Time-reversal invariance and time asymmetry in classical electrodynamics

Synopsis

A notable property of electromagnetic radiation is that, like entropy gain and cosmological expansion, radiating processes are asymmetrical in time. Empirically, the energy received by an absorbing point-particle is always less than the total energy emitted by the source. However, it is not obvious that electrodynamics theory reflects this asymmetry, as its equations are invariant under-time reversal. This disconnect is reflected in the in the fact that advanced fields are mathematically permissible under classical electrodynamics, while in reality only retarded fields are observed. To ease this tension, it can be shown that though the dynamical equations of electromagnetism are time invariant, the time asymmetry of electromagnetic processes can be drawn out of their initial conditions. By considering a toy radiating system with roughly physical initial conditions, it is demonstrated that, though any admission/absorption process may be described using retarded or advanced fields, the latter description will be significantly more complicated than the former. This provides a theoretical argument for treating advanced fields as non-physical.