1st Revision : August 8th 2003 (the extent of theme not changed)
The subject of revision :

4.8 Space flow

At that time already, when the Special relativity was acknowledged, admitting the time dilation and length contraction, even long before, when the theories admitting various space geometries (or the space curvature) were accepted by scientists, the fact that the spacetime continuum has its own structure was accepted. We can hardly imagine the curvatured spacetime without the idea that the things deformed in a curvatured spacetime are firmly bound up with it.

The imagination of the spacetime structure makes possible to define the Unit flow of the space, as the number of the spacetime cells that has passed through the unit area perpendicular to the vector of the speed, within a time unit. Because the number of the spacetime cells is proportional to the volume, it is :
image (29)
the unit space flow in the unit of volume per time unit
the speed of the spacetime cells with respect to the unit area

We have :
image (30)
the area differential
the space flow passing through an area differential.
Determining the space flow in the frame M with regard to frame N, the "contemporary" speed imagemn = v*imagem/n has to be used instead of v , to obtain speed proportional to the spacetime density. The speed imagemn defines the number of spacetime cells of the M-frame spacetime structure, that has passed in direction of its speed through a perpendicular reference area, within time unit of N-frame.

The change of the space (or, spacetime) density however brings the change of the frequency of the spacetime structure. Applying the definition of the time density from chapter 3.2, we can easily derive that the frequency of the spacetime structure must be directly proportional to the time (or spacetime) density. The higher (lower) frequency must be understood as the sign of the higher (lower) energy of the spacetime cell. From this point of view we may consider one spacetime cell as n spacetime quanta if the time density (frequency) became n-times higher (lower). This is why now the spaceflow speed (marked (v)tn) has to be considered as imaget/m/n times higher (lower), and we have :
image (31)
where speed (v)tn
defines the distance in units of M-frame, travelled within time unit of N-frame, if the distance was defined as the lined up series of the spacetime quanta.
See Fig7a :

Fig7a The speed of the space flow


image (32)

image (32a)

image (32b)

stands for the differential of the space flow cells in M-frame, recalculated for the time unit of the reference (N) frame, and,
stands for the differential of the space flow quanta in M-frame, recalculated for the time unit of the reference (N) frame
Space flow into a mass point

Admitting possibility of the existence of the space flow brings us to idea of the spacetime flowing from all directions to a mass point, giving chance to explain the mass point as a spacetime structure of a very high spacetime density, and, to explain the acceleration due to gravity as an acceleration due to change of the speed of the space falling into a mass point. The question where from and to is the spacetime travelling on its way to a mass point cannot be ignored in general, but may be disregarded in this work.
At an angle image = image the spaceflow speed v is orientated in direction with the speed vm/n at which mass point is moving with respect to N-frame. The equation (12a) must be modified for this configuration:
Respecting equation (25), we have:
image (33)

Substituting for images/m/n to equation (32) from (33), we obtain:
image (34)

image (34a)
The area differential on the spherical area of the radius r (see Fig7b):



image (35)

image (35a)

where ln stands for natural logarithm.

We can simply derive that Qmn = Qm = Qn = 4imager2v in equation (35) represents the frame own space flow (reaches the same value in all frames).

image (36)

4.9 Mass (m)

In Special relativity the following transformation equation for the mass was derived:
image (37)

where M is mass of an object as measured by an observer moving at a speed v with respect to the object, and m, called rest mass, is the object's mass as measured in its own frame. This transformation equation is considered as verified, because it was confirmed by many laboratory experiments, especially on synchrotrons and synchrocyclotrons.

We can see that curve spaceflow-speed of the mass-point according to equation (36) is very similar to the curve mass-speed according to equation (37). This is why we may say that quantity of a mass is proportional to quantity of a spacetime flowing into it. The equation (36) therefore may be modified to express also mass- speed dependence:
image (38)

image (39)

The derived formula (38) gives the following results in comparison with formula (37) accepted by Special relativity:

vm/n / c Mass acc. to equation (37) Mass acc. to equation (38)Ratio m2 / m1

In common case, when object X of the mass m moves in frame M at a speed vx/m , and frame M at a speed vm/n in frame N, using equation (38) we may write

For mass of the object X, moving at a resultant speed vx/n, as detected from frame N:
image (40)

For mass of the object X, moving at a speedvm/n in N frame, as detected from N frame:
image (41)

For mass of the object X, moving at a speed vx/m in M frame, as detected from N frame ( it means the mass we detect moving in M frame at a speed vx/m/image m/n ) :
image (42)

Solving relations between equations (40), (41) and (42), we obtain the following formulas:
image (43)

image (44)

image (45)

The mass m of the object X, moving in M-frame at a speed vx/m reaches value Mxm when detected from M-frame:
image (46a)

Dividing equation (44) by Mxm we obtain
image (46)