Alex is correct, time travel is not possible and he is correct that there are logical inconsistencies in any paper which proposes the possibility; however, he is not correct in where he is looking for these errors. If you do a cursory read of my paper, you will discover that I *define* time such that the past is what I know and the future is what I do not know. Under such a definition, the standard concept of time travel is impossible. Time is not a coordinate of a geometry analogous to space but is rather a parameter of the change in knowledge so the concept of travel does not apply directly. Oh, it is possible to redefine *time travel* such that remembering becomes such a trip but I do not believe this is what people consider *time travel*.
Now, as to where one should look for the errors, Alex is wrong because the true source of the error is Einstein himself. My Chapter 3, Part II is, in fact, no more than a somewhat modern recreation of the Lorentz attack on the Problem of the negative outcome of the Michelson Morley experiment. You should carefully read the two paragraphs near the end which begins with "It is interesting to note ...".
That section is immediately followed by Part III General Relativity. This section begins with a discussion as to why my attack has produced no conflict with Quantum Mechanics. Please read carefully the three paragraphs beginning with "In a nutshell ...".
In essence, Einstein mistakenly used time as his fourth coordinate axis when he should have used tau (proper time) as that axis. He could not have comprehended the possibility of that move as he lacked a mechanism to erase the detectability of such a 4th *real* axis. At the time, Quantum Mechanics was not known! The Heisenberg uncertainty principle was not available to him. The Heisenberg uncertainty principle states that the product of the uncertainty in position and momentum must be greater than a specific finite number (see Plank's constant).
From standard special relativity it is eminently clear that mass is totally analogous to momentum (E = sqrt(|P|^2+|M|^2) - using units such that c is one). Clearly, all scientific work is done in laboratories constructed of mass quantized stuff with tools constructed of mass quantized stuff. It follows that, if mass is momentum quantized in the tau direction, then the uncertainty in tau must be infinite and this strange 4th dimension cannot be detected at all (or at least its consequences must be subtle)!!
The proposition also immediately clarifies the problem of a fixed speed of light. You will notice that the fundamental equation I generate is a wave equation very similar to the wave equation for light which generated the original problem for Michelson and Morley. This implies that *everything* is actually moving at the speed of light (add some minor qualifications to the details). We appear to be standing still only because our motion happens to be parallel to the undetectable dimension. Nothing can travel faster than that fixed value because that would mean it is was moving perpendicular to tau and its momentum in the tau direction would have to be zero - i.e., it is massless!!!
Einstein's error generated some dire consequences. First among those consequences is the fact that, if space is Minkowski like, there exist paths in that space which correspond to super luminal velocities. As Alex has accurately stated, time travel can only be mathematically introduced by using these super luminal velocities.
>>> Alex: Harvey, the big flaw of this paper is that it requires superluminal motion to close a time loop.