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Hartle pg 60

The relativity of simulataneity means that it does not make sense in general to say that one event is later than another. An event can be later than another spacelike separated event in one inertial frame and earlier in another. But it does make sense to say which is the earlier of two timelike separated events. That’s because events to the future of P(point in spacetime) are inside its future light cone, and the inside and outside of a light cone are properties of the geometry of spacetime—the same in all frames.

I'm not able to understand that why for timelike, why there is a fixed sequence of events while for spacelike out isn't. Can anyone please explain this?

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Well the author says, that two events can be separated by timelike or spacelike interval.

If two events are separated by timelike interval, this means that one can cause the other, in other words a signal from one can reach the other. Which means, we can say which of the events have happened earlier, and that fact does not depend on a coordinate frame.

On the other hand, if events (A and B) are separated by spacelike interval, this means one cannot cause the other. And we can choose a coordinate frame in which A happens before B, and also we can choose another coordinate frame in which B happens before A. So 'objectively' one cannot tell which of these evens have happened earlier.

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