The movie is nonsensical because of the paradox of time travel

Your problem is you are thinking in absolutes. We now know that there is nothing absolute about the universe. Even the laws are changing but they change in such a way that we think they are also absolute. We now know a lot more about how things work and even thatglimpse shows us that something as solid as metals are not solid at all and in fact is as much air as anything. If you can find the right frequency you can pass right through that solid object. Because that object is made up of waves. Waves can merge and become bigger or smaller or even even something new. Time is not relative either. If you look at time as a wave then everything changes. Even at the level of planks distance between 2 adjacent objects which make up the building blocks of the universe, time in fact becomes one with matter. Since matter itself does not exist and neither does time on that scale. So thinking that if we change time, then we change time in the future is looking at things in absolute terms. What if on one scale, time itself can become matter? It all depends where in point you are looking and you see what happens only there. A way of looking at it would be if time is a wave and you change the frequency, depending on where in the wave you listen to, the sounds would be different. So you change the frequency in the middle, the further away from that point you look, the less the changes, so you can havean almost infinite variation if you add time to a 3 dimensional wave structure. Killing your grand father aka changing the frequency at the center of the wave, would chage time at that point and closer to that point, but depending on how far you get, the less effect it would have or maybe it would affect things even more negatively but that all dpends on your perspective within that dimension. IE where you are looking. You might not exist at one point because you were never created. But there could be many you's in other points. This is why a holographic view of the universe seems like a good idea. Because things change not because of cause and effect but where you look at as well.

My problem with the movie is they have the time-travel guru, the Physics Professor, explain all about paradoxes and how they can't happen. He tells us that since a paradox would erase itself from existence it simply can never exist. He tells us that you can go back in time but not change anything, only observe. He does then tell us that you can make small changes if they don't affect anything, like pulling someone out of time a second before they die.

After all that, what does the movie do? It changes the past. The professor assembles the time-lost doodad and kills himself. History has been altered exactly as he said it couldn't. This causes a "time-quake" which destroys the future but still doesn't erase the future elements which changed the past, which is what a paradox would do.

The events of the film contradict what the rules of the film told us was possible.

The ending might make more sense if they told us the people were being sent into an alternate timeline since this one was being erased.

I am sorry to tell you but you are a moron to think and say here that time travel is impossible when in fact it is scientifically possible and Astronauts and Satalights that Nasa communicate with in space, in fact even a GPS system has to take in account for 'in essence' time travel. Basically It has been a given for quite some time now that Time travel in the future is possible. Now it gets tricky going into the past but there are scientist out there that do believe it can be done. Still, unlike those who believe in the grandfather paradox, they believe that if you were to travel into the past that you would end up starting a new time line and anything you do in this timeline would not effect anything in the timeline you came from. So, like someone else mentioned, you could in this timeline kill your grandfather and still be alive. The only thing he got wrong was that he assumed for some stupid reason that by killing your grandfather in this one new timeline you started, it would then for some reason make you not ever born in every other timeline except for the one you came from. This of course is plain ridiculous and silly. The only timeline effected would be the one you are making changes too and because you are not from that time line but actually from another one, the changes don't effect you unless you do something that like blows the planet up or something like that. The point is, Time Travel is possible... Traveling backwards in time is currently not!

You completely missed the plot of the movie. Try paying attention next time.

Sounds like someone can't watch a movie and suspend his disbelief.