Expert: Philip A. Stahl - 11/4/2011

Question
QUESTION: Did James Maxwell's calculation of the speed of light state that light's speed would vary inversely to electromagnetic fields?

If so, according to his theory would the weak electromagnetic fields of deep space enable light to travel at velocities in deep space far exceeding 186,000 miles/second? Thanks!

ANSWER: Hello,

Maxwell's key wave equations actually say nothing about light propagating with a velocity that will vary inversely to EM fields.

The speed of light c is very specifically given by the ratio:

c = 1/ [u_o e_o]^½

where u_o = 4π x 10^-7 H/m (magnetic permeability of free space)

and

e_o = 8.85 x 10^-12 F/m  (electric permittivity of free space)

And this also is contingent on the field magnitude ratio:

E(x)/ H(y) = [u_o/ e_o]^½  = 377 ohms

which is the impedance of free space.

'Weak" E, H fields *themselves* are neither here nor there, but rather the values of the constants, u_ and e_o, which depend on the *media* in which the EM wave propagates. Thus, the only way the velocity of light changes is if u_0 and e_o are no longer free space (e.g. in vacuo) values, but rather adjusted for some medium.


---------- FOLLOW-UP ----------

QUESTION: Would the electric permittivity and magnetic permeability of free space in our solar system have the same values as that in deep space or near a black hole?

Answer
Hello,

Bear in mind that the density of interstellar gas in a black hole’s vicinity is likely to be relatively larger, on account of gravitational compaction of neighboring interstellar dust, gas arising from the hole’s intense g-field. Thus, values of the permittivity and permeability (e, u) will be in all probability be larger than for their counterparts in vacuo (or for the medium associated with our solar system).

This means EM radiation will plausibly be slowed in velocity in the vicinity of a hole (e.g. V2, but still outside its event horizon)  according to:

V2/V1 = {1/[u e]^ ½}/ {1/[u_o e_o]^ ½}

So : V2 /V1 = [u_o e_o]^ ½}/ [ u e]^ ½

And if V1= c

V2 = {[u_o e_o]^ ½}/ [ u e]^ ½} c

But u > u_o  and e > e_o

Hence,  V2 < c

Apart from this, one will expect gravitational time dilation and a gravitational red shift as one approaches a black hole. In the case of the first, successive clock ticks as one approaches a black hole will be larger and larger for proper time, compared to those for a distant observer. In addition, the frequency of EM radiation will be lower (wavelengths longer) since the frequency difference delta f is proportional to the time difference delta t, say measured by some exterior observer.