Speed of Light when not in a vacuum?

[Orwell1984]

In a vacuum the speed of light is a constant. What if its not in a vacuum?
Okay, as always I'm confused. I'm very interested in physics but am a layman.

Alright, so we know that time is relative to one's distance from a mass, so that as we go further from the Earth, let's say, time moves faster. I take that to mean 1 second on Earth is slower than 1 second outside our solar system. Correct so far?

We also know that the speed of light is 299,792,458 meters per second. Now, since 1 second gets progressively faster as you move away from the Earth, shouldn't the distance that time travels become shorter also as time gets faster? Of course, I'm assuming light does have a constant speed.

Now if the preceding statement is correct, then my real question is why measure the speed of light against a variable like time? Furthermore, when we calculate that a star, for instance, is 10 light years away from us, do we take into account the variability of time such that 10 light years really means, let's say, 9.99999999999999999 light years?

 

[Ibix]

In a vacuum the speed of light is a constant. What if its not in a vacuum?

Then it travels slower than $c$ by a factor of the refractive index, $n$, of the medium. This speed $c/n$ is also constant (it doesn't change with time - assuming the physical properties of the medium aren't changing), but does depend on your frame of reference (it is not invariant, which is to say that observers in motion with respect to the medium will measure different values) unlike the speed in a vacuum.

 

[Orwell1984]

Okay, as always I'm confused. I'm very interested in physics but am a layman.

Alright, so we know that time is relative to one's distance from a mass, so that as we go further from the Earth, let's say, time moves faster. I take that to mean 1 second on Earth is slower than 1 second outside our solar system. Correct so far?

We also know that the speed of light is 299,792,458 meters per second. Now, since 1 second gets progressively faster as you move away from the Earth, shouldn't the distance that time travels become shorter also as time gets faster? Of course, I'm assuming light does have a constant speed.

Now if the preceding statement is correct, then my real question is why measure the speed of light against a variable like time? Furthermore, when we calculate that a star, for instance, is 10 light years away from us, do we take into account the variability of time such that 10 light years really means, let's say, 9.99999999999999999 light years?

 

[Ibix]

For future information, it's worth asking the question you actually want to ask. None of this has anything to do with light traveling in a medium. Note - when I wrote this, post #1 appeared to be just the text quoted in #2. Post #3 has been duplicated in #1 at some point.

Alright, so we know that time is relative to one's distance from a mass, so that as we go further from the Earth, let's say, time moves faster. I take that to mean 1 second on Earth is slower than 1 second outside our solar system. Correct so far?

It is true that if you get two identical clocks and confirm that they both tick at the same rate, then carry one far from the solar system and look back at the other with a telescope, it will appear to be ticking slightly slowly. However I would not say that this means that one second on Earth is slower than one second outside the solar system. One second is one second is one second.

The underlying physics is closer to the idea that you can take a shorter path round a corner by taking the inside path. One meter is one meter is one meter, but there are fewer meters used if you go round the corner on the inside path. Similarly, there are fewer seconds used on the path through spacetime that you follow deep in a gravitational well.

why measure the speed of light against a variable like time?

We don't. The speed of light is defined, as is the second. The meter is a derived unit, following from those two definitions.

Furthermore, when we calculate that a star, for instance, is 10 light years away from us, do we take into account the variability of time such that 10 light years really means, let's say, 9.99999999999999999 light years?

When we say a star is ten light years away, we're rounding off to the nearest tenth of a light year, or even coarser. This kind of effect is on the level of fractions of a light second.

In principle, yes, you'd have to decide exactly what you mean by "distance" when reporting distances in curved spacetime. In practice, it makes no measurable difference.

 

[davenn]

Alright, so we know that time is relative to one's distance from a mass, so that as we go further from the Earth, let's say, time moves faster. I take that to mean 1 second on Earth is slower than 1 second outside our solar system. Correct so far?

No

Now, since 1 second gets progressively faster as you move away from the Earth, shouldn't the distance that time travels become shorter also as time gets faster? Of course, I'm assuming light does have a constant speed.

It doesn't ... 1 sec = 1 sec = 1 sec, regardless of where you are in the universe

 

[davenn]

In a vacuum the speed of light is a constant. What if its not in a vacuum?

The speed of light is slower in any medium other than a vacuum. It's speed depends on the medium
For example, in an optical fibre used for telecommunications, the speed of light is only 70% that of when in a vacuumDave