“Paradox”, as an English word, has it’s origins in Latin and Greek.
But alas, it is still just a word in any language, regardless of how it is spoken, ancient or modern. And thus a verbal utterance that represents the conveyance of a concept. As all words are.
Generally, it refers to the “idea” of the existence of a problem that has no solution.
But again alas, this is nothing but an invention of the mind of man. Nothing that actually occurs in the Universe.
There are no paradoxes in the Universe.
The so called “grandfather” paradox has not, does not, and cannot ever occur simply because the situation that defines it is not possible in the first place. There is no past where/when your “grandfather” is “alive” for you to ever encounter. Any more than there is a future where your “grandson” travels back from to encounter you.
If there is “Time Travel”, it requires much more sophisticated concepts than this simple non-existant “problem”.
The so called “twins” paradox is actually not a paradox at all once one understands the idiosyncrasies of Relativity. Many think they do, but few actually do. Those who consider the “twins” paradox to actually BE a paradox, are among those who don’t.
Hint: Think about what constitutes a “year”, as opposed to watching the hands of your wristwatch move. Remember, “year” is again a word that conveys the concept of a single revolution of the Earth around the Sun.
Both “twins, the Earthbound one AND the travelling one will still have lived in a Universe where the Earth went around the Sun the SAME number of times.
The traveler’s BIOLOGICAL clock would run slower, as do physical clocks under the circumstances, but the Earth will have orbited the Sun the SAME number of times from BOTH of their points of view! Even while the traveler’s watch ran slower.
Time dilation, as a proven effect of differing relative velocities may be an unusual idiosyncracy inherent in the properties of relativity, but…
There is no paradox here.
And it most certainly does not constitute Time travel in and of itself.
There is no paradox ANYWHERE in the Universe for that matter.
How could there be?
The very concept is itself absurd. A mind game. A modernist mythology. Right up there with Jupiter governing the Universe from Mt. Olympus, or Noah’s Ark.
You believe in the “Great Flood” perhaps. Gee, where did all the water come from? (Descended from nowhere out of space?) Where did it go? (Evaporated back into nothingness into space?) Do you have any idea how much water it would take to cover the Earth up to the top of Mt. Everest and beyond? Or how thick the cloud cover would have to be that contained the water that constituted the rain that had to have fallen to make a flood THAT big?
About as much as it takes to drown the idea that “paradoxes” actually exist, from my calculation.