From the local frame of reference (the blue clock), relatively accelerated clocks move more slowly
Relative velocity time dilation
When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other’s (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation.
For instance, two rocket ships (A and B) speeding past one another in space would experience time dilation. If they somehow had a clear view into each other’s ships, each crew would see the others’ clocks and movement as going too slowly. That is, inside the frame of reference of Ship A, everything is moving normally, but everything over on Ship B appears to be moving slower (and vice versa).
From a local perspective, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always appears to pass at the same rate. In other words, if a new ship, Ship C, travels alongside Ship A, it is “at rest” relative to Ship A. From the point of view of Ship A, new Ship C’s time would appear normal too.
A question arises: If Ship A and Ship B both think each other’s time is moving slower, who will have aged more if they decided to meet up? With a more sophisticated understanding of relative velocity time dilation, this seeming twin paradox turns out not to be a paradox at all (the resolution of the paradox involves a jump in time, as a result of the accelerated observer turning around). Similarly, understanding the twin paradox would help explain why astronauts on the ISS age slower (e.g. 0.007 seconds behind for every 6 months) even though they are experiencing relative velocity time dilation.
