  We study the relationship between the quantization of a massless scalar field
on the two-dimensional Einstein cylinder and in a spacetime with a time
machine. We find that the latter picks out a unique prescription for the state
of the zero mode in the Einstein cylinder. We show how this choice arises from
the computation of the vacuum Wightman function and the vacuum renormalized
stress-energy tensor in the time-machine geometry. Finally, we relate the
previously proposed regularization of the zero mode state as a squeezed state
with the time-machine warp parameter, thus demonstrating that the quantization
in the latter regularizes the quantization in an Einstein cylinder.
