Please look at this animation.
The green dots and red dots in the animation represent spaceships. The ships of the green fleet have no velocity relative to each other, so for the clocks onboard of the individual ships, the same amount of time elapses relative to each other, and they can set up a procedure to maintain a synchronized standard fleet time. The ships of the "red fleet" are moving with a velocity of 0.866 of the speed of light with respect to the green fleet. The blue dots represent pulses of light. One cycle of light-pulses between two green ships takes two seconds of "green time", one second for each leg.
As seen from the perspective of the reds, the transit time of the light pulses they exchange among each other is one second of "red time" for each leg. As seen from the perspective of the greens, the red ships' cycle of exchanging light pulses travels a diagonal path that is two light-seconds long. (As seen from the green perspective the reds travel 1.73 $( {\displaystyle {\sqrt {3}}} {\displaystyle {\sqrt {3}}})$ light-seconds of distance for every two seconds of green time.)
The animation cycles between the green perspective and the red perspective, to emphasize the symmetry.
Image and Extract Source Time Dilation Wikipedia
I have calculated, how many ticks moving clock makes during time of travel and how many ticks any clock at rest.
While moving makes 3, any clock at rest makes 6. Well, moving clock dilates. But observer at moving RED clock will think like that: when I started, my clock showed 12 and GREEN clock at rest showed 12. Then, some later, my RED clock shows 3 and GREEN clock at rest shows 6. That means, clocks at rest (time in reference frame) runs faster.
Then RED clock forgets, that it was in motion and becomes one at rest. The GREEN clock now moves in RED frame and dilates. But, I am afraid to say, now the GREEN clock measures that RED clocks run faster.
Well, let’s imagine a sand clock with two flasks A and B. The sand is in the bottom in flask B, flask A is empty. Then we turn the clock upside down. Sand falls into flask A. Now flask B is empty.
Flask A is empty and flask B is empty. There is less sand in the flask B from the point of view of A and vice versa. Paradox. Reciprocity of observations. Symmetry.
If two observers move relatively to each other with velocity 0.9 c, how each of them can be “at rest”? Who moves with velocity 0.9 c? They both? Nobody? GREEN first, RED then?
Isn’t it the same sort of symmetry as in the sand clock?
What is physical reality? One mutual space or different frames that describe it?
Is it necessary to replace once chosen reference frame which describes mutual for the both observers space with a new one?
Finally, can observer think that he is in a state of motion, but not at rest?