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(136b) (136c)
Let us return to:
(136d)
that is, the PT group. Then, in such a space, uniform rectilinear motions exist.
The PT group:
(137)
is constructed from the
(138)
(space-oriented, time-oriented group).
.. The geometric objects of this space are motions. This group acts on motions. Later, we will consider only particle motions, but in general, a geometric object of spacetime is some kind of time-animated hologram. There are sets of points (xi, yi, zi, ti) called event-points. It is clear that the PT group contains elements describing certain symmetries:
(138b)
P-symmetry (P for "parity") refers to space orientation. The action of the first matrix reverses space, yielding:
(139)
The second reverses the arrow of time:
(140)
The third is:
(141)
which reverses both space and time.
...We will encounter similar components in the four components of the "complete Lorentz group," further on. From it, we will construct the complete Poincaré group, which is the tool used to build relativistic elementary particles.
...It is clear that the PT group can "generate" antichronous motions, reverse the arrow of time, through T and PT symmetries. In the following, we will investigate whether these antichronous motions can correspond to real trajectories or not.