Gravitational time dilation does occur during free fall. According to the theory of general relativity, the presence of a gravitational field affects the passage of time. When an object is in a gravitational field or undergoing free fall in that field, time dilation occurs relative to an observer in a different gravitational field or at a different gravitational potential.
To understand why this happens, we need to consider the curvature of spacetime caused by massive objects. According to general relativity, massive objects like planets, stars, or black holes curve the fabric of spacetime around them. This curvature creates a gravitational field, and the strength of the gravitational field depends on the mass and proximity of the object.
When an object is in free fall within a gravitational field, it follows a geodesic path in curved spacetime. In this scenario, the object is not subject to any other forces apart from gravity. Importantly, an observer falling freely alongside the object would also be in free fall, and both would experience the same gravitational field.
From the perspective of an observer located outside the gravitational field or in a different gravitational potential, they would perceive the clock of the object in free fall as ticking slower compared to their own clock. This is due to the difference in gravitational potential between the two observers. The observer outside the gravitational field experiences a weaker gravitational field and is at a higher gravitational potential.
The effect of gravitational time dilation is consistent with the equivalence principle, a fundamental principle of general relativity that states that the effects of gravity are indistinguishable from the effects of acceleration. In free fall, the object is essentially accelerating due to gravity, and the observer falling alongside it experiences the same acceleration.
It's worth noting that the phenomenon of gravitational time dilation is not limited to free fall alone. Any variation in gravitational potential, such as being at different heights in a gravitational field, will cause time dilation. Clocks placed at higher altitudes experience time dilation relative to clocks at lower altitudes due to the difference in gravitational potential.
In summary, gravitational time dilation does occur during free fall. When an object is in free fall within a gravitational field, it experiences time dilation relative to observers outside the gravitational field or at different gravitational potentials. This phenomenon arises due to the curvature of spacetime caused by massive objects and is consistent with the equivalence principle of general relativity.