TenForward: Where Every Vulcan Knows Your Name

Whoa, interesting!

So, I think you would run into a smaller version of the problem that you get with an item that enters a closed time loop.

Imagine that you pick up an apple off of your counter as a snack right before you travel back in time to yesterday. When you arrive, you put the apple back down on the counter and forget about it. The next day ("today," from your perspective), your past self picks it up (from its perspective, again) and goes back in time. The apple is now in a closed loop. It experiences the same day over and over and over again until it rots and crumbles to dust.

Or rather, until it no longer looks appetizing to you as you prepare for your trip to yesterday. At some point, an iteration of you looks at the apple, thinks, "wow, that apple went bad quickly!" and picks up a banana instead.

If it's an object more durable than a piece of fruit, that object won't rot, but it will still degrade. A spoon, for instance, will rust to nothingness as it experiences a near-infinite amount of time all at once. Diamond would degrade into graphite over trillions of cycles through this one-day loop. A supermassive black hole in this loop would immediately evaporate due to Hawking radiation.

For the my-own-grandpa paradox, you'd run into a similar problem (though way weirder, and expressed through statistics). First, you immediately lose 1/4 of your genetic diversity. This is because your grandpa didn't pass his genes into the family tree on the first loop, but even if we handwave that away and say that they stick around somehow, the infinite loop causes random chance to iterate over and over again an infinite number of times in an instant; with enough iterations, I think your grandmother's genes win the genetic coin toss in the end, meaning that your grandfather's genes don't make it through that loop and vanish completely from your genome (we're going to assume that this is your maternal grandmother, by the way, because otherwise your father will be born a woman as a result of not having a Y chromosome).

Also by the time the loop settles into a steady state, your mother will have become her own grandmother, and your father will also be his own grandfather-in-law.

I'm not a geneticist, just a time travel aficionado. So I don't know for sure, but I think that all of this would make your mother a partial genetic clone of your grandmother. You would end up, genetically, as the child of your grandmother and your father. But I don't actually think you would become inbred, incidentally, because the genetic transcription errors that cause inbreeding mutations would probably be replaced on the next iteration with fresh genetic material from your grandmother.

And we're handwaving the question of how you still ended up as "you" through that entire process.

It depends. How much your parents are related will matter a lot. You'll get two extra sets of genes from one grandparent and one parent.

So you and the grandma bang and have a son (+1 new blood). That man has half your genes. He goes on to bang your mom (+1 new blood). Now you're back to your full set of genes. You could be really inbred or perfectly normal. If your parents were cousins or siblings you're more screwed than if they are from different bloodlines since you'll have even more consanguinity than normal cousins or sibling children would.