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Parks introduced a formulation of time dependent weak values in 2008, whichis the formalism we use in this paper. In this paper we extend notions fromtime dependent weak values to show that Hamiltonians associated with weak valuemeasurements can be shown to exhibit even or odd symmetric properties. Theyexhibit PT or anti-PT symmetry, respectively. These symmetries are manifestedduring the measurement process as pointer translations, which have vanishingimaginary or vanishing real parts. The consequence of this that one cancharacterize some of the aspects of these symmetries of the time dependentHamiltonians that arise from time dependent weak values. This allows one togeneralize some work on non-Hermitian variables in quantum mechanics (QM) dueto Bender related to weak values and weak measurement. We also speculate howthese symmetries might apply to distinguishing between the various two-timeinterpretations of QM in the Conclusions of this paper.

PT and Anti-PT Symmetry Arising in Time Dependent Weak Value Measurements