Could spacetime be non-orientable?

[PeterDonis]

Just found two diagrams here

Diagrams by themselves aren't very helpful; there are lots of ways of drawing diagrams with light cones going every which way that don't correspond to any actual solution of the Einstein Field Equation.

The stackexchange thread you linked to references Wald, so I'll need to go look at Wald to see in what context the diagram given appears.

 

[PeterDonis]

Just found two diagrams here

Btw, the OP of the stack exchange thread is wrong when it says the diagrams it refers to are of the only non-time-orientable spacetime ever described "outside of de Sitter space with some identifications" (not sure what that refers to either). Godel spacetime, which I've already described in this thread, is another.

 

[stevendaryl]

Btw, the OP of the stack exchange thread is wrong when it says the diagrams it refers to are of the only non-time-orientable spacetime ever described "outside of de Sitter space with some identifications" (not sure what that refers to either). Godel spacetime, which I've already described in this thread, is another.

Being non-orientable isn’t exactly the same thing as having closed timelike curves. Having CTLCs means there is a timelike path leading back to the same point in spacetime. That by itself doesn’t preclude orientability. For example, consider a spacetime that is topologically a cylinder, with the direction “around” the cylinder being timelike. That’s got CTLCs, but it’s still orientable. You can consistently define timelike vectors as future-pointing or past-pointing.

 

[PeterDonis]

consider a spacetime that is topologically a cylinder, with the direction “around” the cylinder being timelike. That’s got CTLCs, but it’s still orientable. You can consistently define timelike vectors as future-pointing or past-pointing.

Yes, this is true, but note that this spacetime still violates property #2 described in my post #29, so it still can't serve as the basis for the OP's thought experiment.

 

[PeterDonis]

The stackexchange thread you linked to references Wald, so I'll need to go look at Wald to see in what context the diagram given appears.

The first diagram in post #30 is Fig. 8.1 in Wald, but it is only given as an informal example and is not discussed at all, nor is any actual description of such a spacetime in terms of equations (such as a metric) given. So there is no actual proof that there is a solution of the Einstein Field Equation that looks like the diagram.

 

[PeterDonis]

Being non-orientable isn’t exactly the same thing as having closed timelike curves.

Having gone back and looked up some things about Godel spacetime, yes, I realize I was confused on this point:

the entirety of Godel spacetime is non-orientable

Kerr spacetime violates property #2; once you've entered the non-orientable region

the OP of the stack exchange thread is wrong when it says the diagrams it refers to are of the only non-time-orientable spacetime ever described "outside of de Sitter space with some identifications" (not sure what that refers to either). Godel spacetime, which I've already described in this thread, is another.

I found a recent paper that discusses (briefly) the fact that Godel spacetime is time orientable:

https://arxiv.org/pdf/1911.08602.pdf

I would expect that Kerr spacetime is too, for similar reasons (basically, that even though there are closed timelike curves, they are in the "tangential" or "going around with the rotation" direction, so to speak, so they still have a consistent future/past orientation because the rotation in these spacetimes has a definite sense--it's a rotation going around in a definite direction).

That makes me wonder if there is any known spacetime that is an actual solution of the Einstein Field Equation but is not time orientable. As I mentioned previously, the diagram in Wald does not describe one; it's just an informal example and no corresponding solution to the EFE is given. The stack exchange thread mentions "de Sitter space with some identifications", but I have not been able to find any reference that explains what identifications.

 

[martinbn]

That makes me wonder if there is any known spacetime that is an actual solution of the Einstein Field Equation but is not time orientable. As I mentioned previously, the diagram in Wald does not describe one; it's just an informal example and no corresponding solution to the EFE is given. The stack exchange thread mentions "de Sitter space with some identifications", but I have not been able to find any reference that explains what identifications.

https://link.springer.com/article/10.1007/s41114-019-0019-x

Example 1.9

 

[PeterDonis]

https://link.springer.com/article/10.1007/s41114-019-0019-x

Example 1.9

Thanks, I hadn't seen this reference before but it looks like a good one. You've added an item to my reading list.

 

[Jarek 31]

So what could be consequences of time non-orientability?
Any chance for observational verification? e.g. time-reversed star, https://en.wikipedia.org/wiki/White_hole ?

Or imagine a rocket going through such time-inverting path and returning to Earth orbit - so would it have reversed time evolution from our perspective, e.g. "egg unscrambling", lasers stimulating absorption, entropy decrease?

 

[PeterDonis]

So what could be consequences of time non-orientability?

First you need to understand what I have already pointed out before: time non-orientability is not the same as time symmetry or time reversibility. Nor, as @stevendaryl pointed out, is it the same as having closed timelike curves. It is something much more counterintuitive. (Just looking at the examples in the paper @martinbn linked to should make that clear; those examples look like nothing any of us have brought up in this thread.)

