The Lorentz equation is a good example. I've always thought the use of that factor in time dilation should use speed rather than velocity.
Once, while reading about "turn-around effects", I actually looked at the date on the journal to see if it was April 1.
In the time dilation factor, velocity is squared, which is V dot V and returns a scalar equal to |V|2.
In the clock skew formula, clocks change only along the vector direction.
When adding velocities there is a complicated special formula that takes into account the mass increase and conserves momentum. Possibly you can just add momentum vectors, I never tried this.
Was that what you were asking, or did I miss the point?
Speed can be arbitrarily and temporarily endowed with the same, or opposite, direction as the velocity. The dimensions (M,L,T) will not be disturbed.
Robert,
Thanks for your answer. Let me approach this question from a different direction: Why does the Lorentz factor use velocity rather than speed in Relativity? Direction is lost, so speed seems a more appropriate term.
Hi Douglas!
Yes, I suppose that one could make a decent case for replacing the Lorentz-factor "v" with an "s" for "speed".
However, special relativity makes predictions for more than just the case of transverse motion, and if we want to work out the full "SR prediction" for what a detector reports for a signal source moving in any given direction, we need to specify the full relative velocity of the source - not just its speed, but also the alignment of its path with respect to the detector, and the polarity of its motion along that path.
So the more general SR equations need to use "v for velocity " anyway, and if you're already writing "v" in one part of an equation, and the same numerical value appears elsewhere (in the Lorentz factor), then perhaps it's natural to want to write in the same symbol rather than introduce a new one.
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