## Index of Refraction of Outer/Interplanetary Space

In electricity and magnetism, we typically assume that the relative permittivity (or dielectric constant) ε of air is equal to the "permittivity of free space" ε0, and likewise we assume that air has a relative permeability μ equal to the "permeability of free space" μ0. This is equivalent to assuming that air has the same index of refraction n as vacuum.

However, in reality, air has slightly different index of refraction from vacuum; the most obvious example is that there's some wavelength dependence in n that causes rainbows. Pretty much all substances have have an n that's different from that of the vacuum.

So my question is this: what is the index of refraction of the interplanetary space in our solar system, or in outer space (interstellar, intergalactic, etc.)? Since outer space and interplanetary space is not a pure vacuum, it must have a slightly different index of refraction... has this ever been measured? Is it observably different from the vacuum value?

Does quantum field theory predict any changes to the index of refraction of space when we go from a classical vacuum to a quantized electromagnetic field, given that the background radiation is about 3K?

In a nutshell, I want to know if there are any observable or theoretically predicted differences between the ideal vacuum's index of refraction and the index of refraction of real outer space.

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 There are definitely observable consequences to space not being a perfect vacuum. Because space is filled with a low density plasma, the index of refraction is a function of frequency. This means the speed of light in interstellar space is a function of frequency. This means that if I observe a transient source, like a pulsar, the arrival time of the pulses is different depending on the frequency. Radio astronomers use this effect to get information on the distance to radio sources and the density of the intervening interstellar medium. Try looking up "dispersion delay". Here's a good link: http://www.cv.nrao.edu/course/astr534/Pulsars.html

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