The reader might be expecting at this point that having shown that the story of The Jacket does not work under fixed time nor under multiple dimension theory, we are now going to show how it does work under replacement theory. Unfortunately, though, it does not--that is, the story as we see it could not have happened, and for many of the reasons already discussed in relation to the other theories. The resolution of the predestination paradoxes requires finding an original cause that could have brought those events into existence, replaced by the actions of the time traveler, but we have already despaired of such an original cause. The altered ending, in which Jack changes the history of the future based on knowledge of what it was which he undoes in making the change, drives the story into an infinity loop. It cannot happen.
However, that's the simple answer; it does not look at the details, and the details of the story are still interesting. There are several paradoxes, some of which might be resolved, and also several impossibilities that are worth examining.
We must return to the method of time travel, in which Jack is locked in the drawer and removed some hours later, during which time his spirit projects a physical body to a point in the future. It would seem that Jack's spirit (or soul or consciousness or whatever you would call it) must leave his body, and then remains separated from his body for fifteen years (from the moment late in 1992 when he is put in the drawer to the moment late in 2007 when he arrives); it cannot return to his body until after it has had its experience in the future. If we assume that it returns to the body when the drawer is opened, then it can never reach the future that has not yet happened.
Thus when Doctor Becker opens the drawer, Jack will be either dead or catatonic, completely unresponsive at best. If he is catatonic, he will be moved to a ward where he can receive tube feeding, kept alive for some number of years while they attempt to determine what is wrong with him. We cannot guess what they would find on an electroencephalogram; we do not know enough about this spirit journey to know what kind of brain activity remains behind. We can say that he will never awaken, and probably will die before the fifteen years elapses. If he is dead, of course he will be buried in the yard, and there will be some kind of investigation.
Fifteen years later, he appears not far from Jackie, goes home with her, finds his dog tags at her house, and tries to persuade her that he is Jack Starks. If he died, the story works, because she tells him that he died--but she has the date wrong, as he probably did not die on January first, dying either a few days before that date or quite a while after it.
His time ends, and he returns to 1992; history is rewound to the moment the drawer opens, and he awakens. The other history no longer exists, and this one continues. This happens twice more, and again the information he gets from the future is inaccurate; but the trips also interact with each other, as each time the date of his death probably changes, at least slightly, but he does not know this. That is, supposing that in the first instance he was found on Christmas Eve, that is what Jackie tells him on the first trip; he returns to the past, and does not die on Christmas Eve, but instead makes the next trip on Boxing Day, which moves his date of death to the twenty-sixth or twenty-seventh, and that is what she tells him, but it is also what she tells him on the first trip, as that history was rewritten and he arrives in the midst of that.
The film is thus confusing and convoluted; we will attempt to separate the various complications and address them individually.