The equivalence principle states that the effects of gravity are locally indistinguishable from the effects of acceleration. It implies that the experience of an observer in a gravitational field is equivalent to the experience of an observer in an accelerated reference frame.
Acceleration does indeed cause time dilation. According to the theory of relativity, when an observer is in an accelerated reference frame, their experience of time is affected. This effect is known as gravitational time dilation or gravitational redshift. In an accelerated reference frame, clocks run slower relative to an observer in an inertial frame of reference.
However, it's important to note that the equivalence principle applies to gravitational fields and not to all forms of acceleration. The key distinction is that the equivalence principle specifically refers to the effects of gravity as indistinguishable from the effects of acceleration. It does not imply that all forms of acceleration will cause time dilation.
In the case of gravity, the equivalence principle relates the gravitational force experienced by an object to its acceleration. The presence of a gravitational field causes spacetime to curve, resulting in the observed effects of time dilation. Acceleration in a non-gravitational context, such as in a rocket accelerating through space, would not necessarily cause the same type of time dilation as experienced in a gravitational field.
In summary, while both gravity and acceleration can cause time dilation, the equivalence principle specifically relates the effects of gravity to those of acceleration, highlighting their indistinguishability in a gravitational field.