http://www.scottaaronson.com/democritus/lec19.html
ETA: http://scottaaronson.com/blog/?p=368
What I thought
If I live in world A and go back in time and alter things, then I leave a new world A'. What if the new me in world A' ALSO goes back in time to alter things, leaving world A''? If me' changes them back again, you have some kind of grandfather paradox.
I had always had an idea that the obvious resolution is that it will "settle down" to some steady state A'''''''''''''''' which leads to the same A''''''''''''''''. I envisaged this as moving through the possible states until you find a stable world to stop in even though "moving through" would not be relative to the normal timeline.
A proper formulation
However, I was enchanted to read that very nearly this was seriously investigated by someone. Specifically, if you ask "what happens in quantum mechanics, if there is a loop in space where the future leads back round to the past"? Well, then it's obvious: you solve the differential equation of how the world evolves over time, with the constraint the state at the start and end of the loop have to match up. QM (and any theory where you solve differential equations) is full of that sort of thing anyway. A priori "satisfying the differential equation" means a ball doesn't suddenly stop in mid-air abandoning all its momentum -- you just can't imagine the world different -- and just as much, a world where trajectories of objects/probabilities are consistent over the loop.
( Read more... )
ETA: http://scottaaronson.com/blog/?p=368
What I thought
If I live in world A and go back in time and alter things, then I leave a new world A'. What if the new me in world A' ALSO goes back in time to alter things, leaving world A''? If me' changes them back again, you have some kind of grandfather paradox.
I had always had an idea that the obvious resolution is that it will "settle down" to some steady state A'''''''''''''''' which leads to the same A''''''''''''''''. I envisaged this as moving through the possible states until you find a stable world to stop in even though "moving through" would not be relative to the normal timeline.
A proper formulation
However, I was enchanted to read that very nearly this was seriously investigated by someone. Specifically, if you ask "what happens in quantum mechanics, if there is a loop in space where the future leads back round to the past"? Well, then it's obvious: you solve the differential equation of how the world evolves over time, with the constraint the state at the start and end of the loop have to match up. QM (and any theory where you solve differential equations) is full of that sort of thing anyway. A priori "satisfying the differential equation" means a ball doesn't suddenly stop in mid-air abandoning all its momentum -- you just can't imagine the world different -- and just as much, a world where trajectories of objects/probabilities are consistent over the loop.
( Read more... )