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Are there experimental observations of the Abraham-Lorentz force?

The Abraham-Lorentz force is the force a classical charged particle particle exerts on itself due to its own electromagnetic field. It has a rather simple formula that reads $$ \vec{F}_\mathrm{AL} = \...
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Is the Hamiltonian of a relativistic charged particle in an electromagnetic field only an approximation?

Consider a system of two relativistic charged point particles 1 and 2 which interact through their electric and magnetic fields. The equation of motion for the first particle is then given by the ...