B Paradox in the block universe interpretation

[martinbn]

In GR two events are said spacelike separated if there exist a spacelike geodesic connecting them.

Why a geodesic? Why not a spacelike curve?

 

[cianfa72]

Why a geodesic? Why not a spacelike curve?

We had a thread some time ago on this topic, see this thread post.

 

[martinbn]

We had a thread some time ago on this topic, see this thread post.

That is a good point. But, take for example Minkowski spacetime. Take two spacelike separated points, and remove a point along the geodesic segment that connects them. Now this spacetime (Minkowski minus a point) has the two points, and they are not connected by a spacelike geodesic. By your definition they would not be spacelike seperated. I think it is more conviniant if you define two points to be spacelike separated if they are not timelike or null seperated.

 

[martinbn]

In GR two events are said spacelike separated if there exist a spacelike geodesic connecting them. Then you can pick a spacelike hypersurface it belongs to. It actually defines an hypersurface of simultaneity (i.e. a simultaneity convention).

His point (the post you replied to) was that the surface is not unique.

 

[cianfa72]

But, take for example Minkowski spacetime. Take two spacelike separated points, and remove a point along the geodesic segment that connects them. Now this spacetime (Minkowski minus a point) has the two points, and they are not connected by a spacelike geodesic. By your definition they would not be spacelike separated.

Maybe those two events are neither spacelike nor timelike separated -- I'm not sure if it really makes sense

 

[Dale]

Maybe those two events are neither spacelike nor timelike separated -- I'm not sure if it really makes sense

This is one of the reasons that I am not a fan of classifying events as timelike or spacelike separated. It is straightforward to classify a path between the events, but it is not straightforward to generate a unique path between the events. At least not a way that works in general.

 

[PAllen]

This is one of the reasons that I am not a fan of classifying events as timelike or spacelike separated. It is straightforward to classify a path between the events, but it is not straightforward to generate a unique path between the events. At least not a way that works in general.

However, acausal (as suggested by @martinbn, without using that term) or causal connection is highly useful to classify events, even in the most wild spacetimes. Causal means there exists some timelike or null path between them. Otherwise they are acausal. Only in SR (including the requirement of trivial topology) is there an equivalence between these categories and the timelike, null, or spacelike categorization of the unique geodesic between them. So (I agree), timelike, spacelike, or null separation should really only be used in conventional SR. In GR, replace with causal/acausal connection between events.

(As an aside, Godel spacetime has pairs of events connected by a unique geodesic that is spacelike, that are causally connected, all the same - because a timelike non-geodesic path exists between them).

 

[Demystifier]

Summary:: Why do differing temporal points on the block universe time line appear to both be the "present moment".

Where is the flaw in my thinking?

Your thinking is the exact opposite of block universe way of thinking. To think in a block universe manner, try to replace the word "now" with the word "here".