Time dilation is not solely caused by an object's mass. While it is true that gravity can cause time dilation, and massive objects can generate gravitational fields that lead to time dilation, there are other factors that can also cause time dilation, including relative velocity.
In the theory of relativity, both special relativity and general relativity, time dilation occurs due to the interplay between gravity and relative velocity.
In special relativity, time dilation arises from the effects of relative velocity. When two observers are in relative motion with respect to each other, they will measure time to be passing at different rates. The faster an object moves relative to an observer, the more time dilation occurs. This effect is described by the famous equation derived from special relativity:
Δt' = Δt / √(1 - (v^2/c^2))
where Δt' is the dilated time measured by the moving observer, Δt is the proper time measured in the stationary frame of reference, v is the relative velocity between the observer and the moving object, and c is the speed of light.
In general relativity, time dilation is influenced by both relative velocity and gravitational fields. Gravity affects the curvature of spacetime, and in regions of strong gravitational fields, time dilation occurs. This effect is often observed near massive objects such as black holes or in highly dense environments. The gravitational time dilation can be described by the formula:
Δt' = Δt * √(1 - (2GM/(rc^2)))
where Δt' is the dilated time measured near a massive object, Δt is the proper time measured far away from the massive object, G is the gravitational constant, M is the mass of the object, r is the distance from the center of the object, and c is the speed of light.
It's worth noting that the increase in mass with speed, as described by Einstein's mass-energy equivalence (E = mc^2), does not directly cause time dilation. The increase in mass at high speeds is a relativistic effect, but the time dilation itself is a consequence of the relative motion between observers or the presence of gravitational fields.
Therefore, time dilation is caused by a combination of factors including gravity, relative velocity, and the curvature of spacetime.