Which clock is really slower? (Not the Twin Paradox)?

From my perspective, the spaceships are both flying in opposite directions - at 1/4 c. Both clocks are ticking at the same speed, but slow according to my watch.

Each clock actually does tick at the same speed in each one's respective frame of reference. Each clock, when observed from a different frame of reference, actually does does run slowly with respect to the other frame of reference.

With respect to the theory being called "relativity theory" for a reason, it is interesting to note that Einstein originally wanted to call the theory the Theory of Invariance - in other words, that all physical laws were invariant, regardless of the frame of reference. He initially wanted to stress that the clocks were all actually running at the same speed in their own frames of reference, as opposed to running at different speeds from one frame of reference. Of course, the theory has both elements - it is true for all frame of reference (it is invariant) - and things like measured speeds, sizes and time are different relative to the frame of reference from which they are measured.

Since you already know the answer, you know that both A and B are correct in their own reference frames. If A and B have a light-beam clock, each sees his own ticking normally with the photon bouncing up and down in it, while the other's clock's photon must execute a sawtooth pattern and therefore it takes longer to tick. Apply principle of Relativity to all other types of clock.

What seems to be the problem?

As far as I know, it is only possible to compare the clocks and find the slow clock after the ship slows down and goes back to mee the other ship. If the two ships keep moving relative to each other, both will see the other ship's clock as moving slow and this cannot be reconciled without one of the ships accelerating in some direction in order to match velocities. I'm no expert on the subject, though, so I could be wrong.

i've got faith this is a function of Einstein's generic relativity (GR). You plug "prevalent" gravity fields into the area-time "metric" and you get a "answer" that's seen to be genuine. situation is, acceleration due on your deliver's engine is seen to be a gravity field. the situation isn't lots in the formula because it is in the jargon, which makes the destiny situation sound like a carried out deal. there is an option technique of computation. you are able to clean up the situation with the aid of a numerical pc application, utilising particular relativity to little while periods. If the time periods are short sufficient, you will get precisely a similar result as GR. needless to say, you may make a similar results of assuming the adventure will bypass as planned. the adaptation is, you get a result it is valid as much as the element the place certainty deviates from the plan.

Both observers see the other clock running slower.

Its is called "relativity" for a reaons - there is no preferred frame.