Theory: The speed of light changes when it enters or exits the solar system due to a difference in medium (dark matter possibly).
Potential problem 1: refraction
If there was a speed change at the edge of the solar system, refraction would occur. This would manifest in ways similar to the sunset effect.
Solution: the sunset refraction occurs because the angle against the edge of the atmosphere is extreme. No effect is noticed at high noon. Earth's proximity to the edge of the solar system, in contrast, makes it's angle nearly perpendicular in all directions. Wouldn't this negate any sunset effect?
Sub-solution: My research on refraction seems to indicate that what I'll call the "distinction level" of the edge of the mediums has an effect on the level of refraction. So that, if the edge were not solid, but rather tapered, the refraction is reduced.
SO, what would be effect on light entering our solar system if the light were severely slowed–let's say by a factor of 1,000,000 times, to what it is now. What, if any, refractive effects would be observed? How much would these effects change if the tapering of the edge were severe?–Could any refractive effect be overcome by tapering?
Another question, what would be the effect of the light coming from Alpha Centauri if it's system had a similar medium transition at it's edge? How would it be noticable?
This picture illustrates my thoughts:
Best Answer
Tapering makes no difference in Snell's law. If you have a refractive index profile n(z) [approximately independent of x and y], and you know the angle of the light at z1, then you can figure out the angle at another point z2 using Snell's law -- and the angle only depends on n(z1) and n(z2), not n(z) for any other z. It doesn't matter how smooth or sharp n(z) changes. (The profile and smoothness does affect the reflection and transmission amplitudes, but it does not affect the angle.)
The atmosphere is a good example -- the refractive index changes very smoothly from earth to outer space, as the air gets thinner and thinner, but there is still a sunset effect ... and moreover, you can calculate the sunset effect without knowing anything about the refractive index profile of the atmosphere. You only need to know the refractive index on the ground and the refractive index in space.
Therefore, if the refractive index changed at the edge of the solar system, we would see stars in weird, distorted positions, and the distortions would change over the course of the year, as the earth moved relative to the edge of the solar system. (Yes, I know the earth is kinda near the center of the solar sytem, but it still moves to some extent.) The relative positions of stars are measured to extraordinarily high accuracy, so if there were a refractive index change, it would be easily seen, unless the refractive index change were extremely small. I haven't gone through the calculation of exactly how small the refractive index has to be to be undetectable. Certainly a change of 1,000,000 can be ruled out!
-- ADDENDUM --
Here's a more specific way to think about whether it's astronomically observable. Just to be clear, let's do both 1:10^6 and 10^6:1 index contrast.
If the index is 1 inside the solar system and 10^6 outside... (Light travels slow in the interstellar medium.)
Then whatever direction we look, the rays exit the solar system more-or-less normal to the shell at the "edge of the solar system", by Snell's law. No matter where earth is, we see all the stars in almost exactly the positions they would be if we projected them onto the shell. (It would look like the ancient idea of a celestial sphere.) Then the question becomes:
Can we observe the parallax of an object at the edge of the solar system?
The answer is: Yes, very very easily. We can observe the parallax of stars far beyond the solar system, and we can observe that faraway galaxies have a parallax that's much smaller than that. So we can rule this possibility out.
If the index is 10^6 inside the solar system and 1 outside... (Light travels fast in the interstellar medium.)
Then almost any direction we look will have total internal reflection at the edge of the solar system -- we won't see any stars at all, maybe we'll even see a reflection of the sun -- except for the direction where we are looking almost exactly dead-on normal to the imaginary shell at the edge of the solar system. In that direction, there will be a little angular window where we will see all of the stars in every direction squeezed together. I think we can rule this out too!