Ivan Seeking said:
One of my favorite thought experiments from physics is described by Igor Novikov, in The Future of Spacetime. He describe a game of billiards in which a ball entering a certain pocket will enter a time machine, and then emerge in such a way that it interferes with its own path so as to prevent the ball from entering the pocket first place. Were the ball's path changed so that it misses the pocket, we would have a paradox. But it is found that while the ball may be deflected by its future self, it cannot be deflected enough to miss the pocket. THAT is an amazing result, even for a thought experiment.
BobG said:
Why? Just saying that is one way out of a paradox, but it would be more interesting if he'd at least suggest some reason the paradox is avoided. Conservation of momentum across temporal dimensions would be kind of an interesting avenue to explore as a thought experiment - especially since the entire Earth, the Solar System, and the Galaxy are screaming through space at incredibly high speeds, so real time travel would require a substantially large change in position as well as time.
Ivan Seeking said:
Novikov refers to rigorous calculations first discovered by Kip Thorne. [p.78]
I checked just to be sure.
Wrong book. Yes, Novikov refers to Kip Thorne's ideas, but those are discussed in Kip Thorne's "Black Holes and Time Warps" along with Hawking's views on the subject (even though they are briefly mentioned in the book you mentioned) ...
DaveC426913 said:
Relative to what?
It's not just a spurious question. One can deduce that, regardless of
how the time travel might or might not work, we cannot escape the conservation of momentum issue and have to deal with it somehow.
... and, yes, Dave's question is not just a spurious question. It makes a difference.
A time machine definitely can't be envisioned using classical physics. You would wind up with a runaway effect that would violate conservation of energy and momentum (Robert Geroch and Robert Wald). I don't think that saying any radiation or energy would be defocused, resulting in only a small portion of energy reflecting back through a worm hole really resolves the issue. In fact, it's even worse. Instead of the wormhole being destroyed by a runaway feedback loop, you have a stable wormhole creating an imbalance in the entire universe.
You still have a billiard ball from the future appearing in a present with a particular kinetic energy and momentum that duplicates already existing kinetic energy and momentum. In fact, if the time machine were capable of spitting the billiard ball out at different times (instead of just a single time and location), then you could wind up with a billiard ball colliding with itself billions of times, with all of the collisions creating an equilibrium that works for the billiard ball, but not for the rest of the universe that has one billiard ball turning into a sum of masses billions of times greater than the initial billiard ball.
In other words, what happens to the future billiard ball after it has finished deflecting the current billiard ball into the time machine? (This is what I meant about both Novikov and Thorne not going quite far enough.)
That's inductive logic and somewhat inconclusive, but the fact that we do have conservation of energy and momentum certainly indicates that time travel must be incredibly rare, if it exists at all, since there's no reason all of those billiard balls wouldn't be suddenly appearing both in our present and in our past (or some other type of matter/energy besides billiard balls if you don't like that analogy).
Or, perhaps it is inductive logic, but I'm going the wrong the direction in having energy and mass from the future appear in the present. Considering our world's energy problems (even if they are really energy conversion problems at this point), if a civilization were capable of inventing a time machine, it would probably make more sense to pull unused energy and mass from the past into the future. That would wreak havoc with our calculations about the universe's future.
Unfortunately, I don't have enough familiarity with the laws of quantum gravity to go that direction - the direction that Thorne went and the direction that Hawking says would probably lead to the immediate destruction of a time machine as soon as it came into existence.
