{{cite journal

| title = Ungleichförmige Elektrizitätsbewegungen ohne Magnet- und Strahlungsfeld

| year = 1910

| author = Ehrenfest, Paul

| author-link = Paul Ehrenfest

| journal = Physikalische Zeitschrift

| volume = 11

| pages = 708–709

}} In 1913, the Bohr model of the atom abandoned the efforts to explain why its bound electrons do not radiate by postulating that they did not radiate. This was later subsumed by a postulate of quantum theory called the Schrödinger 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.

{{cite journal

| doi = 10.1080/14786443309462219

| title = The Electromagnetic Field of a Moving Uniformly and Rigidly Electrified Sphere and its Radiationless Orbits

| year = 1933

| author = Schott, G. A.

| author-link = George Adolphus Schott

| journal = Philosophical Magazine

| volume = 15

| series = 7

| pages = 752–761

}}

• {{cite web |date=June 19, 2008 |title=Invisibility Physics: Schott's radiationless orbits |website=Skulls in the Stars |url=http://skullsinthestars.com/2008/06/19/invisibility-physics-schotts-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.

{{cite journal

| doi = 10.1103/PhysRev.74.1789

| title = The Self-Oscillations of a Charged Particle

| year = 1948

| author = Bohm, D. | author-link = David Bohm

| author2 = Weinstein, M.

| journal = Physical Review

| volume = 74

| issue = 12

| pages = 1789–1798

| bibcode = 1948PhRv...74.1789B

}} 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:

{{cite journal

| doi = 10.1103/PhysRev.135.B281

| title = Classically Radiationless Motions and Possible Implications for Quantum Theory

| year = 1964

| author = Goedecke, G. H.

| journal = Physical Review

| volume = 135

| issue = 1B

| pages = B281–B288

| bibcode = 1964PhRv..135..281G

}}

{{cquote|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.

{{cite book

| doi = 10.1007/978-1-4757-0650-5_7

| title = Electromagnetism: paths to research.

| chapter = Classical Electron Models

| year = 1982

| author = Pearle, Philip

| editor = Teplitz, Doris

| location = New York

| publisher = Plenum

| pages = 211–295

| isbn = 978-1-4757-0652-9

}} A Reed College undergraduate thesis on nonradiation in infinite planes and solenoids appears in 1984.

{{cite journal

|doi=10.1119/1.14084

|title=Acceleration without radiation

|journal=American Journal of Physics

|volume=53|issue=12|pages=1203|year=1985

|last1=Abbott|first1=Tyler A

|last2=Griffiths|first2=David J|author-link2=David J. Griffiths

|bibcode=1985AmJPh..53.1203A

|osti=1447538

}} 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 in the surrounding medium is less than c.

• The nonradiation condition is important to the study of invisibility physics.{{citation needed|date=June 2016}}

• Sommerfeld radiation condition
• Frank–Tamm formula

{{reflist}}

• [http://skullsinthestars.com/2008/04/19/invisibility-physics-acceleration-without-radiation-part-i/ Invisibility Physics: Acceleration without radiation, part I]

Category:Electromagnetism

Category:Boundary conditions