Under your "killed your grandfather" scenario the paradox destroys the entire premise. If you killed your grandfather you'd never have been born and thus could not go back in time to kill your grandfather.
However with the infinite worlds theory, once you kill your grandfather you've created yet another alternate reality and your scenario could then play out when you return to the future.
Ah.. but that paradox doesn't apply to my theory Dave. What I'm saying is, if you were somehow able to travel into the past, anything you did differently would affect everything except YOU.
For example, let's say you're 20 years old. You travel back in time and find yourself as a kid, let's say at 5 years old. You use an axe and chop off the left arm of your younger self. You then go immediately back to your "present" time.
Would you magically be missing an arm? NOPE.
BUT..
To everyone around you, you WOULD magically now have a left arm. And for eveyone else around you, for the last 15 years you would've had no left arm. And then suddenly, you have one. Because within the parameters of my theory, you can't change yourself in your "present" time with ANY action you commit in the past.
Let's say instead you go back, find your younger self (5 years old again for example) and kill him.
Would you magically die as your younger self died? NOPE.
BUT..
When you returned to your "present" time you'd find that no one would know you. And to everyone in your "present" time, they would remember that some stranger killed "you" when you were 5 years old.
So the Grandfather Paradox doesn't apply to my theory. You COULD go back and kill your Grandfather with no repercution to your physical self. But like I said, your identity would be erased. Your family would be erased. Your Father (assuming you're killing your Fathers Father) would cease to exist. But not you.
And it goes deeper...
I think life is full of countless random acts. So many combinations of events that make bigger events and greater occurances that just the act of going into the past would automatically change your "present".
(
NOTE: I say "present" because time constantly moves forward. So the "present" at this instance where I'm typing it is now the past.. because time has moved forward. So NOW.. it's the "present" and so on..)
I think it would be impossible for absolutely random things to ALL duplicate and repeat exactly the same in the same manner with each visit you made to the past. i.e. even if you travelled to the same time period in the past an observed an event you would see numerous instances of things changing or not playing out exactly the same. Now for YOU, back in the "present" those small changes might not be noticeable but for someone, somewhere they could be monumental. These random events, chance events or however you want to describe them happen every second of every hour of everyday etc. And in my theory.. time isn't something you "instantaneously" jump back and forth into. From the observers point of view (Time Traveler) it would appear to be instantaneous.. but in my theory once the Observer traveled back into the past (let's say 30 years), then went back to the "present" for them, from their POV.. it would be "instantaneous". But in reality, 30 years of normal time would've passed. And imo, regarding all the little random events that make up life, just the act of everything playing out again in those 30 years in and of itself would change the "present". Might not be noticeable at first.. might even just be small insignificant things to the Observer, but changes never the less. And quite possibly those changes could infact be HUGE.
Now with all that said, honestly I don't believe in any of this besides my theory of time travel to the future. I believe that's the only form of time travel possible. And there's no going back. You can only move forward in time. And within the context of my theory.. once you arrived at your future destination (let's say 30 years again), for everyone else 30 years of normal time would've passed, time that included you mysteriously vanishing 30 years ago.
Just my thoughts.
I know, I know..