A new kind of parity and Loschmidt's paradox

Abstract

The conventional parity operation consists of the exchange of ―right‖ and ―left‖, hence its alternative name, ―mirror inversion‖, since it is the one performed by common plane mirrors. Such specificity in the inversion surface, though, is pointed out in this paper as being responsible for its less fundamental character. Here, a new kind of parity is introduced, whose inversion surface is a general, closed one, and consists of the exchange of the inside and outside subspaces that the surface defines. It has been named ―inside-out‖ inversion, or simply, space inversion, and encloses the conventional rightleft parity as the particular case when the inside and outside are identical. As an example, Maxwell‘s equations in free space will be considered. This case is important since the time-reversible character of classical electromagnetism is under question due to the irreversible physical behaviour of radiation. For this case, both space and time inversions will be carried out and compared, and it will be shown that the electromagnetic field in free space is space-invariant, while it is not time-invariant, as commonly assumed.