In all of the lengthy discussion of Butterfly Effect, we have failed to determine whether the story works under some model of time. We have discovered numerous obstacles, and looked for fixes for each of them, but it may help to summarize the problems.
The blackouts are a problem only if we assume that they are caused by his visits from the future. Although the implication is that they are, the evidence suggests otherwise, and the best conclusion is that the blackouts and the time travel are consequences of the same condition.
The picture he draws of himself stabbing two men with a knife is very difficult. We know that he will eventually travel to this time to stab his hands on the spikes on the teacher's desk to fake a miracle so that he can get help to stab two men, and he will draw the picture at that time. However, if the picture was drawn by the one who was about to stab two men, that was also the one who pierced his hands, and we would be more worried about the blood than the drawing. More problematic, the picture is necessary to introduce the psychiatrist to Evan, and get the journals started. We must, then, believe that Evan drew some other disturbing picture during his blackout, a picture he could not reproduce on his return trip because he never saw it.
We cannot know what originally happened when he had a blackout in the kitchen; the scene with the knife is obviously a later iteration of time. Presumably he did nothing significant, as he was already scheduled to see the doctor.
When he visits his father, it must be sufficient to trigger the attack that Evan has a blackout in front of the man, but that is not incredible.
The cigarette burn is the first of many problems which are based on the fact that Evan knows the history he erased but not the history he created. It is necessary to the story that Evan know that he has changed the world, but difficult to devise a time travel theory that supports this. The best we can say is that however time works in this world, the time traveler shifts from history to history, taking the body of his self in that version of events but retaining the memories of the other. We assume that the other history is erased, unmade, but we cannot really know what happened to it, or to the Evan that was in it.
Several other time travel events encounter the problem that Evan intentionally changes history in a way which would undo his reason for having done so. The prime example is his first trip to Miller's basement, where he threatens George Miller to treat Kayleigh better. Kayleigh thus will grow up happy and well-adjusted, there never will have been a porn film, and her forever boyfriend Evan will not know that there was any pain to prevent--a classic infinity loop under replacement theory. The film appears to rely on Niven's Law, that once the future changes the past, it holds its new form even if the cause in the future is changed, but it does so inconsistently.
Evan's miracle makes no sense at all. It is one thing for Evan to perceive his body as changing in response to changes in his past, but it is entirely different for those around him to see this. For them, there must be a continuous history of cause-and-effect which leads to the present moment, and so the scars that Evan gives himself when he returns to being seven must have been there for all the intervening years of the history he creates by that act. His cellmate cannot see them suddenly appear. The cellmate that can see the scars would not even know to be looking for a miracle.
Three times in the movie Evan travels back to the same moment in his life twice--the incinerated dog, the exploding mailbox, and the basement scene. In each case, we must wonder whether the later trip changes the earlier one, and particularly in connection with the last, when each of the traveling Evans has an agenda. When it is just changing events as he remembered them, we can rely on the memory trick that he won't change what he remembers; but when he is working against himself to alter history, we have to wonder where his other self is at that time.
We also recognized that sometimes when he travels to earlier times he changes later events, but other times he does not. It barely holds together on this point.
Much more confusing is the history in which there are no journals. We understand why the Evan who remembers the other histories asks about them, but not why Dr. Redfield has heard him ask about them before. We are forced to wonder about the memories of the Evan of this world yesterday, which apparently were not the memories of this world. That, though, is very difficult to reconcile with anything. How could Evan ever have functioned in this world, if his memories have always been of some other?
In short, there are enough points at which the cracks show, the treatment of time is inconsistent and the story relies on impossibilities to make it work, that we have to conclude that Butterfly Effect does not work under any theory of time and offers no coherent explanation of itself. It is still a fascinating film, but not a possible one.
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