Any chance for observational verification? e.g. time-reversed star, https://en.wikipedia.org/wiki/White_hole ?

The white hole spacetime, which is just Schwarzschild spacetime, is time orientable. So it's irrelevant to your question. So are all the other spacetimes that anyone (including me) has brought up, such as Godel spacetime--as I noted in post #36, I was wrong to think this spacetime was not time orientable; it is time orientable. So is Kerr spacetime, even in the region where it has closed timelike curves.

Or imagine a rocket going through such time-inverting path and returning to Earth orbit - so would it have reversed time evolution from our perspective, e.g. "egg unscrambling", lasers stimulating absorption, entropy decrease?

Again, this has nothing to do with time non-orientability. It is just time reversibility, which is not the same.

I suggest looking at the paper that was linked to and the example @martinbn referenced in it. Then take a while to digest it. (I'm still digesting it.)

 

[Jarek 31]

So what about this rocket going through such vector inverting path and returning to Earth orbit?

You previously agreed for P symmetry, but what about time non-orientability?

 

[PeterDonis]

what about this rocket going through such vector inverting path and returning to Earth orbit?

First we have to figure out whether any such path exists in a non-orientable or non-time-orientable spacetime. Remember that non-time-orientable is not the same as the existence of closed timelike curves. In the examples in Fig. 1.9 of the paper @martinbn linked to, there are no closed timelike curves, but two of them are non-time-orientable. So in those spacetimes, no such path as you describe exists.

Note that your definition of non-orientability in general, that a vector gets "flipped" if it is parallel transported around a closed path, does not mean there exists such a closed path that is timelike. So even if such a closed path exists, that does not mean that a rocket could actually travel around it.

You previously agreed for P symmetry, but what about time non-orientability?

My previous agreement is now irrelevant, since I was under a misapprehension about what non-orientability and non-time-orientability actually imply and don't imply.

I strongly suggest, as I said at the end of my previous post, looking at the examples in the paper @martinbn linked to and then taking some time to digest them. Pretty much everything we have been saying up to now, going by those examples, is irrelevant to the topic of non-orientability and non-time-orientability.

 

[Jarek 31]

The articles I have cited used Klein-bottle-like wormhole as a basic example - like a wormhole, but additionally inverting one of vectors.
The path doesn't have to be closed in spacetime, being closed in space is already interesting - I am writing "returning to Earth orbit".

 

[PeterDonis]

The path doesn't have to be closed in spacetime

For the definition of non-orientable that you gave, yes, it does. Just coming back to the same "point in space" isn't enough; the underlying manifold is spacetime, not space, and the path has to be closed in the underlying manifold.

 

[Jarek 31]

For a rocket traveling through such Klein-bottle-like wormhole inverting time direction, and returning to Earth orbit, I would say that just waiting there it could close the loop in spacetime ("turns out it was already there when launching").

But if you disagree, let's start with simpler scenario of just returning to Earth orbit ...

 

[PeterDonis]

For a rocket traveling through such Klein-bottle-like wormhole inverting time direction, and returning to Earth orbit, I would say that just waiting there it could close the loop in spacetime

"Close the loop in spacetime" means a closed timelike curve. Which, as I have already commented several times now (and as @stevendaryl pointed out before I did), is not the same as the spacetime not being time orientable. Of course it is possible for a spacetime to have both properties; but when you talk about "close the loop in spacetime", if that is possible, it is because of a closed timelike curve being present, not because the spacetime is not time orientable. So if you want to talk about the spacetime being not time orientable, you should focus on effects that happen because of it being not time orientable.

let's start with simpler scenario of just returning to Earth orbit ...

First you have to tell me which non time orientable spacetime you are using. (For example, you could use one of the examples in the paper @martinbn referenced.) Then you have to tell me where "Earth orbit" is in that spacetime and what "returning to Earth orbit" means--what worldline the spaceship is going to follow.

Until you do those things, it is impossible for I, or anyone (including you) to make any valid predictions about what might happen in such a scenario.

 

[diegzumillo]

(parachuting in this conversation)
I believe chirality would be an issue in this universe.

 

[Jarek 31]

Indeed, such hypothetical path inverting spatial direction would turn all molecules into their enantiomers, life into https://en.wikipedia.org/wiki/Mirror_life ... but also matter into https://en.wikipedia.org/wiki/Mirror_matter

Even more interesting would be path inverting temporal direction - e.g. imagine rocket traveling through it and returning to Earth orbit ...

Are they possible? Could be realistically verified observationally?

 

[PeterDonis]

Are they possible?

I have already told you how to answer that question in post #46. Without an actual model, such as the examples in the paper @martinbn linked to, there is no way to answer such a question. Are you going to look at an actual model or not?

 

[PeterDonis]

I believe chirality would be an issue in this universe.

What universe? What model are you talking about?