Question: how long is a meter? Do we know the length of a meter
as well as we know the speed of light? The above value suggests
that we know how long a meter is on the order of 1 in a million.
But the meter was always defined to be the length of some metal
bar in Paris. How crude! Here's a better approach: define the
speed of light to be a constant: call it 299792458 m/s. All
physical theories (that we have thought of that work) employ the
notion of it being constant, and experimental measurements based
on whatever we have called the 'meter' have suggested that value.
Let's define that constant. (Just like we define the constant
3.14159265359...... to be the 'pi')
So, having defined the speed of light to be 299792458 m/s, let's
also define the 'second' in terms of another very precise number
(related to radioactive cesium clocks), and finally let's define
the meter to be "the length of path in vacuum travelled by light
in 1/299792458 second". This way, anybody can find out how long
the meter really is, with very tiny uncertainty, on the order of
one in a billion. Progress! We certainly could not have found
that bar's length with such precision.
Anyway, when we argue long enough about anything, we always seem
to have to rely on what Richard calls a level-3 argument: it is
more useful to treat the speed of light as a constant, since
theories based on that assumption seem to work remarkably well.
If someone can write down a new theory with a variable speed
for light that works as well as relativity or quantum mechanics
(which does treat c as constant in its equations), then perhaps
I'll become interested. I'm not counting on that happening in
my lifetime, though.
- JPS