Consider three points in space A,B,F where F is midway between A and B, all in the same inertial frame. Because A,B,F are in the same frame, their clocks can all be synchronised in advance.

A race is to be held. Two identical spaceships set out from F, at leisure (non-relativistic speeds), and make their way to A and B respectively. Once both ships are in position, a 'start' signal is sent from F, which reaches A and B at the same time - each ship then starts its clock and sets off. Or alternatively, the ships can just agree in advance at what time they will set off, using the already synchronised clocks at A and B as their reference.

The two ships each race at the same near-light speed to the finish point F, arriving together, and all compare clocks.

I think that

- F will consider each ship to be the same age as the other, but having experienced less time than the observer at F.
- Each ship will consider F to have experienced less time than itself, by the same amount - so disagreeing with F about who is older but agreeing between themselves as to the age of F.
- Each ship will consider the other to have experienced less time than itself, disagreeing with each other about who is older.

So - disagreements between the ships and between the ships and F, as to who is older than whom.

Here however, there is no frame change to reconcile the apparent paradox. The journeys really are symmetrical, and so far as I can see, plotting spacetime diagrams doesn't help resolve this either.

Is there something wrong with my understanding that all clocks in a single inertial frame can be synchronised (by bouncing light signals between each other, and using the fact that the time taken for a light signal to reach a remote clock is half that of a round trip back to the start point).

I must be missing the obvious! But what?