# Could the speed of light change outside our solar system

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:

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!

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!

• I think I'm following you somewhat. But, help me understand your line "we would see stars in weird, distorted positions..." My trouble is that we only see the sunset effect when the sun is at the horizon--when it is at an extreme angle with the medium's edge. Objects outside the solar system will never have any such angle due to their distances. So, won't that remove the effect? – Captain Claptrap Nov 5 '13 at 23:37
• No, it does not "remove the effect", it weakens the effect. When the sun is EXACTLY at zenith, there is no sunset effect, but at any other angle, there is an effect, and the effect gets bigger as the sun gets farther away from zenith. We have quite precise telescopes, which could easily measure the sunset effect even if the sun was only slightly away from the zenith. And, we're viewing the sun through a refractive-index change of 1.0003 versus 1 ... you're talking about a refractive index contrast that is a billion times larger, and therefore a billion times easier to see. – Steve Byrnes Nov 6 '13 at 2:06
• Ok, can you give a reference for your statement "We have quite precise telescopes, which could easily measure the sunset effect even if the sun was only slightly away from the zenith"? – Captain Claptrap Nov 6 '13 at 3:01
• Sure ... en.wikipedia.org/wiki/Atmospheric_refraction says that there's a 1 arc-minute shift at 45 degrees from zenith. 1 arc-minute is very very obvious with modern scientific equipment. If it was closer to zenith, the shift would be proportionally smaller. – Steve Byrnes Nov 6 '13 at 13:07
• Yes, but wouldn't stars in the sky be at near 90 degrees relative to the edge of our stellar atmosphere? This seems to help my case more than hurt it. So think of the observations being made from Hubble. All other stars would be at very near 90 degrees relative to the edge of refractive mediums, which according to my understanding of this wikipedia article would be the ideal observation point for negating any potential effects of the refracting mediums. – Captain Claptrap Nov 6 '13 at 19:39

I'd like to add a little to Steve B's answer, which is the one I can best understand so far. His crucial point is that "tapering" (smooth refractive index variation) makes no difference to the deflexion - it's only the beginning and ending values of the refractive index throughout the deflexion that determine the change in angle. To convince yourself of this, think of a ray running through a stack of thin, homogeneous layers and apply Snell's law to each. You'll find that all the "intermediate" indices and refraction angles cancel out.

Now I think on relativistic theoretical grounds we can fairly confidently say (with a possible loophole) that here on Earth we are not immersed in any refracting medium:

1. Recall that $$c$$, from relativity's standpoint, is no longer primarily thought of as the speed of light, it is simply a parameter with dimensions of speed that defines what reality is in a whole class (as $$c$$ ranges over $$[0,\infty)$$) of possible relativities that are all compatible with the postulates of special relativity and which generalize the Galilean transformation (which is simply what we get as $$c\to\infty$$ and Galilean relativity is indeed compatible with the basic symmetry and group theoretic postulates of special relativity). That sentence is a bit "dense" so see my answer here for more info. So we now need to find out by experiment what value of $$c$$ defines our Universe - which of this whole family of relativities we actually live in, if indeed $$c$$ is finite (infinite $$c$$ yields Galilean relativity);
2. From this modern standpoint, therefore, we do not identity $$c$$ by measuring the speed of light in a vacuum, we instead look for examples of velocities which transform under switches between inertial frames in the peculiar way that this group theoretic formulation of relativity foretells if the parameter $$c$$ is finite. This behavior is glaringly obviously different from the Galilean transformation. So it's not about its value, nor what it is associated with. It's about finding the kind of weird frame independence that we found in the Michelson-Morley experiment. Light shows exactly this behavior. One of the things that SR foretells is that it is only and precisely the class of massless particles that have this behavior. So now we interpret the MM experiment as yielding two independent results thus: Result 1: we've (i) found the weird, finite $$c$$ behavior shown by the speed of light, (ii) SR foretells that there can only be one such $$c$$ so now we know that our universe has a finite $$c$$ and it is not the special case of Galilean relativity that holds. Result 2: Light travels at this speed $$c$$ and so light must be propagated by a massless particle. Note that, would the MM experiment have turned out differently today, we'd interpret it not as telling against SR, but as yielding mass bounds on light.

