Vladimir Varićak

“ It seems convenient to introduce a name for length U. In my cited Serbian paper I have called it pseudo velocity. The easiest way would be, if we simply denote U and u as (physical) velocity and denote v as reduced velocity. As long as they are small, they practically cannot be distinguished. The pseudo velocity of light is infinitely great. By this definition it seems natural to us, that the velocity of light constitutes the upper limit for velocities. [8] ”

“ Now we want to investigate whether this definition is not in sharp contrast to the ordinary illustration of velocities. The distances proportional to the relevant velocities are used in ordinary mechanics as representing the velocities of uniform motions. Formula (2) leads to the same result at the limits of our ordinary experience. Only at velocities nearly comparable to the velocity of light, a notable difference occurs that quickly leads to infinite distortion. ”

“ The speed of light plays in physics the role of an infinitely great velocity. It cannot be reached by an accumulation of velocities less than the speed of light; it also cannot be changed by addition or subtraction of a velocity less than the speed of light. Now, by a suitable definition we can simply make that the speed of light is represented by an infinite quantity. As unit length we take , i.e. ”

“ We denote l as the new time that emerges from the old time by multiplication with the speed of light c as measured in the resting medium. We don't want to think of the considered clock as adjusted in the usual way, but as a simple clockwork that indicates, how often a certain (always repeating) process under the same circumstances, has happened since a certain event indicating the beginning of time counting. ”

“ It is known which role this invariant plays in Minkowski's four-dimensional interpretation of relativity theory.
5. The Lorentz-Einstein transformation.
The Galilei-Newton transformation
represents the translation along the X-axis in euclidean space. The Lorentz-Einstein transformation
similarly can be interpreted as a translation along the X-axis in Lobachevskian space.
If we remain in the plane then we can say: The Lorentz-Einstein transformation defines a motion along the distance line with the X-axis as its center line. ”

“ In Lobachevskian geometry no parallelograms exist; the resultant of two velocities cannot be represented by a diagonal of a parallelogram. As a consequence the components are noncommutative. Because of simplicity we take two velocities under an angle . From formula (5) we obtain
from which we can easily derive
or
In figure 3 we have
In hyperbolic geometry the sum of two angles in any triangle is less than two right angles. ”

“ For a normally incident light ray we have , also , the formula (66) goes over to
The relation of the frequencies and the amplitudes can in this case be illustrated as the relation of two coaxial limiting arcs. The corresponding figure would be the same as in Fig. 11, we only have to take . ”