4: Space Inversion and Time Reversal

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In this chapater we extend the set of transformations of apparatuses considered in Chapter 3 to include space inversion and time reversal. The space inversion transformation corresponds to viewing the preparation and measurement processes in a mirror. The time reversal transformation corresponds to viewing a motion picture of the preparation and measurement process in reverse. ln this chapter we explore consequences of assuming that Lorentz invariant systems a-re also space inversion invariant are time reversal invariant. Unlike the Poincare transformations (3.24) fo (3.27), the space inversion and time reversal transformations cannot be characterized by continuous transformations from the identity. A consequence is that the time reversal operator is an antilinear antiunitary operator. Space inversion is discussed in Section 5.1 and time reversal is discussed in Section 5.2. Some derivations are given in Section 5.3.