First start with one observer. The observer considers himself at rest. The observer has an infinite number of rods, which all have the same length. Using his rods, he builds a 3D grid. At all the cross sections he places an identical clock. The clock operates by means of a light signal which oscillates between two mirrors. Each cycle of such a clock is considered a tick of the clock.
Next all the clocks synchronised. The general idea is first two synchronize two clocks in 1 direction. This is done by selecting a point half way between those 2 points. A light flash emitted from that point can be used to synchronize these 2 clocks. When 2 clocks are synchronized, he can use these 2 points to synchronize 4 clocks etc.
In order to test if his reference frame is at rest the observer should select 2 clocks A and B. Next, he places a third clock C near A and he synchronizes the clock C with A. The final step is to move clock C from A to B.
In reflection 2 we also have one reference with two clocks A and B which are considered at there. We also have a moving clock C which can be considered at rest in its own reference frame #2. In frame #2 the two clocks A and B are moving. What you also need in frame #2 is a 'second' point D at rest in that frame. Using the two points C and D (at rest) and the moving clock A, which moves from C to D you can perform the same experiment as in reflection 1 and decide which frame is at rest.
In general, it is not easy to define a system at rest.
For our Solar System, we can consider the Sun at rest.
For our Galaxy, the Milky Way, we can consider the Black Hole Sagittarius A* at rest.
If we study the Milky Way and de Andromeda Galaxy, which both move towards each other, it should be the centre of gravity.
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