  In nonrelativistic quantum mechanics and in relativistic quantum field
theory, time t is a parameter and thus the time-reversal operator T does not
actually reverse the sign of t. However, in relativistic quantum mechanics the
time coordinate t and the space coordinates x are treated on an equal footing
and all are operators. In this paper it is shown how to extend PT symmetry from
nonrelativistic to relativistic quantum mechanics by implementing time reversal
as an operation that changes the sign of the time coordinate operator t. Some
illustrative relativistic quantum-mechanical models are constructed whose
associated Hamiltonians are non-Hermitian but PT symmetric, and it is shown
that for each such Hamiltonian the energy eigenvalues are all real.
