The Principle of Reciprocal Time Dilation
by Wolfgang G. Gasser
There are two principally different kinds of time-dilation, which can be combined in different ways. In case of two clocks, one next to the other, only one clock can run slower than the other. Reciprocal time-dilation is impossible. This is the kind of time dilation, occurring in particle accelerators and cyclotrons. The high-speed particle, considered as a clock, runs slower than any clock placed in the accelerator. This time-dilation is rather asymmetric and absolute than reciprocal, mutual, symmetric and relative.
Only a second kind of time dilation allows for reciprocal time-dilation. In order to realize it in the simplest form, one must compare one clock with a number of other clocks, all running at the same pace, yet each with a different time offset. One possible realization: Clocks are fixed on a long tape and adjusted in such a way that a clock (despite running at the same pace) is the more in advance (i.e. in the future), the more the clock is situated in front (positive x-axis), e.g. advancing each 0.2 sec per meter in front. An observer moving at constant speeds of 1 m/s relative to the tape gets the impression that his own time runs slower than tape-time (1 sec per 1.2 sec).
This principle of time-dilation entails two important consequences: The tape cannot be closed (resp. made cyclic), as in one direction all is 'future' and in the other direction all is 'past'.
The second consequence: If the moving observer changes direction (moving at same speed of 1 m/s) and the clocks on the tape are not readjusted with new time offsets, then observer time runs faster than tape-time (1 sec per 0.8 sec). The analogous of the (normal) twin-paradox resolution is this: The tape-clock where the moving observer is situated at direction-change is bound by the presence of the observer, so it cannot be changed. Yet all other clocks receive new time-offsets:
0.0--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-- 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 5.0--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-- 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 10.0--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0
10.0--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--14.0 13.8 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0
20.0--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--24.0 23.8 23.6 23.4 23.2 23.0 22.8 22.6 22.4 22.2 22.0
We also recognize that the direction change does not work properly, if the moving observer is expanded, as more than one clock is bound:
10.0 10.0--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4 11.6 11.8 12.0 10.0 10.0--+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--14.0 13.8 13.6 13.4 13.2 13.0 12.8 12.6 12.4 12.2 12.0