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

Posted 10 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 10 years ago
 Degrees are dimensionless. So they do not interfere with dimensioned units.
Posted 10 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 10 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 10 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 10 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