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S4h. Can particles go backward in time?
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In the old relativistic QM (e.g., in Volume 1 of Bjorken and Drell)
antiparticles are viewed as particles traveling backward in time.
This is based on a consideration of the solutions of the Dirac equation
and the idea of a filled sea of negative-energy solutions in which
antiparticles appear as holes (though this picture only works for
fermions since it requires an exclusion principle). One can go some way
with this view, but more sophisticated stuff requires the QFT picture
(as in Volume 2 of Bjorken and Drell and most modern treatments).
In relativistic QFT, all particles (and antiparticles) travel forward
in time, corresponding to timelike or lightlike momenta.
(Only 'virtual' particles may have unrestricted momenta; but these are
unobservable artifacts of perturbation theory.)
The need for antiparticles is in QFT instead revealed by the fact that
they are necessary to construct operators with causal (anti)commutation
relations, in connection with the spin-statistic theorem. See, e.g.,
Volume 1 of Weinberg's quantum field theory book.
Thus talking about particles traveling backward in time, the Dirac sea,
and holes as positrons is outdated; it is today more misleading
than it does good.