Given that you can travel back in time and have a baby there, or alternatively, send your baby back in time, would it be possible that this baby one day becomes your own mother (gives birth to you)? In other words, you would be your own grandmother.
This is intended to be a purely biological/genetic question. My main concern is that under normal circumstances you inherit about 25% of each of your grandparents' genes. Here however, you are one of your grandparents, so you would have to inherit 100% of this grandparent's genes and 0% of the other three grandparents. However, I have only limited biological knowledge, so I'm not sure if these assumptions are accurate. Another concern is incest. As you are your own grandmother, the one you have sex with will be your grandfather. (Again, note that for the scope of this question I'm only interested in the biological concerns of incest, not the social/cultural ones)
I have two ideas of a solution that I'd like to share, but I'm not sure if they are biologically possible:
Your egg that is about to become your daughter (and also mother) contains the exact same portion of DNA as your mother's egg that became you. From what I know, eggs (and also sperms) contain a random sample of ~50% of your mother's genes. So, could it be possible (though unlikely) that this random sample contains exactly those 50% that you previously inherited from your mother? This way, you and your mother/daughter only differ by the 50% of genes that the two fathers contributed to each of you. Genetically, you are half siblings.
Denote the two fathers
F2. Also, denote yourself
M1and your daughter/mother
M2. Via some bootstrap paradox mechanism (see below), it just so happens that your genetic fingerprint contains
F1's genes and
F2's genes, or in other words
M1 = 1/3 F1 + 2/3 F2. If now
M1has a child with
F1, it will be
1/2 M1 + 1/2 F1 = 1/6 F1 + 1/3 F2 + 1/2 F1 = 2/3 F1 + 1/3 F2 =: M2
and if this
M2has a child with
F2, it will be
1/2 M2 + 1/2 F2 = 1/3 F1 + 1/6 F2 + 1/2 F2 = 1/3 F1 + 2/3 F2 = M1
My concern with this is that, even though the ratios of genes match, it's still unlikely that the randomly sampled egg of your daughter happens to contain exactly those genes that are needed to create you, and not a sibling of yours.
Please feel free to uncover any flaws in these two solutions. You may also use them as starting point for your own solution. Or, you may come up with something entirely different. But maybe, I'm missing something fundamental about how genetics/inheritance works. In that case please provide an explanation of why this absolutely never ever could work, no matter how obscure and incestuous the scenario might be.
In case it's relevant to answer the question, here is how time travel is supposed to work:
Time is deterministic. Time travelers can of course try to change something, but they are doomed to fail. Everything will happen as it has always happened. Maybe this fact will resolve my concerns regarding unlikely events that I raised above, because they, well, just happen.
The bootstrap paradox (or causal loop: https://en.wikipedia.org/wiki/Causal_loop) is a thing. There are several examples of items and information that don't have an origin, they just exist. For example a time traveler takes some book back in time and hands it over to the young author before he has written it or even thought about it. And only because he reads his own book from the future he knows how to write it. The mother-daughter-paradox I'm asking for would be just another example of a bootstrap paradox, where in that case the genes (or some portion thereof) would have no origin.