# Could we construct an experiment to measure the speed of light greater than c?

As I understood we were not able but then i read John Rennie's question and answer here:

Does light really travel more slowly near a massive body?

And got me a little bit curious.

He says:

We can extend our analysis to find the speed of light in the shell coordinates at radial distances greater and less than the shell distance. The argument is essentially the same as above so I’ll just give the result:

$$\frac{dr’}{dt’} = \pm c \frac{1- r_s/r}{1 – r_s/R} \tag{4}$$

And this looks like (for $R = 2r_s$):

Like the Schwarzschild observer the shell observer sees the coordinate speed of light fall when the light is closer to the massive object than they are, but the shell observer sees the light move faster than $c$ when the light is farther from the object than they are.

Question:

1. Is it really possible to construct an experiment where we would measure the speed of light faster then c?

You don't need to do a new experiment in order to see the coordinate velocity of light be different from $c$. A coordinate velocity can be any number you like, simply by your choice of coordinates. Pick any experiment that measures $c$, change coordinates, and express the speed of light in those new coordinates. For almost any choice of coordinates, the coordinate speed of light will be unequal to $c$.
The coordinates in which the speed of light equals $c$ are the local Minkowski coordinates of an inertial observer.