I am not a physicist by training, but I have studied special relativity enough to understand why simultaneity is a relative concept, and so why if you synchronize clocks in one inertial frame, an observer in another inertial frame wouldn't agree that they are synchronized. Usual textbook example is this: Consider two clocks located at opposite ends of a train which is moving with constant velocity. There is a light source in the middle of the train. It sends two light pulses towards the two clocks simultaneously and clocks begin to run when they receive these light pulses. Observer on the train says that the two clocks are synchronized because for him, light pulses have traveled equal distances. But an observer on the platform disagrees because for him light pulses have traveled unequal distances. This happens because light speed is the same for all inertial observers.
This example makes me wonder if this peculiarity arises because we have used light wave, which does not require a medium to travel, and hence must have constant speed for all inertial observers. What if we used some material wave instead, say sound?
Say there is a long horizontal tube closed off at both ends, and filled with water. The two clocks are placed at opposite ends of the pipe. A sound wave is generated at the center of the tube which travels through water towards both ends, and clocks begin to run once they receive the sound wave. The entire setup is inside the moving train. Observer on the train will as before say the clocks are synchronized.
But how can the observer on the platform now disagree that the two clocks are synchronized?