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.
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
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
Degrees are dimensionless. So they do not interfere with dimensioned units.
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,
Doug
P.S. Someone referenced our # of genetic codes on the Wikipedia genetic code article. Your calculations agree with two publications.
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)