  The founding fathers of the quantum theory already struggled with the
different roles of space and time in quantum theory. Position is by default
represented by an operator, whereas time is usually treated as a parameter.
Time operator models exist, in particular a certain Time Operator model denoted
the Temporal Wave Function (T.W.F.). This one extends the Born's rule to the
time domain. The statistics of pure exponential decay does not allow to exclude
this Born rule for time. However the tiny violation of the combined discrete
symmetries $P$ (parity) and $C$ (charge conjugation) observed in the K-meson
system allows us, as we prove in this paper, to discriminate between the
standard predictions, made in the framework of the so-called mass-decay matrix
formalism, and the T.W.F. predictions. We also present experimental data of a
particular $CP$ violating decay channel, that is in contrast with the
prediction of T.W.F. approach model, resulting in its falsification.
