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(136b)
(136c)
Let us return to:
(136d)
i.e. to the PT-group.
Then, such a space is [one where] there are uniform rectilinear motions.
The PT-group:
(137)
is built from the
(138)
(Space-oriented,
time-oriented group).
..Geometrical
objects of such a space are motions. This group acts on motions.
Later, we will only consider particles' motions, but, in general, a geometrical
object of space-time is some sort of hologram animated in time. There are
sets of (xi , yi , zi , ti ) points which are called event-points.
Clearly, the PT-group
contains terms which describe some symmetries:
(138b)
P-symmetry (P for "parity"
) refers to space orientation. The action of the first matrix reverses space,
giving:
(139)
The second reverses the
time-arrow:
(140)
The third is:
(141)
which reverses both space
and time.
...We
will find similar components again with the four components of the "complete Lorentz
group", further on. From the latter we will build the complete Poincaré
Group, which is the tool for building relativistic elementary particles.
...Clearly,
the PT-group can "create" antichronous motions, reverse the arrow of time, through
T and PT symmetries. In the following we will investigate whether these antichronous motions may correspond to real paths or not.
