Yes, clocks do experience gravitational time dilation in the presence of a gravitational field. Gravitational time dilation is a consequence of general relativity, which states that the gravitational field affects the passage of time.
According to general relativity, the closer a clock is to a massive object, such as a planet or a black hole, the slower it will tick relative to a clock located further away from the gravitational source. This means that time runs slower in a stronger gravitational field compared to a weaker gravitational field.
To illustrate this concept, let's consider an example: Suppose we have two identical clocks, one located on the surface of a massive planet and another located far away in space where the gravitational field is significantly weaker. The clock on the surface of the planet, experiencing a stronger gravitational field, will tick more slowly compared to the clock in space.
This effect has been experimentally confirmed through various observations and measurements. For instance, atomic clocks placed at different altitudes on Earth have been found to exhibit small differences in their tick rates due to the variation in the strength of the gravitational field with altitude.
Gravitational time dilation is a fundamental aspect of general relativity and has important implications for our understanding of space, time, and the behavior of clocks in the presence of gravity.