Abraham–Lorentz force

In the <a href="/facts/Physics/a7aH2y08">physics</a> of <a href="/facts/Electromagnetism/oAkmALHT">electromagnetism</a>, the Abraham–Lorentz force (also known as the Lorentz–Abraham force) is the reaction force on an accelerating <a href="/facts/Charged_particle/2zqBJGse">charged particle</a> caused by the particle emitting <a href="/facts/Electromagnetic_radiation/Ynx7ujCW">electromagnetic radiation</a> by self-interaction. It is also called the radiation reaction force, the radiation damping force, or the self-force. It is named after the physicists <a href="/facts/Max_Abraham/WbFbE3GT">Max Abraham</a> and <a href="/facts/Hendrik_Lorentz/JbBpKFyr">Hendrik Lorentz</a>.
The formula, although predating the theory of <a href="/facts/Special_relativity/vsFFc63E">special relativity</a>, was initially calculated for non-relativistic velocity approximations. It was extended to arbitrary velocities by <a href="/facts/Max_Abraham/WbFbE3GT">Max Abraham</a> and was shown to be physically consistent by <a href="/facts/George_Adolphus_Schott/RcJP439U">George Adolphus Schott</a>. The non-relativistic form is called Lorentz self-force while the relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of <a href="/facts/Classical_physics/gGnINVPE">classical physics</a>, not <a href="/facts/Quantum_physics/BRc3Mzgr">quantum physics</a>, and therefore may not be valid at distances of roughly the <a href="/facts/Compton_wavelength/og2h1J2q">Compton wavelength</a> or below. There are, however, two analogs of the formula that are both fully quantum and relativistic: one is called the "Abraham–Lorentz–Dirac–Langevin equation", the other is the self-force on a moving mirror.
The force is proportional to the square of the object's <a href="/facts/Electric_charge/xxsBfmlB">charge</a>, multiplied by the <a href="/facts/Jerk_(physics)/8T5H2g0C">jerk</a> that it is experiencing. (Jerk is the rate of change of <a href="/facts/Acceleration/UVDmjYvR">acceleration</a>.) The force points in the direction of the jerk. For example, in a <a href="/facts/Cyclotron/Q8APwhWm">cyclotron</a>, where the jerk points opposite to the velocity, the radiation reaction is directed opposite to the velocity of the particle, providing a braking action. The Abraham–Lorentz force is the source of the <a href="/facts/Radiation_resistance/VRdjWPpL">radiation resistance</a> of a radio <a href="/facts/Antenna_(radio)/pGlcXBvc">antenna</a> radiating <a href="/facts/Radio_wave/XmB6WPpF">radio waves</a>.
There are pathological solutions of the Abraham–Lorentz–Dirac equation in which a particle accelerates in advance of the application of a force, so-called pre-acceleration solutions. Since this would represent an effect occurring before its cause (<a href="/facts/Retrocausality/K8tUvDrR">retrocausality</a>), some theories have speculated that the equation allows signals to travel backward in time, thus challenging the physical principle of <a href="/facts/Causality_(physics)/bkoXXhU3">causality</a>. One resolution of this problem was discussed by <a href="/facts/Arthur_D._Yaghjian/XCAzy3bD">Arthur D. Yaghjian</a> and was further discussed by <a href="/facts/Fritz_Rohrlich/aXrNhHJM">Fritz Rohrlich</a> and Rodrigo Medina. 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.

Abraham–Lorentz force open-in-new

Abraham–Lorentz force