is the spacetime density acc. to formula (12), or (12a).
Substituting for angle from equation (10), we obtain :
where m/n/ is the
spacetime density acc. to formula (12) or (12a).
It can be derived
The equation (14) and (14a) give the following resultant speed for the four basic directions:
It can be shown that:
Substituting c for vx/m
we obtain vr/x/n =c
Substituting c for vm/n we have
Taking vr/x/n=0 in the equation (16e), it is vx/m=vn/m ,
and we obtain:
is the speed of the N reference frame relative movement with respect to the M reference frame, and,
is the speed of the M reference frame relative movement with respect to the N reference frame.
Considering the equation (17) and looking from the unprimed systems N at objects M, moving at speed
vm/n with respect to the N systems and comparing this speed with the speed
vn/m of the frames N with respect to the objects M, measured by observers staying in objects M,
we can find out the reference frames systems at which in any case (at very low speeds as well) the inequality
vm/n > vn/m stays true. Such reference frames systems do not move with respect
to the spacetime structure and may be considered as preferred (or basic). This discovery is in contradiction with
one of the fundamental principles on which the Special theory of relativity is based.
Respecting the derived equations, we may say, that while speed of light in a common reference frame reaches value c in
all directions, the galileian projection of the speed of light from one reference frame to another reaches different value in
general, depending on an angle of a light beam with respect to direction of a respective frame speed with reference to
a frame into which the light speed c is projected.
In consequence of anisotropic distribution of the spacetime density in a primed frame it is necessary to remind, that the
calculation of the spacetime densities and resultant speeds derived for motion of a reference frame M in the preferred frame N
may be used for any two reference frames, provided that calculating relations between frames N and M, orientation stays
the same. The angles must be related to the same speed vector. The results of calculations however do not give results
explicit enough for critics of the Special relativity, because the speeds vm/n and
vn/m must be exchanged one with another when M is taken as a reference frame instead of N.
In case the spacetime densities in common frames N and M and the speed of their relative motion were calculated with
relation to a preferred reference frame, the results would become explicit. There are evidently quantities and phenomena
requesting to be calculated with reference to the preferred frame, as potential energy and gravitation. On the contrary,
another quantities, like acceleration, force, linear momentum and kinetic energy, in a primed frame, do not depend on
a primed reference frame speed with respect to the preferred frame. The problem will be dealt with perhaps in part two of this work.