Time-like Intervals and Causality

[*FaerieLight*]

Hi
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$\Delta$t)²+($\Delta$x)²+($\Delta$y)²+($\Delta$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

 

[PeterDonis]

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.

Yes, this is correct. Light is a causal influence.

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

No, this is not correct, because there is no such thing as "the reference frame of the light". There's a FAQ entry on this:

https://www.physicsforums.com/showthread.php?t=511170