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© Michael H. Shulman , 2005 Special Relativity, and the Universe evolution 1. Introduction As is well known, according to Special Relativity (SR) a transition from an immovable reference system to any moving one may by interpreted as some rotation in the Minkowski space. Moreover, the translations are used in such space, that is the main subject of the paper. But at first we will briefly remind some aspects of a rotation in an pseudoeuclidian space. Unfortunately, the imaginary angle rotation correct geometrical interpretation is very seldom in the training courses on the SR, and it differs from usual euclidean real angle rotation. In fact, when we come from an immovable reference system to any moving one, the tme axis turns on the angle depending on velocity, and the light world line must stay the bisectrix. Therefore, the space axis also turns on the same angle (see [Taylor, and Wheeler, 1966]). The world line of a light flash is shown as a dotted line on the figure 1. A moving reference frame is also shown as it will be present in the immovable reference system. So, this moving reference frame doesn't stay rectangle, it seems to be an oblique frame!

Fig. 1. A moving system reference in an immovable one To count the past and the inverse motion, we have to continue the time and spatial axis through zero. When we change an angle of rotation, the scale of the moving coordinate frame changes too. The more this angle value, the more this scale becomes longer (or time and space distances seem to be shorter). So, to come from one inertial reference frame to the other we use the Lorenz transformation, that is a rotation one in a 4D pseudueuclidean space. Such transformations constitute the Lorenz group which includes rotations in three purely spatial and three time-spatial planes. Meanwhile, the more large transformation group exists in this space, named Poincaret group. It contains not only rotations (Lorenz group), but also time and spatial translations. Therefore, the Poincaret group is specified by 10 parameters. A linear differential operator (generator) may be used for each of 6 rotations and 4 translation, giving a small devation of a vector when a corresponding transformation parameter (rotation angle or translation value ) has a small fluctuation. These mathematical operators are proportional to the basic physical operators (angular momentum, velocity, pulse, and energy). This is a base for the link between the corresponding concervation laws and the Minkowski space symmetry relative to rotations and translations.


2. SR, and the World chronological evolution For parallel translation in time (Poincaret translation) it seems to be the only one of its kind as a self-mapping of all 4-events that correspond with a shift of time zero point. In this case we have a light cones family (coming from a spatial point), that is shown on the figure 2. In the course of time the points of one cone (for example, s1) become to the points of the next points (for example, s2) , these points belong to the same time vertical line (for example, passing coordinate x1).

Fig. 2. A light cones family corresponding with Poincaret translation But this chronological evolution model is not solely possible, and it doesn't meet the relativistic invariance condition (that is the more important). In fact, when we choice another reference system, the line passing coordinate x1 will not parallel the new time axis. Besides, the new distances along the new time axis between light cones will not equal to the old ones. Therefore, two choiced geometric famylies (light lines and vertical lines) don't permit to invariantly parametrize all the set of 4D events, i.e. their real evolution in time.

Fig. 3. A light cones family corresponding with E-translation To obey the relativistic invariance conditions we have to choice another time-space frame (see fig. 3). As is known, when we use any Lorenz transformation only hypersurfaces family t2c2 ­ r2 = const is invariant, and their mutual distances along time axis stay the sames in each reference system. Further, any line position that connects the point of origin with a given 4D point also is invariant


in each reference system. Really, we found the Lorenz invariant system frame! The same manner we may parametrize the spacelike area outside initial light cone, but we will not do it here. In fact, we also determined some evolution of 4D events at any translation along the time axis. Actually, if the distances between all choised hypersurfaces along the time axis are equal one to another, then their projections to the time axis (in each reference system) will be equal too. So, we have have the right to determine such new type of the time translation, the points of a hypersurface just become to the corresonding points of another surface, like to "quasiparallel" shift of these surfaces! I propose use the term "E-translation" for this "chronological" operator that realizes such evolutional shift (from the "evolution" or from "Einstein"). This E-translation doesn't determine a parallel translation along the time axis in any casual system reference. In essence, it determines an interval shift in the Minkowski space. Further, all the spatial translations and all the rotation must be determined in any 4D point not for casual system reference, but relative to the corresponding hypersurface, and to the corresponding velocity direction. In the aggregate all these modified transformation form the new 10parameters E-group (a closed operation set), and allow to the corresponding generators. Particularly, energy E-operator corresponds with a Minkowsky space symmetry along to a given inertial motion word line, not along to a casual time axis. BIBLIOGRAPHY [Taylor, and Wheeler, 1966] E. F. Taylor, J. A. Wheeler, Spacetime Physics, W. H. Freeman and Company, San Francisco and London, 1966.