Moreover, any kind of "medium" breaks the symmetries that underly special relativity, unless the medium does not interact with the massless particles we are using as our yardstick to measure $$c$$ with. Velocities of light in optical mediums transform under boosts quite differently from $$c$$. The matter of the medium throws up a "preferred" reference frame because the atoms / molecules in it "hold on to the light" for small time intervals in a process of cyclic absorption and re-emission that begets a "slowing of light" and thus an effective refractive index. The delays are nonzero and thus are dilated under boosts, leading to a dependence on frame of the refractive index.

Simply put, were we in any medium that interacts with light, we would almost certainly know it were there through Michelson-Morely kinds of experiments. We would get a non null result to the MM experiment i.e. the Earth's motion would affect the measured lightspeed, but we still wouldn't see the Galilean relativity that Michelson and Moreley foresaw. We'd see something in between, and we could even get good estimates on $$c$$ and how much greater than the speed of light it were. So we can be fairly sure that dark matter, if we're in it, has a refractive index of 1 and, if it does interact with light and the EM field, it does so in a weird and subtle way which we haven't yet worked out how to detect.

On Copernican grounds, we can argue that it is unlikely that the deep space between stars has a nonunity refractive index if, as we know, the space around our Earth almost certainly does not. It would be pretty weird if our little patch of space were so special that only here can lightspeed assume the universal constant $$c$$. So both here and in deep space, we have good reason to assume $$n=1$$ and that dark matter, if it is there, does not change this fact.

This leaves the last possibility of a layer towards the Solar System's edge of nonunity refractive index between us and the far stars. Okay, so now we return to Steve B's answer. This means that there must be no angular deflexion as in your "sunset" effect. There could be, though, a sideways shift of a ray through the medium depending on direction (see my drawing). Now, our galaxy is rather thick compared with the Solar System, so the sideways shift wouldn't make any difference to our ability to see stars. The source I could dig up The cosmoquest.org forum tells me that the angle between the Solar and Galactic ecliptic is about 60 degrees, hence my drawing.

Let's suppose we have a star that is such that its rays pass through the layer unshifted at some time in the year. Six months later there is a sideways deflexion of the ray $$d$$. If the medium were perfectly unchanging and were thick enough, we would see the inclination $$\theta_s(t)$$ of the star change with time $$t$$ in a way that would not agree with a simple triangulation without a within-year-varying horizontal shift $$d(t)$$. Snell's law within the medium would show itself. The effect would be subtle, but eventually by fitting inclination versus time models assuming simple triangulation to many stars, we'd see deviations that couldn't be explained any other way. In contrast, simple triangulation models do give accurate fits to the observed $$\theta_s(t)$$. Moreover, depending on what the medium is, its distribution might shift randomly with time, giving further distortions that we would detect in the end.

So it's not altogether impossible that we live in a light-interacting medium, but its highly unlikely we are immersed in it, an extremely good guess that the distant stars are not immersed in it and, if there are light-interacting medium at the edge of the Solar System, it's likely to be either very thin or with a refractive index very, very near to 1.

# Update for Questions:

Wait a minute. It occurs to me that for what I proposed, my refractive index numbers were way off in my calculators. I gave the extra solar medium an index of 1000000 thinking this would speed up light. But isn't that backwards? Wouldn't my index be less than one in order to account for faster light? What should the index be for a faster speed? A number smaller than one but greater than zero, or a negative number? Neither seem to work in the calculators.

The only way that the magnitude of the refractive index's real part can be less than one is within the narrow wavelength bands of so-called anomalous dispersion that happen for some materials. This means that the phase velocity is more than $$c$$ in these narrow bands. The signal propagation velocity on the other hand cannot be greater than $$c$$ without violating special relativity. See the "Group and Phase Velocity" section of the "Dispersion" Wikipedia page Anomalous dispersion, with its drastic dependence on wavelength, is really noticeable. We'd therefore see only very narrow parts of the spectrum of one star owing to the frequency dependence of $$d(f)$$. Negative real-part refractive index with magnitude more than one can also happen, but, as far as we know, it does not arise in nature and only arises in sophisticated metamaterials. Of course, maybe dark matter has this behaviour too. But even so, it shouldn't change my or Steve B's arguments. In a negative index material rays stay on the same side of the unit normal, so it's pretty bizzare indeed. see the "Negative Index Metamaterials" Wikipedia page.

• I hadn't thought of the possibility of a layer. Good stuff. +1 – Captain Claptrap Nov 7 '13 at 2:23
• Wait a minute. It occurs to me that for what I proposed, my refractive index numbers were way off in my calculators. I gave the extra solar medium an index of 1000000 thinking this would speed up light. But isn't that backwards? Wouldn't my index be less than one in order to account for faster light? What should the index be for a faster speed? A number smaller than one but greater than zero, or a negative number? Neither seem to work in the calculators. – Captain Claptrap Nov 7 '13 at 2:31

To build on Steve B.'s answer and give visual proof, I thought I'd post what I found after our discussion.

