Some interesting links
http://arxiv.org/pdf/gr-qc/0703100.pdf
28-May-2007
Stability of Closed Timelike Curves in the G¨odel Universe
Val´eria M. Rosa
Departamento de Matem´atica, Universidade Federal de Vi¸cosa, 36570-000 Vi¸cosa, M.G., Brazil
Patricio S. Letelier†
Departamento de Matem´atica Aplicada-IMECC, Universidade Estadual de Campinas, 13081-970 Campinas, S.P., Brazil
PACS numbers : 04.20.Gz, 04.20.Dw, 040.20 Jb
Stability of Closed Timelike Curves in the G¨odel Universe
From the top of page 2:
"All our experience seems to indicate that the physical laws do not
allow the appearance of CTCs. This is that, essentially, says the
Chronology Protection Conjecture (CPC) proposed by Hawking in 1992
[16]."
http://physics.stackexchange.com/qu...ke-curves-to-be-impossible-in-quantum-gravity
There are a lot of other links which I haven't scanned. That second one has this:
These are some notes to complement previous answers.
Your concerns are sound: a rigorous definite way to rule out CTCs has
not been found. What we have is arguments (and quite nice looking
ones) to illustrate that every known universe with CTCs looks
unphysical.
Second, there are two nicely-written pedagogical letters written by
Kip Thorne addressing your question [1],[2]. They mainly focus on
physical aspects of the known CTC solutions, and three popular
mechanisms that could prevent CTCs: violation of the averaged null
energy conditions (the first argument cited in the post), classical
instabilities of chronology horizons, and quantum field instabilities
(following the notation of [2], section 4). Although he does not seem
to believe in CTCs personally, at the end of [2] he states that this
is still an open question:
It may turn out that on macroscopic lenghscales chronology is not
always protected, and even if chronology is protected
macroscopically, quantum gravity may well give finite amplitudes
for microscopic spacetime histories with CTCs [29].
[29] Friedman J 1992 in Proceedings of the 4th Canadian Conf. on
General Relativity and Relativistic Astrophysics eds G Kunstatter
et al (Singapore: Word Scientific) pp. 183-199.
Finally, regarding the argument against CTCs that uses logical
paradoxes, which has already appeared in the post: it is not clear to
many people whether CTCs inevitably lead to causal paradoxes. Several
studies have pointed out that causal-paradoxes of time travel could
disappear once one takes quantum mechanical effects; or maybe their
meaning could simply change [3],[4],[5],[6]. For instance, in the
framework used in the first reference the grandfather's paradox does
not violate causality. In connection with this, although it is known
that some of these models of CTCs [7],[8] lead to counter-intuitive
collapes of computational complexity classes, this is not exactly the
same as a causal paradox.
The link [1] to a Kip Thorne PDF seems to be the jackpot:
http://www.its.caltech.edu/~kip/scripts/ClosedTimelikeCurves-II121.pdf
"Closed Timelike Curves" Kip S. Thorne
One of the questions reviewed: Do the laws of physics prevent CTCs
from ever forming in classical spacetime?
From page 2:
"However, the combination of general relativity's laws and the laws of
quantum fields in curved spacetime may well provide a chronology
protection mechanism, though we might be sure of this until we
understand the laws of quantum gravity much more deeply than today."
Lots of complicated details to the PDF, which I am not qualified to
present. There is this end note:
"In summary, these studies are giving us glimpses of how CTSs
influence physics; but whether those glimpses are teaching us
something deep and important or just playing fun mental games, is far
from clear."
Note: The paper is from Feb, 1993.