That's funny, I thought a Paradox was something which only seems to be self-contradictory and impossible but which turns out to be true.
Hmm, that does seem to be the main definition given in dictionaries, I'll concede that. But if so, that's more a vernacular usage than a scientific/mathematical one.
I slip on a marble. One cause of that effect is the marble. It turns out that after I slip on the marble, I pick it up, travel back in time to before my past self enters the room, and in a fit of masochism place the marble on the floor so that my past self will slip on it and cause the original event.
That's all fine, non-linear, and great, but where the hell did the marble come from? It's the same situation with Bashir, if he is the seed of his own genesis, then where the hell did the seed come from? It's a closed loop, that's the paradox.
But a paradox is something which only seems impossible, the solution to the problem is that it isn't a closed loop, at some point an alternate timeline was created in which the marble arrived at the place in which I slipped upon it in some fashion other than my time-meddling self placing it there. To be more precise, that timeline in which I wasn't responsible for the marble's placement would have been the original, and the "closed marble loop" created subsequently would be the new alternate one.
Actually, no. In terms of the actual laws of physics, it is entirely possible for an event to be its own cause. There is nothing in the laws of the universe that forbids that from being the case. It seems impossible to us because it defies our everyday experience and expectations. But there are plenty of things in physics that do that, like the way objects behave in zero gravity or vacuum.
After all, asking where the marble "came from" is the wrong question, because the marble existed before it was placed there, and the particles that make it up existed before they became a part of it. In physical terms, the question is only, what led those particles into that configuration or position at that moment in time? And physical law allows in principle for a self-consistent feedback loop in time, a particle or object being influenced by its own future self. After all, time is simply another dimension.
In fact, in terms of physics and mathematics, that's the
only kind of time travel that's allowed. In classical terms, an equation can only have one solution, so an event can only happen one way; the only way the equation of a closed timelike curve can have a meaningful answer is if it's self-consistent, if an event causes itself to happen rather than causing itself
not to happen. Of course, Many-worlds quantum theory seems to offer a loophole for that, since the interaction can still be consistent if the time travel creates an altered but separate history while the original remains unchanged. However, applying quantum physics to reverse time travel actually closes that loophole; since a time traveler from the future is part of a history that resolved a certain way, that was "measured" a certain way, that time traveler's interaction with past objects makes them part of that same measured system and guarantees that they will resolve the way the time traveler originally experienced them. Even if there are multiple timelines, a time traveler is "stuck" in his or her original one and can never experience any others. So the situation in real physics is pretty much the opposite of the usual storytelling conceit where time travel
creates an alternate timeline.
