I'm wondering whether these new lives have to be in chronological order. If one person dies on Wednesday do they have to be in someone born on Thursday or can they be born on Tuesday? Or 1000 years ago?
If we can't find the soul then presumably it has no physical nature and therefore no mass. Having no mass it can be accelerated to light speed and beyond. See, normal matter increases in mass as it gets closer and closer to the speed of light and needs more and more energy to accelerate it. At least that's how I keep having it explained to me. So without mass it can hit light speed and beyond and go back in time. Thus, someone can reincarnate into someone who was born before their previous host body died.
Where I eventually go with this thinking is that there's only one soul. It moves back and forth through time living out life after life. Sometimes it lives in people. Sometimes it might live in animals. One might go so far as to call it God.
This means that everyone you know is you. Everyone you've ever heard of is you. Your parents were you. Your friends are you. The members of the Westboro Baptist Church are you. The President is you. The guy who locks his daughter in the basement for 14 years as a sex slave is you. So is his daughter. Steve Jobs was you. So are all the people making iPads in China. Even I'm you.
Recently I started thinking that all of the previously stated hypothesis might make this Hell. As much as you might want to improve your life and the world around you, you can't because you're stopping you. Not just as in "the only one stopping you from calling her is you". It's because all the decisions you have made or will make are preventing these changes from happening. You want to stop global climate change, but you're also the head of the coal company that needs to keep making money as well as all the coal miners who think they can't do any job but that, and you're driving every other car on the road. You want to fix the education system, but you're every parent who doesn't care how their kid does in school and everyone who wants to defund schools. The world really is against you... and it's you.
Not that I believe anything I've said here.