Motion in the FER - the Time and the SUPERTIME

If we use the idea of "motion", then we should introduce an additional "time-like" dimension, in relation to which the "motion" will be determined. This additional dimension will be called "THE SUPERTIME".

The SUPERTIME is a parameter determining a distance between two points in the FER and it is described in the FER with a following relation:
ΔT²=Δa²+Δb²+Δc²+Δd²

The SUPERTIME does not depend on the trajectory. It is identical for the both trajectories in this picture

While the SUPERTIME does not depend on the shape of the trajectory, then the time does. The longer trajectory (between the two points), the shorter time passed in the frame of the body moving along this trajectory

The Time and the SUPERTIME

The dependance between the SUPERTIME - T -, the proper time - t' - of the observed (moving) object and the distance - x_i - can be written as follows:

In the case of pair: observer - observed object, the time of the observer s is equal to the SUPERTIME T. This is valid only for moving along straightlines

It can be said: The bigger distance passed by the body in space, the lower distance passed by the body in time

The incresae of the SUPERTIME can be divided between the two components: the increase of a distance passed in space and the increase of the proper time
Therefore the SUPERTIME can be described in the complex form:

T = t*exp[i(π/2 - ϕ)]

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