Can Gravity affect the Speed of Light?
Light is, of course, affected by gravity but not in its speed, technically. Gravity cannot affect the locally measured speed of light or the actual speed of light but it can affect the observed/calculated speed of a light coming from a distant point in space due to the spacetime curvature and bending of the path of the light.
When we say that light travels at 299792458 m/s (approximately) in a vacuum (denoted as c) we mean the speed that was locally measured.
First of all, gravity can only affect light in 2 ways. It can bend the path of light or it can change the energy of light by shifting the frequency of the light (we are not concerned about the second one in this article).
According to Special Relativity, the speed of light is always constant for all observers i.e. if I measure the speed of light at my location I will always get the same value and this is true whether I’m sitting in my chair, riding around a city, revolving around the earth, falling into a black hole or whatever.
But according to General Relativity, the above statement is only true if the spacetime is flat i.e. if the spacetime is curved then all observers everywhere will measure the same value of c only if the measurement is done locally at their locations.
This means that if I measure the speed of light at my location I will always get the maximum value of speed to be c but if I measure the speed of light coming from some point that is distant from me, I may get a value different from c if there is a huge mass in my way bending the light’s path. Specifically, if I’m sitting well away from a black hole and I measure the speed of light near its surface I will get a value less than c.
When gravity bends the path of light, we may get a different value for the speed of light if we calculate it from a distant location, (but the value is always lesser than c) because of the time delay and distance incorrectly calculated according to the apparent position of the source.
But locally, the vacuum speed of light still remains constant i.e. if I locally measure it at my spot devising some experiment I would get the value of the speed of light to be c. However, as seen by a distant observer, the time it takes for light to travel between two points increases if there is a huge mass in the way of light (as given in image), he would observe the speed of light to be different from c. So this way the measurement of the speed of light is changed or affected by gravity without actually affecting the real speed of light.
For example, it may take an infinite amount of time (as measured by a distant observer) for light to come out of a black hole. In this case, he will measure the speed of light as zero despite the fact that, once again, locally measured vacuum speed of light is always c.
TD; LR Gravity may seem like affecting the speed of light for a distant observer due to spacetime curvature but the locally measured speed of light by the observer will still be c = 299792458 m/s i.e. the measurement of the speed of light may appear to have been changed or affected by gravity without actually affecting the real speed of light.
