The aim of this paper is to re-establish the reversibility of classical electrodynamics in terms of the "expectation values" given by quantum electrodynamics. The reversibility requirement combined with the charge conjugation necessitates that charged fields should obey certain types of statistics. However, the reversibility requirement as such does not determine the statistics, showing that it is the requirement of charge-invariance that has the power to determine the statistics of charged fields. A new interpretation will be given to the old problem concerning the conflict of electromagnetic reversibility versus "retarded" potential. Four different kinds of tensors, four different kinds of spinors (pseudospinors), bi-spinors (eight-component spinors) and bi-tensors are introduced as useful representation vectors of the entire congruent group including spatial and temporal inversions.