Yes, time dilation does occur for falling objects in the presence of a strong gravitational field. This phenomenon is known as gravitational time dilation.
Gravitational time dilation arises from the curvature of spacetime caused by massive objects. According to Einstein's general theory of relativity, mass and energy warp the fabric of spacetime, creating a gravitational field. In regions of stronger gravitational fields, such as near massive objects like planets, stars, or black holes, time runs slower compared to regions of weaker gravitational fields.
To understand the concept, consider a scenario where there are two observers, one situated in a strong gravitational field (e.g., on the surface of a planet) and another at a location with weaker gravity (e.g., far away from any massive objects). The observer in the stronger gravitational field would experience time passing more slowly compared to the observer in the weaker field.
This effect can be attributed to the curvature of spacetime caused by the presence of mass. The greater the gravitational field, the more spacetime is curved, and consequently, the slower time flows. This means that clocks closer to a massive object will tick more slowly relative to clocks farther away.
One famous experiment demonstrating gravitational time dilation is the Pound-Rebka experiment conducted in 1959. It involved measuring the frequency shift of gamma rays emitted by a source at the bottom of a tower compared to a detector placed at the top. The results confirmed that time dilation occurs due to gravity.
Gravitational time dilation has significant implications for our understanding of the universe, including phenomena such as black holes, gravitational waves, and the behavior of light near massive objects.