Re: [Phys-l] Why question(s), again?

[John Denker <jsd@av8n.com>]

On 01/11/2011 01:58 PM, David Bowman wrote:
> The reason light travels at 299792458 m/s is that the meter is
> defined as 1/299792458 of a light-second.  If other definitions were
> used for the meter and/or the second we would expect to have
> different numerical values for c.

That's entirely true and important, although it would probably
be the second (not the first) point I would make.

IMHO the most important thing is the idea of "c";  the numerical
value of "c" can come later.  Specifically, I like to say that
"c" is to rotations in the XT plane as "radian" is to rotations
in the XY plane.  *Then* we can ask
 -- how big is a radian in terms of more familiar units like degrees?
 -- how big is "c" in terms of more familiar units like mph or m/s?

I would also add that the magnitude (and units) on "c" are mostly
due to accidents of history rather than logic.  But such accidents
are not rare.  Here is an analogy:

At the equator, one degree of longitude is the same as one degree
of latitude ... or more precisely, |d/d(latitude)| is equal to
|d/d(longitude)|.  In contrast, as we move away from the equator,
|d/d(longitude)| becomes smaller than |d/d(latitude)|.  In
particular, if you want to know your heading, you must not 
simply take the atan2 of dX/d(latitude) and dX/d(longitude).
You need to apply a fudge factor to account for the fact that
distances in the two different directions are measured in 
different units.

So it is with space and time.  For reasons partly rooted in
practicality, and partly rooted in traditions that predate any
understanding of special relativity, we conventionally measure 
time and space using different units.  The numerical value of
"c" is nothing more than a fudge factor to convert time-units
to space-units and vice versa.  If we are going to rotate things
in the XT plane, we really need to treat X and T on the same
footing.