Causality in GR (was Is event sequencing relative? )

[bcrowell]

causality in GR (was "Is event sequencing relative?")

The recent thread on causality, titled "Is event sequencing relative?," has gone in two directions, one discussing frame-dependence of time-ordering in SR, and the other discussing causality in GR. The SR posts were much more voluminous than the GR posts, which IMO made it difficult to have a good dialog on the GR issues. Therefore I've started a new thread for the GR stuff.

I thought the following post (#73 in the original thread) was very interesting:

This is true, but one thing to note about this is that a lot of the CTC solutions require an infinite universe that has some "unrealistic" properties throughout, like a dense rotating cylinder of infinite length (the Tipler cylinder) or for the entire universe to have some nonzero rotation (the Godel metric, discussed here). If you want to create a finite region where CTCs are allowed in an otherwise "normal" universe, like time travel based on a traversable wormhole, a result by Hawking proved that you must use exotic matter which violates the "weak energy condition" (see third paragraph here), and at least in the case of wormholes some other energy conditions need to be violated too (see here, and note that quantum effects like the Casimir effect may not be sufficient). It's not known whether matter or fields that violate all these energy conditions are actually allowed by the fundamental laws of nature, so GR solutions involving them may not correspond to anything that could be realized in nature, even in principle (and this is before we get into the issue of whether CTC solutions might be one where GR's predictions would depart significantly from those of a theory of quantum gravity--some analysis suggests that in semiclassical gravity the energy density would always go to infinity on the boundary between the CTC region and the non-CTC region, which would indicate this is a situation where semiclassical gravity breaks down and a full theory of quantum gravity is needed)

The link to the archived web page by Sviestins was very informative. I wasn't aware of the model-independent work by Clemence on setting an upper limit on the rotation of our universe, and I also hadn't heard of the conjectured link between rotation and CTCs (which, however, seems to be speculative).

One thing that was unclear to me from the Sviestins page was this. We can clearly determine, by local measurements, whether our lab is rotating, and we can then, if we choose, stop the rotation of our lab. This tells us nothing about cosmology unless we then compare our nonrotating lab with the universe. Sviestins talks about the idea of then looking out the window at distant galaxies to see if they appear to be rotating relative to the nonrotating lab. He also says this can be defined equivalently in terms of the vorticity of the four-velocity of matter. What I'm not clear on is what happens when you have a vacuum solution. For example, the Petrov metric is a vacuum solution with CTCs. If the conjecture is that spacetimes with CTCs must have rotation, then I'm not clear on how you would even define the conjecture in a case like the Petrov metric.

Another example that gives me doubts about the rotation-CTC connection is that you can take a flat spacetime and identify $t=t_1$ with $t=t_2$. This example clearly has no rotation, and yet it has CTCs.

Actually Sviestins himself expresses uncertainty about the rotation-CTC connection, and even about whether it can be stated in a meaningful way.

The rest of JesseM's post has to do with the chronology protection conjecture. I'm not a specialist, but to me the status of the CPC seems very unsettled.

In the classical case, you have to assume some kind of energy condition. But basically the only energy conditions that anyone's been able to formulate either turn out to be false in general or are too weak to be useful. An interesting paper on this is "Twilight for the energy conditions?," Barcelo and Visser, http://arxiv.org/abs/gr-qc/0205066 .

In the quantum-mechanical case, IMO (again as a non-specialist) it's much too early to make any definitive statements about anything. E.g., JesseM refers to analyses using semiclassical gravity. But semiclassical gravity has foundational problems (it blows up and has to be renormalized), and it also makes goofy predictions that seem IMO unlikely to be right (black stars).

 

[Ambitwistor]

First, I would like to thank you for starting this new thread on causality in GR. It is a topic that is often overlooked in discussions of general relativity and I am excited to see it being brought to the forefront of this forum.

I found the post you referenced to be very thought-provoking as well. The idea that CTCs may require an infinite universe or exotic matter is a fascinating one, and it raises important questions about the physical plausibility of these solutions. As you mentioned, it is unclear if such matter or fields that violate energy conditions are allowed by the fundamental laws of nature. This brings up the issue of whether these solutions are physically realizable in our universe, or if they are simply mathematical curiosities.

The link to the archived web page by Sviestins was also very informative. I agree with your uncertainty about the rotation-CTC connection, especially in cases like the Petrov metric where the rotation may not be well-defined. It seems that the conjecture may not apply to all spacetimes with CTCs, and further research is needed to fully understand the relationship between rotation and causality.

As for the chronology protection conjecture, I agree that its status is unsettled. The energy conditions required for its validity are either too weak or turn out to be false in general. And as you mentioned, the use of semiclassical gravity in these analyses also raises questions about their validity.

In summary, the issue of causality in GR is a complex and ongoing topic of research. The connections between CTCs, rotation, and energy conditions are still not fully understood, and it is possible that a full theory of quantum gravity may be needed to fully address these issues. Thank you for bringing this important discussion to the forum and I look forward to further insights and discussions on this topic.