Well, some sci-fi would have us believe in time lines - go back in time, change stuff, go back to your own time line having created an alternative one. Similar to the 'there's an infinite number of universes where every reality is played out' idea.
I suppose it could all depend on how fast time travels. Surely it travels the speed of time, which is about 60 second per minute, methinks. So it all depends how long you take getting back to your own time.
Except shouldn't your own timeline be being eaten away slowly? In which case, would your own timeline's history alter itself, or would nothing happen until eventually the 'temporal horizon' burns its way past you? And then, would you die or would you simply be altered and converted into this new time line?
Oh, and if you go back in time and killed your younger self, when you died would there already be one you in Heaven already?
Okay, so none of this is really relevent to Jane's family tree, but it provides sufficent paranoia about what will happen when and if humans invent time travel. Tra la la.
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I shouldn't know this, because I'm no longer a Trekkie, but it was actually Samuel Clements (IE Mark Twain). I still have detailed memories of when I was a nerd...
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I hope you're not implying that all Star Trek fans are nerds.