You know, if time travel was possible, it would have to actually be done somehow - through a sort of procedure, which would of course very much depend on how the universe actually works regarding "time". So I think the question is not as much whether time travel is possible or not, but rather whether there exists a logically possible procedure which qualifies as time travel. Here's a bunch of possibilities:
1) Replace the present universe with a past universe, place time machine.
2) Start a new timeline with a past universe, move time machine there.
3) Assume that the universe is a giant 4D hypercube, one dimension of which is time. A machine, at every "tick" of its own clock, modifies each slice along the time dimension to correspond to a function of the previous. All time travel does is pop in a copy of the time machine in a previous slice. The effect would be a wave rippling through the hypercube from the insertion point to the time the time machine was activated. The length of the ripple would likely be the time difference. In this system, time travel would essentially "break" the structure of spacetime in such a way that... it ceases to act as a timeline. For instance, you very well might jump from the present to an unrelated ripple where Hitler was already killed. Also, jumping back to the present after having changed the past would reveal no changes, because the ripple has to get there first (it could work if the machine waits). In fact, this system would quickly become a chaotic mess. Note that the clock of the universe-running machine I spoke of keeps running forwards.
4) Same thing, except that the machine keeps an index corresponding to the present slice, and only updates the successor of that slice. Time travel would simply encode a signal for the machine to read, and as it reads it, it copies the time machine in a previous slice, and decrements its index accordingly. As with 3), this system would put spacetime out of sync, but it wouldn't be as chaotic. Note that "going backwards in time" is equated to decrementing the index.
In all cases, the time travel procedure itself works forwards in the universe-machine's time. There's no way around this. 3) and 4) are interesting in that they modify a reification of the timeline - the trick is that in doing so they put past and present out of sync. All of these implementations appear like time travel. Personally, I'd make the leap that they
are time travel. Feel free to disagree.
vonFiedler said:
If I kill my ancestor I do not fade into nothing because matter cannot become nothing.
This is what we posit to be a physical law,
not a metaphysical necessity. If you're going to speak of the possibility of time travel, you can't ignore the possibility that there exists mechanisms that can outright erase matter. Heck, it is perfectly possible that there exist ways to consistently and majorly break every single law of physics, but that they are so contrived that we have never found them.
This being said, the idea that enacting a paradox makes you fade into nothing is indeed pretty stupid, since you can't enact a paradox to begin with.