(Submitted June 11, 1997)
Why is the velocity of light the max speed despite its dependence on the
permeability and dielectric constants?
The speed of
light in a given medium does indeed depend on the permeability and
dielectric constants. As you likely know together
these form the index of refraction n = (epsilon * mu).5 In turn
the index of refraction determines the velocity by v = c/n. The values
of mu and epsilon for all known materials is greater than the value in
a vacuum, so the speed of light has a maximum value in a vacuum. The
precise reason why the values for mu and epsilon are smaller in media
rather than a vacuum is a little outside of astrophysics and is more
under the domain of materials science or solid state physics.
A brief historical sketch of the speed of light and its measured
value starts in 1675 with the astronomer Roemer, who noticed an unexplained
difference in the transit times of the moons of Jupiter. What he saw was,
depending on the time of year, the moons of Jupiter would pass in front
of the planet at a time that was slightly off the predicted time, with
the offsets up to about 16 minutes. Since the orbits of the moons can
be assumed to be quite regular, Roemer correctly attributed the difference
to the variable distance that the light must travel before we observe the
transits. When the Earth is closer in its orbit to Jupiter the light must
travel less of a distance than when the Earth is on the opposite side of
its orbit. Roemer had a good estimate of the diameter of Earth's orbit,
and he deduced a reasonable value for the speed of light. Measurements of
the speed of light improved, and Foucault conducted one in 1846 which used
rapidly rotating mirrors on hills that were separated by several miles.
When James Clerk Maxwell was working on his theory of electromagnetic
radiation, he realized that electromagnetic waves were actually predicted
by this theory. Their velocity, in terms of electromagnetic constants,
was so close to the measured value of the speed of light that he immediately
inferred that light was therefore an electromagnetic wave.
I hope this helps answer your questions.
Jeff Silvis and Padi Boyd
for the Ask an Astrophysicist