From: Topher Cooper (topher_at_[hidden])
Date: 2006-06-14 13:10:05
At 11:24 AM 6/14/2006, you wrote:
>Andy Little wrote:
> > I'm unclear what you mean by velocity being unitless. Do you mean
> that velocity
> > is treated as a dimensionless or numeric type in the relativistic system?
> It means that for the sake of computation, it carries no units and no
>dimensions. So, if I wanted to talk about a velocity of a particle that
>is moving at 70% of the speed of light, and I make the scale choice that
>the speed of light is 1, then the velocity is v = 0.7. There are no
>units to include.
Just in case there is someone out there who needs a bit more
explanation as to why this would be:
Everywhere in the equations of relativistic physics that a velocity
(V) appears, it is divided by C. Numerical simplification can be
gotten by choosing units of distance and/or time so that C comes out
to be 1, but it would still have units of Rd/Rt, where Rd and Rt are
the chosen units of distance and time. To come out dimensionally
correct, therefore, the equations would still require a division by C
(a numeric but not dimensional no-op). By using V/C, a unit-less
quantity, to represent the concept of velocity, the equations
themselves are simplified.
The cost, by the way, is less implicit checking via dimensional
analysis. You could use an angle in radians (also dimensionless)
where you meant a velocity and everything would be dimensionally correct.
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