First off, I'm not suggesting in any way that time travel is possible. That is-- I'm not suggesting a person can bore through a physical construct built of time and travel into the past or the future. That seems unreasonable to me-- since there is no obvious structure that is made of material we experience as "time".
Of course, it is theoretically possible to rearrange matter inside a bubble to resemble a previous arrangement. And, it is theoretically possible to predict the future and rerrange matter to resemble a future arrangement inside a bubble. It goes without saying though-- if you would like to physically transport a device that does that and matter inside the device (in its current state) to a different arrangement, you will need to use matter outside of the bubble to replace elements that make up the device and matter inside the device. Especially if you intend to "travel" into the past. Obviously, the device and matter inside the device would be in an entirely different state if you traveled to a point before the device was constructed.
Now, I turn to the "grandfather paradox". According to the grandfather paradox, if a person traveled into the past and murdered their grandfather, the time traveler would cease to exist. But if the time traveler ceased to exist, the time traveler would never travel into the past and murder their grandfather-- a paradox. This does not make sense. Thus, I wrote this article.
The scenario described in the grandfather paradox assumes the future and the past are linked-- in a loop. That's not the way backwards time travel is supposed to work. The idea of backwards time travel is to add matter to the past that did not physically exist before a time traveler traveled backwards in time. So, the matter is added. An event occurs (a time traveler murders their grandfather). And, a time traveler returns to the present-- presumably the moment the time traveler will travel backwards in time.
So, what happens after that? Well, matter was added to the past that prevents a child of the time traveler's grandfather from giving birth to the time traveler. So right away-- the presumption that the time traveler returns to the future the moment a copy of the time traveler travels into the past is wrong. There is no clear reason the time traveler will be given birth to. However, matter was deposited into the past that ended the life of the time traveler's grandfather. And, the matter was sent into the future after the grandfather's life was ended. So, there *is* a clear reason to assume a device containing a time traveler will arrive in the future. There is no reason to assume that will not happen.
Here's where things become interesting. And, this is the only "link" between the future and the past. If the time traveler traveled backwards in time and arrived at a point before the time traveler arrived in the past to murder their grandfather, there would no longer be a clear reason the murderer would arrive in the past. The time traveler could stand and watch their grandfather, calmly live out his life and give birth to one of the time traveler's parents. No copy of the time traveler would arrive in the past and end the life of the time traveler's grandfather. There's no good reason to assume that would happen.
There *is* sort of a paradox, though. It's actually a non-terminating loop. If the time traveler then returned to the point in time the time traveler went into the past the second time, it could create a non-terminating loop. A copy of the time traveler would have had a chance to build a machine, travel into the past, and murder the time traveler's grandfather. Afterwards, that version of the time traveler would have traveled to a point in time before the new time traveler traveled into the past to murder the time traveler's grandfather and arrived at the instant the original time traveler traveled to that point in time. Both versions would collide. I'm not clear what would happen-- but, it would likely be catastrophic for the original time traveler.
Assuming the original time traveler would disintegrate and the new time traveler did not notice, the new time traveler would return to the future. And, another version of the new time traveler would annihilate the new time traveler. The original time traveler would create a non-terminating loop. This would doom all the matter inside the bubble to repeat a period of time between the point the time traveler arrived in the past (before the point the time traveler originally murdered their grandfather) and the point the time traveler arrived in the future. Obviously, I would not recommend this!!!
Assuming the new time traveler noticed they disintegrated an older version of themselves, they could obviously prevent a non-terminating loop from starting. If both versions were disintegrated, this would also create a non-terminating loop. But, neither version would return to the future the second time. If the new time traveler was disintegrated but the old one was unharmed, there would be no non-terminating loop. But, that seems unlikely. It's also possible the original time traveler would arrive in the future and the new time traveler would arrive at the same time. Again-- someone's gotta go. But, there would be no non-terminating loop. If matter making up both versions of the time traveler combined to form a single being, I assume that would be the same thing as both versions being annihilated. It would leave behind a mess or possibly cause a small nuclear or chemical explosion.
On the other hand, if the original time traveler was aware they could start a non-terminating loop, they could travel to a different point in the future after arriving in the past before they murdered their grandfather. They could travel to a point before a new time traveler traveled into the past to murder their grandfather. Now, there would be two versions of the time traveler-- one that traveled into the past and murdered the time traveler's grandfather before traveling into the past to undo the change-- and a version that did not have a chance to do that.
From there, the possibilities are virtually endless. The original time traveler could convince the new time traveler not to travel into the past. And, the two could work together as clones. However-- there is only one time traveler that would have come from the new timeline (if you want to call it a "timeline"). And, that is the time traveler that did not travel into the past. The time traveler that traveled into the past would have erased their original grandfather and parents. The only grandfather and parents left would belong to the time traveler that didn't travel into the past.
The original time traveler could destroy the new one. In effect, they would "steal" that time traveler's identity. Also, a person could travel backwards in time and return to a point in the future before they traveled backwards in time and clone themselves indefinitely. It's an interesting concept. But, there is certainly no reason to assume there is a "grandfather paradox". It is more reasonable to assume a time traveler can create a non-terminating loop inside a bubble. That's a scary thought! D: