Space Inversion

(P), the transformation that changes the signs of the spatial coordinates of events (x, y, z), defined in some Cartesian coordinate system. Thus, in a space inversion x → –x, y → –y, and z → –z. Such a change may be interpreted as either an active or a passive transformation. As an active transformation, it represents a transition to a set of events that are a mirror image of the given set of events—that is, the change in the signs of the coordinates of a point corresponds to the position of the point obtained as a result of the reflection of the point in the origin. Space inversion as a passive transformation means that the set of events under consideration is described in a coordinate system obtained from the given system by reversing the directions of all three coordinate axes.

As experiment has shown, natural processes resulting from strong and electromagnetic interactions are symmetric with respect to the space-inversion transformation. This fact underlies the physical significance of the transformation: for any such process, the “mirror symmetric” process occurs in nature and proceeds with the same probability. In the quantum mechanical description, symmetry with respect to the space inversion transformation implies the existence of a special quantity, called parity, which is conserved in processes involving strong and electromagnetic interactions. Weak interactions, by contrast, do not have this symmetry, and parity is not conserved in the processes caused by them. Weak interactions, however, are symmetric with respect to what is called combined inversion, (CP), which is the successive performance of the transformations of space inversion and charge conjugation (C). In the general case, the requirements of the theory of relativity and the locality of interaction (the interaction of fields at one point) imply that natural processes must be symmetric with respect to the successive performance of the three transformations of charge conjugation, space inversion, and time reversal (T). This result is known as the CPT theorem.