I have, in fact, seen a potential design for a time machine which violates no known laws of physics and could take you back in time only as far as the point where the machine itself was built. This would prevent the "patent filing leapfrog" that you are talking about.
Before anyone wonders why this machine has not been built, it requires a rapidly rotating rod, several light years long, about the diameter of the Sun. To travel in time you need to orbit the rod at extremely high speed, and your direction relative to the spin of the rod determines which direction you travel through time.
In theory it should work. But reducing theory to practice is somewhat beyond our current means. :-)
It was a paper I was shown by a professor over 20 years ago. Said professor is now long-retired and I do not have the paper.
As he described it to me then, the paper presented an exact solution with an infinite bar, and then heuristic arguments that a very long but finite bar would demonstrate the same effects. The underlying mechanism is, of course, the result of a form of frame dragging.
The professor who showed it to me said that he was convinced that the math in the infinite model was correct, and was still deciding if he was convinced by the heuristic argument.
Googling quickly, http://en.wikipedia.org/wiki/Ronald_Mallett describes a similar scheme, which might even be the same one. Whether or not it is the same, the 1992 paper from Hawking that was discussed would show that the heuristic argument is wrong. However since I was shown this paper while I was in undergrad, Hawking's paper would not have come out yet, and the professor who showed it to me can not be faulted for not having found the necessary flaw.
I have, in fact, seen a potential design for a time machine which violates no known laws of physics and could take you back in time only as far as the point where the machine itself was built. This would prevent the "patent filing leapfrog" that you are talking about.
Before anyone wonders why this machine has not been built, it requires a rapidly rotating rod, several light years long, about the diameter of the Sun. To travel in time you need to orbit the rod at extremely high speed, and your direction relative to the spin of the rod determines which direction you travel through time.
In theory it should work. But reducing theory to practice is somewhat beyond our current means. :-)