I'm sure I must have something very confused but I'm just reading through SE questions and articles and this seems to be a contradiction. Until recently I had no problem as I assumed that acceleration did in fact cause time dilation, then I read numerous answers from people stating clearly that when calculating time dilation, only the distance travelled matters, not the path taken. For instance it is claimed that for a body experiencing centripetal acceleration, only the tangential velocity is relevant to the time dilation effect, not the radial acceleration.
I have 2 issues with this:
- The Equivalence Principle states that being in an accelerating reference frame is indistinguishable from standing still in a gravitational field. We know that gravity causes time dilation, so why not acceleration?
- The Twin Paradox is supposed to be resolved by the acceleration effect. Otherwise the time dilation is completely reciprocal and no difference will be seen between the clocks. Therefore acceleration must be causing time dilation?
How can these statements be reconciled? One page tells me acceleration is irrelevant, the next tells me it's equivalent to gravity. Both cannot be true.