How do you add relative velocities?

von Zbigniew Oziewicz

How do you add relative velocities?
Zbigniew Oziewicz

NPA, August 2004. Revised March 25, 2007

Abstract:
Following Minkowski [1908], we consider the relative velocity to be the Minkowski space-like vector (and not to be the Minkowski bivector as it is in the Hestenes theory [Hestenes 1974]). The Lorentz boost entails the relative velocity (as a space-like
Minkowski vector) to be ternary: ternary relative velocity is a velocity of a body with respect to an interior observer as seen by a preferred exterior-observer. The Lorentz boosts imply non-associative addition of ternary relative velocities. Within Einstein’s special relativity theory, each preferred observer (fixed stars, aether, etc), determine the unique relative velocity among each pair of massive bodies. Therefore, the special relativity founded on Minkowski’s axiom, that each pair of reference systems must be related by Lorentz isometry, needs a preferred reference system in order to have the unique Einstein’s relative velocity among each pair of massive bodies. This choice-dependence of relative velocity violate the Relativity Principle that all reference systems must be equivalent.

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