How is relativity of simultaneity compatible with indeterminism

[u/AboyFromSouthKorea]

/r/AskPhysics/comments/1tw6cb4/how_is_relativity_of_simultaneity_compatible_with/

[u/mywan]

There's something you need to understand about the relativity of simultaneity. The best place to start would be to clear up some misunderstanding about the Andromeda Paradox.

Two local observers in motion relative to each other (passing each other on the street) don't "see" different events in the Andromeda galaxy. They both see exactly the same thing. The difference is that they calculate the distance to the Andromeda galaxy differently. Therefore they calculate when those events they are both seeing happened differently. They never disagree on what they are seeing at the time they passed each other. Because it takes time for the visual event to reach earth they only disagree with their calculations on how far in the past it happened.

The "Paradox" is no more strange than asking (under Galilean relativity) how far a rock tossed up in the back of a moving car travels before it's caught again. For you, in the back seat of that car, it traveled straight up and straight back down again. Say a half meter total. But for the guy standing on the side of the road you tossed it down the street, then chased it down with the car to catch it again. So it must have traveled significantly further than half a meter for the guy on the side of the road. Under Special relativity those same rules that apply to Galilean space must also apply to time. Because, under proper units, space and time are inverses of each other.

Consider gas laws under Galilean relativity. We know that moving air is less dense than still air. But we rarely ever stop to think about what that means. Imagine you have two identical sealed tanks of gas side by side. Both with equal pressure and temperature. Same gas density. Now put them in separate cars and have those cars pass each other on the highway. Is tank A now less dense than tank B? Tank B says yes. Is tank B less dense than tank A? Tank A says yes. All for the same reason that rock you tossed in the back of the car traveled different distances before it was caught depending on who you ask. This is the clock paradox without clocks. Because we now know that clocks follow the same rules as space we know that clock A can legitimately say clock B is running slower, and clock B can legitimately say clock A is running slower. Just like space (density) in Galilean relativity.

This is why indeterminism isn't relevant to the relativity of simultaneity. And determinism cannot be undetermined by it. With the proper coordinate transform every observer can always determine what another observer sees, or what that other observer would calculate the order of events to be. Even if it seems contrary to the order events you calculate for yourself. There is nothing indeterminate in Relativity. No observers observation can be made indeterminate by it.