I found that the angle of stars to our own "stellar atmosphere" is actually near 0 degrees of "normal" for the purposes of calculation using Snell's law. This calculator I found shows what I mean:

The cool thing about this calculator is that when you enter a value, the red rays actually show you how it would look. The only limitation I see with this calculator is that it only lets you go to one decimal place for the angles and only as high as 1000 for the refractive index. Since my proposed values were much more extreme, I had to move on to something more precise...

The calculator below shows that with my proposed scenario, the angle of refraction would indeed bend the light in a way that would be obvious to observers on Earth:

Unless I'm mistaken, with a 10 degree refraction, I don't believe any stars would be visible at all to observers on Earth! So, my proposal is... absurd.

Edit 1, correction

Ok. I think my refractive index numbers were wrong in the above calculators. Since I'm proposing that the deep space medium has light traveling 1,000,000 times faster than in our solar system, the first index should be (I believe) 1 and the 2nd medium should be 1,000,000. This gives a resulting angle of .00000000009! Maybe my proposal was not absurd after all?

• I believe that most of the known equations assume c to be constant. If it varied, some basic conclusions of physics would be incorrect. Take time dilation, for example. Would time dilation be so drastically changed by changes in c due to changes in medium? Most likely, time dilation is constant regardless of medium, which is why medium is not factored into the relativity equations. If c varied, because it would be due to changes deeper than which substance surrounds light, it would likely not be noticeable, as proposed by relativity. – TheEnvironmentalist Nov 7 '13 at 3:46

Simple answer: The speed of light is not changed, space-time is what has changed.

My real attempt: Your question actually includes two different distortions on light...

The first is the gravitational distortion, this does not actually modify the time for light to get from point A to point B, it actually modifies the position of B. If this happens on a large scale, like in space, much of the light directed away from us may never be seen.

The second is a change in electronic and magnetic permeability of the space the electro-magnetic wave is traversing. Though experiments have been done to adjust the speed of light in this way it has not been proven to truly permanently change the frequency/momentum of light. Thus the moment light exits such a permeability it will return to the speed in free space.

After close examination of your question... I see a suggestion that due to a tapering of the index we cannot observe a dramatic adjustment in light speed outside our system. I think this would have been noted by resulting signals from one of the Voyagers. Let us presume this change is outside the rage of the Voyager craft. This sudden change in index would be due to gravitational effects therefore the space-time is what has been altered, making the effective distance for any physical object the same as what has been calculated by astronomers.

• I'm suggesting a medium change, not gravitational. Think of it like the solar system is a spherical fish bowl, only with no glass and a tapered rather than a solid/liquid edge. And, the refractive index of the medium in our solar system is much greater than water. – Captain Claptrap Nov 5 '13 at 2:00
• If some other medium than matter (electronic and magnetic permeability) or space (gravitational distortion) exists, than we have bigger discoveries to make than simply the idea we are surrounded by this medium. More like, how can we observe this new medium in laboratory tests. If this is true and light traverses faster outside our system, than things in space are a much greater distance away than we think. BTW: couldn't the Voyage craft at least be at the "distinction level". – Luke Burgess Nov 5 '13 at 13:52
• Suppose the medium is dark matter. Scientists agree that it exists, there's a lot of it and it cannot be observed/detected yet. So for all we know, we are in it. – Captain Claptrap Nov 5 '13 at 23:15

If c did change then I'm sure scientists would have noticed it when they received radio signals from voyager.

• Exactly what still functioning instrumentation does Voyager have that could detect differences in light speed? Please explain. Or are you saying the difference could be detected in the time it takes for the signals to reach us? I would think Voyager would have to be a lot further out in order for there to be any noticeable difference, since any increase in speed would be lost as soon as it reached the heliopause don't you? – Captain Claptrap Nov 5 '13 at 23:18
• The radio signals are made of light so the receiver on Earth would be the instrument for detection so yes the time it takes for the signal to travel the sistance. This would look like Voyager was speeding up or slowing down. A recent report on the accoustics/sounds of space that voyager picks up was just released. This showed that the heliosphere has expanded and contracted and Voyager has been in and out of the solar system a number of times. – Jitter Nov 7 '13 at 20:16