First of all, let me state that my question is not about time dilation as observed between inertial reference frames moving at different velocities, which is completely symmetrical. It's about time dilation due to gravitation/acceleration (e.g. the case of individuals againg at different rates).
Reading the following thread:
a couple of doubts crossed my mind.
An user answers:
you can't say the time dilation is due to velocity or due to acceleration, just that it's due to relative motion.
It's at the end of the second answer, from above. Note that the guy has a big bunch of gold badges, so I'd trust him.
Another user, below, says:
Now as a gravitational acceleration has the same effect on clocks as a rocket powered acceleration, and as a clock in a rocket powered acceleration will get slower and slower the longer the acceleration occurs, then a clock that exists say for 100 million years on the earth and is subject to gravity for the entire period and therefore an acceleration for 100 million years will tick more slowly now in 2015 than it did 100 million years ago.
So, a clock on Earth will slower steadily with respect to a clock in the intergalactic space, even if those two clocks are in no relative reciprocal motion. Is that correct? Is the first guy wrong?
A closely related issue: 1g of acceleration may seem an eerie thing, but it's not so: it has been calculated that a spaceship accelerating at a constant rate of 1g, can manage a tour along the observable universe, and get back to earth, within the lifespan of those inhabiting the ship. Obviously, they will find Earth aged billions of years. Now, if acceleration by gravity is the same as acceleration by rocket drive, we on Earth should see the rest of the universe aging at a much faster rate with respect to us, like those on the spaceship.. After all, it's the same 1g both for them and for us. Am I right? (Obviously not, but why?)
Another thought experiment: We are in a region more or less empty space, and suddenly a messive object pops up. We begin accelerating toward that object, at a conspicuous rate, or, in other words, are put in relative motion with respect to the object, and our respective relative velocities grow steadily. Note, however, that we are in free fall, and our accelerometer says "0 g". We experiment no forces, and still our velocity increases. Will we experiment any phenomena of time dilation and aging differences with respect to the people on the surface of the object?