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COMMENSURABILITY

Recall that a geometrical clock is defined as a pair of radar units whose emission of monochromatic wave trains yields two well defined mutual frequency shift factors ($k_{AB}$ at B and $k_{BA}$ at A) and whose reflective surfaces support an electromagnetic pulse bouncing back and forth between them.

Geometrical clocks differ from one another by virtue of their differing frequency shift factors and hence their differing ticking rates. Moreover, these rates are in general not even uniform. Nevertheless a comparison of these clocks is possible. The general idea is to consider the ratio of their ticking rates. These ratios open the door to identifying a commensurable property even among certain geometrical clocks which run nonuniformly relative to their resident atomic clocks. The implementation of this endeavor is best done in two steps: first for adjacent clocks, then for distant ones.



Subsections

Ulrich Gerlach 2003-02-25