a4110
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(136b) (136c)
回到：
(136d)
即PT群。因此，在这样的空间中，存在匀速直线运动。
PT群：
(137)
由以下构建而成：
(138)
（时空方向性群）。
.. 这种空间中的几何对象是运动。该群作用于运动。稍后，我们只考虑粒子的运动，但一般来说，时空中的几何对象是一种随时间动态变化的全息影像。存在由点(xi, yi, zi, ti)组成的集合，称为事件点。显然，PT群包含描述某些对称性的元素：
(138b)
P对称性（P代表“宇称”）涉及空间方向。第一个矩阵的作用是反转空间，得到：
(139)
第二个矩阵反转时间箭头：
(140)
第三个是：
(141)
它同时反转空间和时间。
...我们将在后面再次遇到与“完整洛伦兹群”的四个分量相似的成分。从该群出发，我们将构建完整的庞加莱群，这是构建相对论性基本粒子的工具。
...显然，通过T对称性和PT对称性，PT群可以“产生”反时序运动，反转时间箭头。接下来，我们将探讨这些反时序运动是否可能对应真实的轨迹。
原始版本（英文）
a4110
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(136b) (136c)
Let us return to :
(136d)
i.e to the PT-group. Then, is such space, There are uniform rectilinear moves.
The PT-group :
(137)
is built from the
(138)
(Space oriented, time-oriented group).
..Geometrical objects of such a space are movements . This group acts on movements. Later, we will only consider particles' movements, but, in general, a geometrical object of space time is some sort of hologram animated is 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, gives :
(139)
The second reverses the time-arrow :
(140)
The third is :
(141)
which reverses both space and time.
...We will refind similar components with the four components "complete Lorentz group", further. From the latter we will build the complete Poincaré Group, which is the tool to build relativistic elementary particles.
...Clearly, PT-group can "create" antichron movements, reverse the arrow of time, through T and PT symmetries . In the following we will search if these *antichron *movements may correspond to real paths or not.