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 Point D receives the signal a little later. However, if we lay through the point B and D a circle with center $$O'$$ upon the abscissa axis, then $$X'Y'$$ is the system, in which the arriving of the light signals at points B and D was simultaneous. This system $$S'$$ moves in respect to S with velocity $$u = OO'$$. In the same way we could also define a reference frame in which the points A and B are simultaneous.

However, if point B is located at a limiting circle with the X-axis as its axis and adjacent to the ordinate axes at point A, then the perpendicular drawn at the bisecting point of line AB will be parallel to the X-axis. In this case there is no reference frame, in which the points A and B would be simultaneous.

Let us draw through O the limiting circles G and $$G_1$$, with the positive or the negative side of the abscissa axis as their axis. Any point in the interior of those two limiting circles can be arranged in the reference frame as simultaneous with O. As, for example, point $$M_1$$. If $$H_1$$ is the bisecting point of line $$OM_1$$, then the perpendicular raised in $$H_1$$ upon this line will intersect the X-axis in finite distance. If $$M_2$$ is located upon G, then the perpendicular raised in $$H_2$$ will be parallel to the X-axis. If we make this consideration for a point $$M_3$$ between those two limiting circles, the perpendicular raised in $$H_3$$ will diverge from the X-axis, because $$OH_{3}>OH_{2}$$. The points on the limiting circles G, $$G_1$$ and in the hatched areas cannot be simultaneous with O in any reference frame.

In space we also would have two limiting spheres emerging from the rotation of those limiting circles around the X-axis.

According to relativity theory of optical phenomena in moving bodies, the speed of light in vacuum in the primed