Time-like Intervals and Causality

In summary, the conversation is discussing the concept of causality and the invariant interval, which determines the order of events in different reference frames. The question is raised about whether the invariant interval can be less than or equal to 0 for causally connected events, and it is explained that this is possible for light-like intervals. However, there is no such thing as "the reference frame of the light" and the concept of causality still applies.
  • #1
*FaerieLight*
43
0
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[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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  • #2
*FaerieLight* said:
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.

*FaerieLight* said:
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
 

FAQ: Time-like Intervals and Causality

1. What is a time-like interval?

A time-like interval is a concept in physics that measures the amount of time between two events that are causally related. It is a measure of the time that would be experienced by an observer who is moving at a constant velocity between the two events.

2. How does a time-like interval differ from a space-like interval?

A space-like interval measures the distance between two events that are not causally related and can be observed from different reference frames. A time-like interval, on the other hand, measures the time between two causally related events and can only be observed from a single reference frame.

3. What is causality and how does it relate to time-like intervals?

Causality is the relationship between cause and effect, where one event is the direct result of another event. Time-like intervals are closely related to causality because they measure the time between two causally related events. In other words, if event A causes event B, then the time-like interval between the two events is the amount of time it takes for the cause (A) to lead to the effect (B).

4. Can time-like intervals be negative?

No, time-like intervals cannot be negative. In physics, time is always measured as a positive quantity, and a negative time-like interval would imply that an event occurred before its cause, which is not possible according to the laws of causality.

5. How does the concept of time-like intervals impact our understanding of time travel?

The concept of time-like intervals is crucial in understanding the limitations of time travel. According to the theory of relativity, time travel is only possible within time-like intervals, meaning that it is only possible to travel to events that are causally related to our present. This means that traveling to events in the past is not possible, as they have a space-like interval and are not causally related to our present.

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