Electromagnetic mass

4/3 problem of the electromagnetic mass of electronsClassical charged particleselectromagnetic mass of a charged particleelectromagnetic rest masselectromagnetic worldviewPoincaré stresses
Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles.wikipedia
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J. J. Thomson

J.J. ThomsonJoseph John ThomsonSir J. J. Thomson
It was first derived by J. J. Thomson in 1881 and was for some time also considered as a dynamical explanation of inertial mass per se.
He examined the electromagnetic theory of light of James Clerk Maxwell, introduced the concept of electromagnetic mass of a charged particle, and demonstrated that a moving charged body would apparently increase in mass.

Length contraction

Lorentz contractionLorentz–FitzGerald contractionFitzGerald contraction
On the other hand, already in 1899 Lorentz assumed that the electrons undergo length contraction in the line of motion, which leads to results for the acceleration of moving electrons that differ from those given by Abraham.
So he had to introduce another ad hoc hypothesis: non-electric binding forces (Poincaré stresses) that ensure the electron's stability, give a dynamical explanation for length contraction, and thus hide the motion of the stationary aether.

Oliver Heaviside

HeavisideHeaviside, OliverHeaviside|Heaviside's operators
This idea was worked out in more detail by Oliver Heaviside (1889), Thomson (1893), George Frederick Charles Searle (1897), Max Abraham (1902), Hendrik Lorentz (1892, 1904), and was directly applied to the electron by using the Abraham–Lorentz force.
In the late 1880s and early 1890s, Heaviside worked on the concept of electromagnetic mass.

Mass–energy equivalence

mass-energy equivalencemass-energyE=mc²
Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence.
This concept was called electromagnetic mass, and was considered as being dependent on velocity and direction as well.

George Frederick Charles Searle

G. F. C. SearleGeorge Searle
This idea was worked out in more detail by Oliver Heaviside (1889), Thomson (1893), George Frederick Charles Searle (1897), Max Abraham (1902), Hendrik Lorentz (1892, 1904), and was directly applied to the electron by using the Abraham–Lorentz force.
Searle is known for his work on the velocity dependence of the electromagnetic mass.

Kaufmann–Bucherer–Neumann experiments

Kaufmann's experimentsresults supporting the predictions of Lorentz, Einstein, and the special theory of relativity
In 1905 Kaufmann conducted another series of experiments (Kaufmann–Bucherer–Neumann experiments) which confirmed Abraham's and Bucherer's predictions, but contradicted Lorentz's theory and the "fundamental assumption of Lorentz and Einstein", i.e., the relativity principle.
This was connected with the theoretical prediction of the electromagnetic mass by J. J. Thomson in 1881, who showed that the electromagnetic energy contributes to the mass of a moving charged body.

Walter Kaufmann (physicist)

Walter KaufmannKaufmannWalter Kaufman
From Searle's formula, Walter Kaufmann (1901) and Abraham (1902) derived the formula for the electromagnetic mass of moving bodies:
Kaufmann's early work (1901–1903) confirmed for the first time the velocity dependence of the electromagnetic mass (later called relativistic mass) of the electron.

Higgs mechanism

electroweak symmetry breakingHiggsAbelian Higgs model
As to the cause of mass of elementary particles, the Higgs mechanism in the framework of the relativistic Standard Model is currently used.

Renormalization

renormalizablerenormalisationrenormalized
Such questions are discussed in connection with renormalization, and on the basis of quantum mechanics and quantum field theory, which must be applied when the electron is considered physically point-like.
The mass of a charged particle should include the mass-energy in its electrostatic field (electromagnetic mass).

Friedrich Hasenöhrl

F. HasenöhrlFriedrich Hasenohrl
In 1904, Friedrich Hasenöhrl specifically associated inertia with radiation by studying the dynamics of a moving cavity.
:for the so-called "electromagnetic mass", which expresses how much electromagnetic energy contributes to the mass of bodies.

Classical electron radius

electron radiusclassical particle radiusclassical radius
where e is the charge, uniformly distributed on the surface of a sphere, and a is the classical electron radius, which must be nonzero to avoid infinite energy accumulation.
* Electromagnetic mass

Abraham–Lorentz force

radiation reactionAbraham–Lorentz–Dirac forceradiation reaction force
This idea was worked out in more detail by Oliver Heaviside (1889), Thomson (1893), George Frederick Charles Searle (1897), Max Abraham (1902), Hendrik Lorentz (1892, 1904), and was directly applied to the electron by using the Abraham–Lorentz force.

Spacetime

space-timespace-time continuumspace and time
Laue found a solution equivalent to Poincaré's introduction of a non-electromagnetic potential (Poincaré stresses), but Laue showed its deeper, relativistic meaning by employing and advancing Hermann Minkowski's spacetime formalism.
In addition, Einstein in 1905 superseded previous attempts of an electromagnetic mass-energy relation by introducing the general equivalence of mass and energy, which was instrumental for his subsequent formulation of the equivalence principle in 1907, which declares the equivalence of inertial and gravitational mass. By using the mass-energy equivalence, Einstein showed, in addition, that the gravitational mass of a body is proportional to its energy content, which was one of early results in developing general relativity.

Fritz Rohrlich

Another solution was found by authors such as Enrico Fermi (1922), Paul Dirac (1938) Fritz Rohrlich (1960), or Julian Schwinger (1983), who pointed out that the electron's stability and the 4/3-problem are two different things.

Classical mechanics

Newtonian mechanicsNewtonian physicsclassical
Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles.

Electromagnetic field

electromagnetic fieldselectromagneticEMF
Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles.

Self-energy

quantum particleDyson equationmass renormalization
Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles.

Electric charge

chargeelectrical chargecharged
Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles.

Mass

inertial massgravitational massweight
It was first derived by J. J. Thomson in 1881 and was for some time also considered as a dynamical explanation of inertial mass per se. Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence.

Momentum

conservation of momentumlinear momentummomenta
Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence.

Velocity

velocitiesvelocity vectorlinear velocity
Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence.

Albert Einstein

EinsteinEinsteinianA. Einstein
Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence.

Special relativity

special theory of relativityrelativisticspecial
Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence.

Elementary particle

elementary particlesparticleparticles
As to the cause of mass of elementary particles, the Higgs mechanism in the framework of the relativistic Standard Model is currently used.

Standard Model

standard model of particle physicsThe Standard ModelStandard Model of Physics
As to the cause of mass of elementary particles, the Higgs mechanism in the framework of the relativistic Standard Model is currently used.