What Distinguishes Timelike from Non-Spacelike Curves in Spacetime?

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In summary, timelike and non-spacelike refer to different types of curves in spacetime, with timelike curves representing the paths of objects moving through time and non-spacelike curves representing the paths of objects moving through space. The distinction between these curves is based on the mathematical concept of spacetime interval, with timelike curves having a positive interval and non-spacelike curves having a negative interval. Examples of timelike curves include planetary orbits, falling objects, and walking, while non-spacelike curves include objects moving at the speed of light and faster than the speed of light. This concept is important in science, particularly in understanding the behavior of objects in spacetime and in fields such as
  • #1
emma83
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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.
 
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  • #2
emma83 said:
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").
 
  • #3


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.
 

Related to What Distinguishes Timelike from Non-Spacelike Curves in Spacetime?

What is the difference between timelike and non-spacelike?

Timelike and non-spacelike refer to different types of curves in spacetime. Timelike curves represent the paths of objects that are moving through time, while non-spacelike curves represent the paths of objects that are moving through space.

How do we distinguish between timelike and non-spacelike curves?

The distinction between timelike and non-spacelike curves is based on the mathematical concept of the spacetime interval. Timelike curves have a positive spacetime interval, while non-spacelike curves have a negative spacetime interval.

What are some examples of timelike curves?

Examples of timelike curves include the paths of planets orbiting around a star, the trajectory of a falling object, and the motion of a person walking down the street. In these cases, the objects are moving through time, but not through space.

What are some examples of non-spacelike curves?

Non-spacelike curves include the paths of objects moving at the speed of light, such as photons, as well as the paths of objects moving faster than the speed of light, which are not physically possible. These curves represent objects moving through space, but not through time.

Why is the concept of timelike vs non-spacelike important in science?

The concept of timelike vs non-spacelike is important in science because it helps us understand the behavior of objects in spacetime. It is a key component of Einstein's theory of relativity and is crucial in fields such as astrophysics, cosmology, and quantum mechanics.

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