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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.

POSTED BY: Douglas Youvan
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Degrees are dimensionless. So they do not interfere with dimensioned units.

POSTED BY: Daniel Lichtblau


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.

POSTED BY: Douglas Youvan

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?


POSTED BY: Douglas Youvan
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 BY: Douglas Kubler

If coordinate vector of a point is given by

coor[t_] := {Quantity[x[t], "Meters"], Quantity[y[t], "Meters"]}

enter image description here

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]

enter image description here

which also can be rescaled as dimensionless

D[coor[t], time]/speed

enter image description here

POSTED BY: Sam Carrettie
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