No, acceleration is not the cause of time dilation. According to the theory of special relativity, time dilation occurs due to relative motion, not acceleration.
In special relativity, the concept of time dilation arises from the fact that the speed of light is constant in all inertial reference frames. When two observers are in relative motion with respect to each other, they will measure different elapsed times between events. This effect is a consequence of the spacetime geometry and is not related to acceleration.
The time dilation formula, known as the Lorentz transformation, takes into account both the relative velocity between the two observers and the constant speed of light. It shows that as an object's velocity approaches the speed of light, time slows down relative to a stationary observer. This effect is observed in various experiments and has been confirmed by numerous experiments and observations.
Acceleration does play a role in general relativity, which is a theory that extends special relativity to include gravity. In general relativity, gravitational time dilation occurs when there is a difference in gravitational potential between two locations. This can be observed, for example, near massive objects like black holes or in gravitational fields of varying strength.
In summary, time dilation is primarily caused by relative motion, not acceleration. While acceleration does have an effect on time in the context of general relativity, it is not the primary cause of time dilation as described by special relativity.