What Distinguishes Timelike from Non-Spacelike Curves in Spacetime?

[emma83]

Hello,

What is the difference between a timelike and a non-spacelike curve ?
Is it only that "non-spacelike" includes timelike and null curves, or is there another difference ?

Thanks a lot for your help.

 

[robphy]

Hello,

What is the difference between a timelike and a non-spacelike curve ?
Is it only that "non-spacelike" includes timelike and null curves, or is there another difference ?

Thanks a lot for your help.

A nonspacelike can include curves whose tangent vector at each point is "either timelike or null" (not just "always timelike" or "always null").

 

[Entropia]

Hello,

The difference between a timelike and non-spacelike curve lies in their relationship to the concept of causality. A timelike curve represents a path through spacetime that is consistent with the laws of causality, meaning that events along this curve can influence each other. On the other hand, a non-spacelike curve represents a path through spacetime that is not consistent with causality, meaning that events along this curve cannot influence each other.

In terms of the "non-spacelike" category, it does include both timelike and null curves. A null curve represents a path through spacetime that has zero length and is therefore not subject to the laws of causality. This can be thought of as a path that is "instantaneous" in a sense, as events along this curve cannot influence each other.

I hope this helps clarify the difference between timelike and non-spacelike curves. Let me know if you have any further questions.