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# How can the units of a velocity (vector) be cancelled by speed (scalar)?

Posted 9 years ago
 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. Another example would be from aviation: aircraft get "vectored in". That's 3D if you include altitude.
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Posted 9 years ago
 Degrees are dimensionless. So they do not interfere with dimensioned units.
Posted 9 years ago
 Dan,Yes I know. But this seems to me to be a case where mathematics does not properly represent the physical universe. In a vector, why would speed be more important than direction?Will anything go wrong if speed is used instead of velocity in the SR equations?Thanks again, DougP.S. Someone referenced our # of genetic codes on the Wikipedia genetic code article. Your calculations agree with two publications.
Posted 9 years ago
 Thank you so much, Sam. Your example will motivate me to start using units, which I have avoided to date!If I am at v=0.5 *c, or 0.5 in "natural units" on a course of Celestial North (0,0,0 degrees), what happens to those degrees when I square my v and divide by c^2 in the Lorentz equation?Doug
Posted 9 years ago
 Thank you so much, Sam. Your example will motivate me to start using units, which I have avoided to date! I had to back out of units. While convenient - I could always print speed as miles per hour without referring to the underlying data - the cost in execution time was significant. (Example coming - someday)
Posted 9 years ago
 If coordinate vector of a point is given by coor[t_] := {Quantity[x[t], "Meters"], Quantity[y[t], "Meters"]} and time is defined as time = Quantity[t, "Seconds"] and constant speed as speed = Quantity[c, "Meters"/"Seconds"] then time derivative of coordinate vector will give velocity in proper units: D[coor[t], time] which also can be rescaled as dimensionless D[coor[t], time]/speed 