Jim Kelley wrote:
If the length of the second were different, then so would be the speed
of light ...

To see why that is false, refer to Lorentz's
transformation for time at a velocity near
the speed of light. Time can vary all over
the universe while the speed of light remains
constant (at least by definition :-). Since
time is one dimension for the speed of light,
the problem is self-correcting.

If tomorrow's second were 1/2 half of today's
second, nobody would even notice.

If someone used a cesium clock near a black
hole to come up with a "standard" second, it
would be nowhere near the same length of time
as a cesium clock on Earth. Time passes very
slowly near the event horizon of a black hole
but light keeps on trucking at the speed of
light.
--
73, Cecil http://www.w5dxp.com