The Godel solution is a curiosity, not useful for constructing a time machine. Two recent proposals, one by Morris, et al. [2] and one by Gott [3], have the possibility of actually leading to practical devices (if you believe this, I have a bridge to sell you). As with Godel, in these schemes nothing is locally strange; time travel results from the unusual topology of spacetime. The first uses a wormhole (the inner part of a black hole, see fig. 1 of [2]) which is held open and manipulated by electromagnetic forces. The second uses the conical geometry generated by an infinitely long string of mass. If two strings pass by each other, a clever person can go into the past by travelling a figure-eight path around the strings. In this scenario, if the string has non-zero diameter and finite mass density, there is a CTC without any unusual topology.

If tachyons exist as physical objects, causality is no longer invariant. Different observers will see different causal sequences. This effect requires only special relativity (not GR), and follows from the fact that for any spacelike trajectory, reference frames can be found in which the particle moves backward or forward in time. This is illustrated by the pair of spacetime diagrams below. One must be careful about what is actually observed; a particle moving backward in time is observed to be a forward moving anti-particle, so no observer interprets this as time

t One reference | Events A and C are at the same frame: | place. C occurs first. | | Event B lies outside the causal | B domain of events A and C. -----------A----------- x (The intervals are spacelike). | C In this frame, tachyon signals | travel from A-->B and from C-->B. | That is, A and C are possible causes of event B.Another t reference | Events A and C are not at the same frame: | place. C occurs first. | | Event B lies outside the causal -----------A----------- x domain of events A and C. (The | intervals are spacelike) | | C In this frame, signals travel from | B-->A and from B-->C. B is the cause | B of both of the other two events.

The unusual situation here arises because conventional causality assumes no superluminal motion. This tachyon example is presented to demonstrate that our intuitive notion of causality may be flawed, so one must be careful when appealing to common sense. See the FAQ article on tachyons, for more about these weird hypothetical particles.

- Kip S. Thorn, "Black Holes and Time Warps" Norton and Co (1994)
- S.W. Hawking, and G.F.R. Ellis, "The Large Scale Structure of Space-Time," Cambridge University Press, (1973).
- M.S. Morris, K.S. Thorne, and U. Yurtsever, PRL, v.61, p.1446 (1989). How wormholes can act as time machines.
- J.R. Gott, III, PRL, v.66, p.1126 (1991). How pairs of cosmic strings can act as time machines.
- S. Deser, R. Jackiw, and G. 't Hooft, PRL, v.66, p.267 (1992). A critique of Gott. You can't construct his machine.
- D.G. Boulware, University of Washington preprint UW/PT-92-04. Available on the hep-th@xxx.lanl.gov bulletin board: item number 9207054. Unitarity problems in QM with closed timelike curves.
- "Nature", May 7, 1992. Contains a very well written review with some nice figures.