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In the physics of electromagnetism, the Abraham–Lorentz force (also Lorentz–Abraham force) is the recoil force on an accelerating charged particle caused by the particle emitting electromagnetic radiation. It is also called the radiation reaction force or the self force. The formula predates the theory of special relativity, and is not valid at velocities of the order of the speed of light. Its relativistic generalization is called the "Abraham–Lorentz–Dirac force". Both of these are in the domain of classical physics, not quantum physics, and therefore, may not be valid at distances of roughly the Compton wavelength or below〔(F. Rohrlich: ''The dynamics of a charged sphere and the electron'' Am J Phys 65 (11) p. 1051 (1997) ). "The dynamics of point charges is an excellent example of the importance of obeying the validity limits of a physical theory. When these limits are exceeded the predictions of the theory may be incorrect or even patently absurd. In the present case, the classical equations of motion have their validity limits where quantum mechanics becomes important: they can no longer be trusted at distances of the order of (or below) the Compton wavelength… Only when all distances involved are in the classical domain is classical dynamics acceptable for electrons."〕 There is, however, an analogue of the formula which is both fully quantum and relativistic, called the "Abraham–Lorentz–Dirac–Langevin equation" – see Johnson and Hu. The force is proportional to the square of the object's charge, times the jerk (rate of change of acceleration) that it is experiencing. The force points in the direction of the jerk. For example, in a cyclotron, where the jerk points opposite to the velocity, the radiation reaction is directed opposite to the velocity of the particle, providing a braking action. It was thought that the solution of the Abraham–Lorentz force problem predicts that signals from the future affect the present, thus challenging intuition of cause and effect. For example, there are pathological solutions using the Abraham–Lorentz–Dirac equation in which a particle accelerates ''in advance'' of the application of a force, so-called ''pre-acceleration'' solutions. One resolution of this problem was discussed by Yaghjian,〔 〕 and is further discussed by Rohrlich〔 and Medina. == Definition and description == Mathematically, the Abraham–Lorentz force is given in SI units by : is the jerk (the derivative of acceleration, or the third derivative of displacement), μ0 is the magnetic constant, ε0 is the electric constant, ''c'' is the speed of light in free space, and ''q'' is the electric charge of the particle. Note that this formula is for non-relativistic velocities; Dirac simply renormalized the mass of the particle in the equation of motion, to find the relativistic version (below). Physically, an accelerating charge emits radiation (according to the Larmor formula), which carries momentum away from the charge. Since momentum is conserved, the charge is pushed in the direction opposite the direction of the emitted radiation. In fact the formula above for radiation force can be ''derived'' from the Larmor formula, as shown below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Abraham–Lorentz force」の詳細全文を読む スポンサード リンク
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