Is the speed of light in the Universe always $c$?

Question

Every one here knows that $c=(ε'×μ')^{-1/2}$. But what if ε' and μ' are different values in other parts of the visible universe. Maybe near the center of a Quasar galaxy or even a Neutron star?

Answer 1

First, the speed of EM waves in vacuum, when measured locally is always c.

Of course in media, the speed of light could be different then c.

The speed c is only the limit when measured locally.

As per GR, it is very good to learn about the Shapiro effect. The speed of light passing near the Sun (as seen from Earth) will be less then c. Why is that?

It is because the speed of light is calculated by the distance it travels, divided by the time passes.

Now here on Earth, our clocks run faster compared to the clocks at the Sun. That is because the Sun's stress-energy is bigger, and its gravitational effects are stronger and it slows down time near the Sun (compared to the clock on Earth).

Now when we are trying to calculate the path, the Sun's stress-energy curves spacetime and light travels in a spacetime that is not flat as it passes the Sun.

Now if we calculate the speed of light as it passes the Sun, our clocks here on Earth show more time to pass, so we will divide by a bigger amount of time.

If you divide the path that the light travels, with a time that is bigger, you will get a speed less then c.

Analogously, if you would measure the speed of light as it passes near the Earth, when viewed from the Sun, it would be more then c. It is because clocks at the Sun would run slower (compared to clock near the Earth), and so less time would pass on the clocks at the Sun, where the observer is. You would divide the path with a time that is less (compared to the time that passes near the Earth), and so you would get a speed more then c.

This is one of the basic experimental tests of GR.

So the speed of EM waves is c everywhere in vacuum in the universe, when measured locally.

But when measured non-locally, it might vary.

Now this speed is the speed of Gravitational waves too.

Answer 2

the idea that the constants of nature might be different in different locations in the universe has been around for a while, and astronomers have tried to determine if this is true or not. To date, no solid evidence has turned up that the constants of nature vary from place to place or from time to time.

There's been a fair amount written about how the universe would be structured if the different constants of nature varied slightly from the values we measure them to possess today. Even small changes in, for example, the value of the gravitational constant or the ratio of strengths of the electromagnetic and gravitational force would cause the universe to evolve into something radically different from what we observe and experience now.