Nonradiation condition
Encyclopedia
Classical nonradiation conditions define the conditions according to classical electromagnetism
under which a distribution of accelerating charge
s will not emit electromagnetic radiation
. According to the Larmor formula
in classical electromagnetism, a single point charge under acceleration
will emit electromagnetic radiation, i.e. light
. In some classical electron models a distribution of charges can however be accelerated so that no radiation is emitted. The modern derivation of these nonradiation conditions by Hermann 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 radiate if and only if
it has Fourier components synchronous with waves traveling at the speed of light
.
on an atom dominated the early work on atom
ic 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 meanwhile, 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 meson
s. Then in 1964, Goedeke 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. Goedeke was led by his discovery to speculate:
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 solenoid
s appears in 1984. An important advance occurred in 1986, when Hermann Haus derived Goedeke’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 Cerenkov radiation in which the speed of light of the surrounding medium is less than c.
Classical electromagnetism
Classical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents...
under which a distribution of accelerating charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
s will not emit electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
. According to the Larmor formula
Larmor formula
In physics, in the area of electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J...
in classical electromagnetism, a single point charge under acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
will emit electromagnetic radiation, i.e. light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
. In some classical electron models a distribution of charges can however be accelerated so that no radiation is emitted. The modern derivation of these nonradiation conditions by Hermann A. Haus
Hermann A. Haus
Hermann Anton Haus was a Slovene-American physicist, electrical engineer, and Institute Professor at the Massachusetts Institute of Technology. Haus' research and teaching ranged from fundamental investigations of quantum uncertainty as manifested in optical communications to the practical...
is based on the Fourier components of the current produced by a moving point charge. It states that a distribution of accelerated charges will radiate if and only if
If and only if
In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....
it has Fourier components synchronous with waves traveling at the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
.
History
Finding a nonradiating model for the electronElectron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
on an atom dominated the early work on atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
ic models. In a planetary model
Rutherford model
The Rutherford model or planetary model is a model of the atom devised by Ernest Rutherford. Rutherford directed the famous Geiger-Marsden experiment in 1909, which suggested on Rutherford's 1911 analysis that the so-called "plum pudding model" of J. J. Thomson of the atom was incorrect...
of the atom, the orbiting point electron would constantly accelerate towards the nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
, and thus according to the Larmor formula
Larmor formula
In physics, in the area of electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J...
emit electromagnetic waves. In 1910 Paul Ehrenfest
Paul Ehrenfest
Paul Ehrenfest was an Austrian and Dutch physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem.- Biography :Paul Ehrenfest was born and grew up in Vienna in a Jewish...
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
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...
of the atom, which postulated that electrons orbiting the nucleus in particular circular orbits with fixed angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
and energy would not radiate. Modern atomic theory
Atomic theory
In chemistry and physics, atomic theory is a theory of the nature of matter, which states that matter is composed of discrete units called atoms, as opposed to the obsolete notion that matter could be divided into any arbitrarily small quantity...
explains these stable quantum states with the help of Schrödinger's equation.
In the meanwhile, our understanding of classical nonradiation has been considerably advanced since 1925. Beginning as early as 1933, George Adolphus Schott
George Adolphus Schott
George Adolphus Schott FRS was a British mathematician. He is best known for developing the full theory of radiation from electrons travelling at close to the speed of light....
published a surprising discovery that a charged sphere in accelerated motion (such as the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
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
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
. In 1948, Bohm and Weinstein also found that charge distributions may oscillate without radiation; they suggest that a solution which may apply to meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s. Then in 1964, Goedeke 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
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
and could conceivably be used to describe fundamental particles. Goedeke was led by his discovery to speculate:
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 solenoid
Solenoid
A solenoid is a coil wound into a tightly packed helix. In physics, the term solenoid refers to a long, thin loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it. Solenoids are important because they can create...
s appears in 1984. An important advance occurred in 1986, when Hermann Haus derived Goedeke’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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
). When a distribution
Distribution function
In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables, f, which gives the number of particles per unit volume in phase space. It is the number of particles per unit volume having approximately the velocity near the place and time...
has no lightlike Fourier components, such as a point charge in uniform motion, then there is no radiation. Haus uses his formulation to explain Cerenkov radiation in which the speed of light of the surrounding medium is less than c.
Applications
- The nonradiation condition is important to the study of invisibility physics.
- Randell Mills uses the nonradiation condition as the foundation for his model of the hydrogen atom, in which the electron is a two-dimensional extended membrane of negative charge that is stable according to this condition. Mills' model is controversial and not accepted by the scientific community, which currently accepts the theory of quantum mechanics in which the electron does not need to obey classical physics.