The phenomenon observed in GPS satellites, where their clocks run slower than clocks on Earth's surface, is indeed evidence of time dilation. However, this effect is a consequence of the theory of relativity, specifically general relativity, rather than a change in the speed of light.
General relativity, also proposed by Albert Einstein, is a theory that describes how gravity arises from the curvature of spacetime caused by mass and energy. In the presence of a massive body, like Earth, spacetime becomes curved, and the path of light is affected as it travels through this curved spacetime.
The time dilation effect in GPS satellites is a combination of both special and general relativity. Here's how it works:
Special Relativity: According to special relativity, when an object moves at a significant fraction of the speed of light, time appears to pass more slowly for that object relative to a stationary observer. This is called time dilation due to relative velocity. In the case of GPS satellites, they are moving at a very high speed relative to observers on the Earth's surface, so their onboard atomic clocks appear to run slightly slower than clocks on the Earth.
General Relativity: General relativity predicts that time also runs differently in regions with different gravitational potentials. Clocks in stronger gravitational fields appear to run more slowly relative to clocks in weaker fields. This effect is known as gravitational time dilation. Near Earth's surface, where the gravitational field is stronger, clocks tick more slowly compared to clocks farther away from the Earth.
The combination of these two relativistic effects causes the observed time dilation in GPS satellites. The satellites are moving at high speeds relative to Earth's surface, and they are also farther away from Earth's center (in weaker gravitational fields) compared to observers on the ground.
Importantly, the effect is not due to a change in the speed of light. The speed of light remains constant in a vacuum, and it always travels at approximately 299,792,458 meters per second, as confirmed by countless experiments.
The precision of GPS systems requires accounting for both special and general relativistic effects to ensure accurate timekeeping and position calculations. If these relativistic corrections were not taken into account, GPS location accuracy would degrade significantly over time. The fact that these corrections are necessary and have been verified through experiments is strong evidence in favor of the validity of both special and general relativity.