[4] There are, however, two analogs of the formula that are both fully quantum and relativistic: one is called the "Abraham–Lorentz–Dirac–Langevin equation",[5] the other is the self-force on a moving mirror.
Since this would represent an effect occurring before its cause (retrocausality), some theories have speculated that the equation allows signals to travel backward in time, thus challenging the physical principle of causality.
[8] Furthermore, some authors argue that a radiation reaction force is unnecessary, introducing a corresponding stress-energy tensor that naturally conserves energy and momentum in Minkowski space and other suitable spacetimes.
The formula is consistent with special relativity and reduces to Lorentz's self-force expression for low velocity limit.
The covariant form of radiation reaction deduced by Dirac for arbitrary shape of elementary charges is found to be:[12][13]
[14] However, dipole antenna experiments by Heinrich Hertz made a bigger impact and gathered commentary by Poincaré on the amortissement or damping of the oscillator due to the emission of radiation.
[15][16][17] Qualitative discussions surrounding damping effects of radiation emitted by accelerating charges was sparked by Henry Poincaré in 1891.
[18][19] In 1892, Hendrik Lorentz derived the self-interaction force of charges for low velocities but did not relate it to radiation losses.
[20] Suggestion of a relationship between radiation energy loss and self-force was first made by Max Planck.
[21] Planck's concept of the damping force, which did not assume any particular shape for elementary charged particles, was applied by Max Abraham to find the radiation resistance of an antenna in 1898, which remains the most practical application of the phenomenon.
[22] In the early 1900s, Abraham formulated a generalization of the Lorentz self-force to arbitrary velocities, the physical consistency of which was later shown by George Adolphus Schott.
The reason for this is twofold: These conceptual problems created by self-fields are highlighted in a standard graduate text.
[Jackson] The difficulties presented by this problem touch one of the most fundamental aspects of physics, the nature of the elementary particle.
While there is still hope that this may eventually occur, the present quantum-mechanical discussions are beset with even more elaborate troubles than the classical ones.
It is one of the triumphs of comparatively recent years (~ 1948–1950) that the concepts of Lorentz covariance and gauge invariance were exploited sufficiently cleverly to circumvent these difficulties in quantum electrodynamics and so allow the calculation of very small radiative effects to extremely high precision, in full agreement with experiment.
The self-fields in quantum electrodynamics generate a finite number of infinities in the calculations that can be removed by the process of renormalization.
The simplest derivation for the self-force is found for periodic motion from the Larmor formula for the power radiated from a point charge that moves with velocity much lower than that of speed of light:
A more rigorous derivation, which does not require periodic motion, was found using an effective field theory formulation.
[28][29] A generalized equation for arbitrary velocities was formulated by Max Abraham, which is found to be consistent with special relativity.
An alternative derivation, making use of theory of relativity which was well established at that time, was found by Dirac without any assumption of the shape of the charged particle.
In other words, it forms the length (or time, or energy) scale where something as light as an electron would be fully relativistic.
However the antidamping mechanism resulting from the Abraham–Lorentz force can be compensated by other nonlinear terms, which are frequently disregarded in the expansions of the retarded Liénard–Wiechert potential.
Radiation damping acts as a limiting factor for the plasmonic excitations in surface-enhanced Raman scattering.
[32] The damping force was shown to broaden surface plasmon resonances in gold nanoparticles, nanorods and clusters.
[33][34][35] The effects of radiation damping on nuclear magnetic resonance were also observed by Nicolaas Bloembergen and Robert Pound, who reported its dominance over spin–spin and spin–lattice relaxation mechanisms for certain cases.
[36] The Abraham–Lorentz force has been observed in the semiclassical regime in experiments which involve the scattering of a relativistic beam of electrons with a high intensity laser.
However, interesting phenomena arise when a collection of charged particles is subjected to strong electromagnetic fields, such as in a plasma.
In such scenarios, the collective behavior of the plasma can significantly modify its properties due to radiation reaction effects.
Theoretical studies have shown that in environments with strong magnetic fields, like those found around pulsars and magnetars, radiation reaction cooling can alter the collective dynamics of the plasma.
[39][40][41] Specifically, in the high magnetic fields typical of these astrophysical objects, the momentum distribution of particles is bunched and becomes anisotropic due to radiation reaction forces, potentially driving plasma instabilities and affecting overall plasma behavior.