? Not to derail the topic but how does Time travel equal Immortality?
If you've got the power, the energy, to idly send people through time: you've got the energy to do all kinds of other things: like perfecting biology, space travel, all sorts of crazy computer shit.
Will a human body live forever? No, of course not. Could good medicine and technology extend the human life span ridiculously? Yup. Could good enough technology and computing figure out how to transfer a living human consciousness without breaking continuity? Absolutely. And right there, for probably less effort than sending someone through time: you've effectively made them functionally immortal.
If you've got the power to violate time, you've got the power for functional immortality. Unless time travel turns out to be so ludicrously simple and cheap, there's always better ways to spend that kind of power... Like moving your planet to account for global warming, or getting a high level AI to calculate the last digit of PI before the end of business friday.