# Causality in GR (was Is event sequencing relative? )

1. Aug 5, 2010

### bcrowell

Staff Emeritus
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:

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).