The fact that GPS satellite clocks run slower is actually evidence of both time dilation and the effect of gravity on the speed of light. This phenomenon is a consequence of Einstein's theory of general relativity, which predicts that both time dilation and changes in the speed of light occur in the presence of a gravitational field.
According to general relativity, gravity affects the fabric of spacetime, causing it to be curved or warped around massive objects. When light passes through this curved spacetime, its path is bent, which results in a change in its apparent speed. This effect is known as gravitational time dilation.
In the case of GPS satellites, they operate in a weaker gravitational field compared to the Earth's surface. The satellites are further away from the massive object (Earth) and experience a slightly weaker gravitational pull. As a result, the gravitational time dilation effect causes time to pass slightly faster for the satellites relative to an observer on the Earth's surface.
However, the speed of light in a vacuum is a fundamental constant of nature that is considered to be invariant. According to the theory of relativity, the speed of light in a vacuum is constant regardless of the observer's reference frame or the presence of gravitational fields. This means that the speed of light does not change when it travels parallel to a gravity source.
In summary, the observed time dilation effect in GPS satellite clocks is a consequence of both gravitational time dilation and the constancy of the speed of light. It provides evidence for the validity of Einstein's theory of general relativity, which accurately describes the behavior of light and time in the presence of gravity.