(2009) Suzumiya Haruhi No Yuuutsu

The original run just explained it using the flip book analogy to describe how Asahina was able to travel back in time without disrupting the flow of time, but they did not examine how she affects this temporal plain. Originally, for me at least, it was hard to figure out what rules they were basing this time travel on. At first I thought it was maybe based on CTC of general relativity in which time is not a strait line, and therefor future events can cause past events, or the cause of an event can even happen at the exact same time. This because time is circular rather than linear. However, just the act of traveling back in time within this understanding invokes the grandfather paradox in which ones presence would create changes that could cause a ripple effect across the time plane thus possibly entering the universe into a paradoxical loop. It seemed as though they explained this though the fact tha Asahina was so conscientious about not revealing the past to kyon in an effort to minimize her paradoxical affects. But then when the older Asahina visited kyon and was so very wary of meeting her past self it made me wonder if possibly they followed the quantum mechanics form of time travel through the pauli exclusion principle. This would mean that changing time only meant creating a new time plane, thus accounting for why Suzumiya prevents backward time travel. Likewise, it would also explain why Asahina cannot meet her past or present self as their molecular similarity would cause them to repulse one another and thus negate their existence quite violently. However, in this episode future Asahina meets her past self, and even pokes her, thus showing that they may not run along that string of quantum mechanics when deciding how time travel works. Now it could just be that future Asahina is just different enough to prevent the pauli exclusion principle from comming into effect but I just would rather view it as a disregard for that rule of time travel. This then brings us to Kyon meeting Haruhi and thus influencing her future. This now falls under the Novikov self-consistency principle, in which time travelers cannot change the past other than what can be changed. Because of this new revelation on Suzumiya Time Travel I now believe that they still use the CTC to explain how Asahina travels through time, quantum mechanics to explain why we cannot go back in time beyond 3 years ago, and now we use Novikov self-consistency principle to show how Asahina and others can affect each time plane they visit.