Gravitational time dilation is a phenomenon predicted by Einstein's theory of general relativity. It states that time passes more slowly in regions of stronger gravitational fields. This means that clocks closer to massive objects, such as stars or black holes, will appear to run slower when observed from a distance.
The Shapiro time delay is a consequence of gravitational time dilation and occurs when electromagnetic signals, such as light or radio waves, pass through a gravitational field. As these signals travel through the curved spacetime near a massive object, their path is bent by the gravitational field.
According to general relativity, light follows the curvature of spacetime, which is influenced by the presence of mass. As a result, the path of the light is longer than it would be in flat spacetime. Since the speed of light is constant, this means that the signal takes longer to travel through the gravitational field than it would in the absence of gravity.
The Shapiro time delay is particularly noticeable when the signal passes close to a massive object, such as the Sun. When light from a distant star passes near the Sun on its way to Earth, the path of the light is bent by the Sun's gravitational field. This bending of the light causes a delay in its arrival time compared to what would be expected in the absence of gravity.
The Shapiro time delay has been experimentally confirmed through precise measurements of the time it takes for radar signals to travel past the Sun. These measurements have provided strong evidence for the validity of general relativity and its predictions regarding gravitational time dilation and the bending of light in the presence of massive objects.