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For 2 timelike seperated events A and B you can find different inertial reference frames in which A and B happen in different order.But what if the entropy of a system after A happens is much higher than the entropy of the system after event B happens then could we observe in any reference frame the entropy of the system to be reduced?But wouldnt that violate the 2nd law of Thermodynamics?

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Your first sentence is incorrect. If A and B are timelike separated, their order cannot change, even if the time interval and space interval between them change with the observer.

If they are spacelike separated, different observers can see them in different order, but they also cannot have any casual effect on one another. So they cannot have any effect on the entropy of a common system unless they and the system are timelike separated. In which case their order is fixed.

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  • $\begingroup$ No.Lets perform the following thought experiment.Imagine 2 lightnings striking at points A and B.If you are stationary relative to both you will see them hit the ground at the same time.However lets jump on a moving train moving in the direction from point A to point B.Now you will clearly see the lightning hitting the ground A first ,then B.The event of lightning A and event of lightning B hitting the ground are timelike seperated. $\endgroup$
    – appliedSciences
    Commented Apr 6, 2023 at 1:32
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    $\begingroup$ In your example, the lightning strikes at A and B are spacelike separated. This implies there exists a reference frame where the events happen simultaneously, but at different spatial locations. Try for yourself: the formula is $\Delta s ^2=c^2 \Delta t ^2 - \Delta x ^2$. $\Delta s < 0$, spacelike, $\Delta s > 0$, timelike, $\Delta s = 0$, lightlike (null). Say that in the ground (stationary) frame, A and B are located 2 light seconds apart, and occur at the same instant. $\endgroup$
    – RC_23
    Commented Apr 6, 2023 at 2:17
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    $\begingroup$ Ok thanks a lot! $\endgroup$
    – appliedSciences
    Commented Apr 6, 2023 at 2:23

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