Electromagnetic mass

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.

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

It was recognized by J. J. Thomson in 1881[1] that a charged sphere moving in a space filled with a medium of a specific inductive capacity (the electromagnetic aether of James Clerk Maxwell), is harder to set in motion than an uncharged body.

(Similar considerations were already made by George Gabriel Stokes (1843) with respect to hydrodynamics, who showed that the inertia of a body moving in an incompressible perfect fluid is increased.

[2]) So due to this self-induction effect, electrostatic energy behaves as having some sort of momentum and "apparent" electromagnetic mass, which can increase the ordinary mechanical mass of the bodies, or in more modern terms, the increase should arise from their electromagnetic self-energy.

This idea was worked out in more detail by Oliver Heaviside (1889),[3] Thomson (1893),[4] George Frederick Charles Searle (1897),[5] Max Abraham (1902),[6] Hendrik Lorentz (1892, 1904),[7][8] and was directly applied to the electron by using the Abraham–Lorentz force.

When one body attracts another one, the electromagnetic energy store of gravitation is according to Wien diminished by the amount (where

He wrote:[4] [p. 21] When in the limit v = c, the increase in mass is infinite, thus a charged sphere moving with the velocity of light behaves as if its mass were infinite, its velocity therefore will remain constant, in other words it is impossible to increase the velocity of a charged body moving through the dielectric beyond that of light.In 1897, Searle gave a more precise formula for the electromagnetic energy of charged sphere in motion:[5] and like Thomson he concluded: ... when v = c the energy becomes infinite, so that it would seem to be impossible to make a charged body move at a greater speed than that of light.From Searle's formula, Walter Kaufmann (1901) and Max Abraham (1902) derived the formula for the electromagnetic mass of moving bodies:[6] However, it was shown by Abraham (1902), that this value is only valid in the longitudinal direction ("longitudinal mass"), i.e., that the electromagnetic mass also depends on the direction of the moving bodies with respect to the aether.

to unity, thus:[8] So, eventually Lorentz arrived at the same conclusion as Thomson in 1893: no body can reach the speed of light because the mass becomes infinitely large at this velocity.

[14][15] In the following years experiments by Alfred Bucherer (1908), Gunther Neumann (1914) and others seemed to confirm Lorentz's mass formula.

These pressures or tensions in the electromagnetic field were derived by James Clerk Maxwell (1874) and Adolfo Bartoli (1876).

(unlike contemporaries like Thomson[4] who used fluid descriptions) This represents a violation of the reaction principle that was accepted by Lorentz consciously.

He continued by saying, that one can only speak about fictitious tensions, since they are only mathematical models in his theory to ease the description of the electrodynamic interactions.

He tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields and radiation are involved.

But this electromagnetic fluid is not indestructible, because it can be absorbed by matter (which according to Poincaré was the reason why he regarded the em-fluid as "fictitious" rather than "real").

As it was later done by Einstein, an easy solution of this would be to assume that the mass of em-field is transferred to matter in the absorption process.

However, since only matter and electromagnetic energy are directly observable by experiment (not the non-em-fluid), Poincaré's resolution still violates the reaction principle and the COM-theorem, when an emission/absorption process is practically considered.

This leads to a paradox when changing frames: if waves are radiated in a certain direction, the device will suffer a recoil from the momentum of the fictitious fluid.

He then goes on to address the possibility that all matter might share this same quality and thereby his position changes from viewing aether as a "fictitious fluid" to suggesting it might be the only thing that actually exists in the universe, finally stating "In this system there is no actual matter, there are only holes in the aether."

Finally he repeats this exact problem of "Newton's principle" from 1904 again in 1908 publication[23] in his section on "the principle of reaction" he notes that the actions of radiation pressure cannot be tied solely to matter in light of Fizeau's proof that the Hertz notion of total ether drag is untenable.

Again, an electromagnetic explanation must be sought of all the known forces, in particular of gravitation, or at least the law of gravitation must be so modified that this force is altered by velocity in the same way as the electromagnetic forces.Thus Poincaré's mass of a fictitious fluid led him to, instead, later find that the mass of matter itself was "fictitious."

However, Hasenöhrl stated that this energy-apparent-mass relation only holds as long a body radiates, i.e. if the temperature of a body is greater than 0 K.[26][B 3]: 359–360 The idea that the principal relations between mass, energy, momentum and velocity can only be considered on the basis of dynamical interactions of matter was superseded, when Albert Einstein found out in 1905 that considerations based on the special principle of relativity require that all forms of energy (not only electromagnetic) contribute to the mass of bodies (mass–energy equivalence).

This is for example the case in the current quantum field explanation of mass of elementary particles in the framework of the Standard Model, the Higgs mechanism.

Because of this, the idea that any form of mass is completely caused by interactions with electromagnetic fields, is not relevant any more.

Later it was shown by physicists like Richard Chace Tolman[30] that expressing mass as the ratio of force and acceleration is not advantageous.

[B 6] Many different reformulations of the Abraham–Lorentz force have been derived – for instance, in order to deal with the 4⁄3-problem (see next section) and other problems that arose from this concept.

[B 7] A rigorous derivation of the electromagnetic self-force, including the contribution to the mass of the body, was published by Gralla et al.

Another solution was found by authors such as Enrico Fermi (1922),[33] Paul Dirac (1938)[34] Fritz Rohrlich (1960),[35] or Julian Schwinger (1983),[36] who pointed out that the electron's stability and the 4/3-problem are two different things.

However, binding forces like the Poincaré stresses are still necessary to prevent the electron from exploding due to Coulomb repulsion.

[B 4] Also other solutions have been proposed, for instance, Valery Morozov (2011)[37] gave consideration to movement of an imponderable charged sphere.