The observed time dilation in GPS satellites is indeed evidence for the theory of general relativity, specifically the gravitational time dilation. It demonstrates that the rate at which time flows is influenced by the strength of the gravitational field.
The time dilation effect observed in GPS satellites is not due to the speed of light changing when it travels parallel to a gravity source, but rather it arises from the interplay between the curvature of spacetime caused by the Earth's gravitational field and the satellites' relative motion.
In the theory of general relativity, massive objects like the Earth cause spacetime to curve, and this curvature affects the passage of time. Clocks closer to a massive object, where the gravitational field is stronger, will tick more slowly compared to clocks in weaker gravitational fields.
GPS satellites are in motion relative to observers on the Earth's surface, and they are also located at higher altitudes where the gravitational field is slightly weaker compared to the surface. These two factors, relative motion and weaker gravity, combine to produce a measurable time dilation effect.
To account for this effect, the onboard atomic clocks on GPS satellites are intentionally designed to run slightly faster than clocks on the Earth's surface. This ensures that the clocks in the satellites remain synchronized with clocks on the ground and maintain accurate timing for GPS measurements.
If the time dilation effect were due to a change in the speed of light parallel to a gravity source, it would have broader implications for our understanding of fundamental physics. However, extensive experimental evidence, including not only the observations in GPS satellites but also other experiments such as the Pound-Rebka experiment and the Hafele-Keating experiment, consistently supports the framework of general relativity and the concept of gravitational time dilation.
In summary, the observed time dilation in GPS satellites is considered evidence for the general relativistic effects of gravitational time dilation rather than a change in the speed of light parallel to a gravity source. The theory of general relativity has been extensively tested and validated through various experiments and observations, providing a robust framework for our understanding of gravity and spacetime.