Space-Time Invariance, Weird Names and Some Questions

[RadiantL]

Hi, so I was going over my lectures notes and I was looking at the Invariance, S² for space time.

I was just wondering why they call it time-like for S²<0 and space-like for S²>0 because,

S²>0 says that there is an inertial frame where events occur at the same time (this has to do with time, why call it space like?)

and

S²<0 says that there is an inertial frame where events occur at the same position
(this has to do with space, why call it time like?)

So yeah, why the weird naming?

Also I was wondering, according to my notes it says when events are time like they can be connected by a signal slower then light, and could be causal.

So can there be events where they can be connected by a signal and not be causal? ... And in S.R, when books say causal, they mean an event causes another right?

Thanks

 

[Muphrid]

Timelike and spacelike refer to the intervals or directions. If two events happen at the same time, then all the stuff between them is only space. If two events happen at the same position, then the only stuff between them is time.

Yes, causal means that an event causes another. Sometimes we expand the word a bit to say that one event could influence another (as opposed to that influence being impossible, as it is if two events are spacelike separated).

This should also help you understand timelike intervals. An object that follows a timelike trajectory or goes along an interval is basically going forward in time like you'd expect most things would, so any point in spacetime that object can reach by timelike trajectories is within its region of influence--a region that extends forward in time and through space. This region is called a light cone because in some diagrams, people put the x and y axes in a plane and the t axis perpendicular, and the region takes on a cone shape. Lightlike trajectories define the boundary of the cone, and everything between them is a possible path for most ordinary objects.

 

[ghwellsjr]

The proper term is "spacetime interval" which is an invariant (does not depend on the reference frame) for the interval between two events. If it is time-like, that means that you could measure the interval with an inertial clock present at the two events. If it is space-like, that means that you could measure the interval with an inertial ruler that is present at the two events. If it is light-like, that means you cannot measure the interval. The interval between any two events falls into one of those three types.

 

[RadiantL]

Thanks Murphid and ghwellsjr, really cleared things up :)

 

[sardar]

for your question and observations. The terms "time-like" and "space-like" may seem counterintuitive at first, but they are actually quite fitting when considering the concept of space-time invariance. In special relativity, space and time are not separate entities, but are interconnected and can be transformed into each other. Thus, calling something "time-like" means that it behaves more like time than space, and vice versa for "space-like."

As for your question about events being connected by a signal and not being causal, it is possible in special relativity for events to have a time-like separation but not be causally connected. This is because in special relativity, the concept of causality is based on the order of events as perceived by different observers. If an event appears to happen before another event for one observer, but after for another, then it is not considered to be causally connected.

In terms of your last question, yes, when books refer to causality in special relativity, they are typically referring to one event causing another event to happen in a specific order. This can be a bit different from the everyday use of the word "causal," which may refer to a broader range of cause-and-effect relationships.

I hope this helps clarify some of the concepts you were discussing in your lecture notes. Keep asking questions and exploring these fascinating topics!