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If two events are separated by a time-like interval, then all inertial reference frames will agree on the order of the two events. For example, if event A occurred before event B in one inertial reference frame, then event A occurred before event B in all inertial reference frames.

The invariant interval, given by I = -(c[itex]\Delta[/itex]t)^{2}+([itex]\Delta[/itex]x)^{2}+([itex]\Delta[/itex]y)^{2}+([itex]\Delta[/itex]z)^{2}, for two events separated by a time-like interval is always less than 0.

My question is, for two events that are causally connected, can the invariant interval be less than or equal to 0? Or does I have to be strictly less than 0 for such events?

I'm not sure because as far as I'm aware, there can only be a causal connection between two events if it is possible for a signal to travel between the two events, so that means that two events can be causally connected if they are separated by a light-like interval too, ie, I = 0. But if this is the case, then in the reference frame of the light, doesn't event A and event B occur at the same time then, in which case there isn't any causal connection between event A and event B?

Thanks

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# Time-like Intervals and Causality

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