so maybe time doesn't fly like an arrow...

[jrtom]

...but like a magic missile (i.e., anywhere you want it to, once you've figured out how to aim it):

NYT: Remembrance of Things Future: The Mystery of Time

So many people are going to be so disappointed if it turns out that the universe does not, in fact, care (on some levels, anyway) whether we think that its processes should be logical. :)

Comments

different kinds of time

[amnesiadust.livejournal.com]

If such a region existed, it seems to me that you wouldn't be able to interact with it in any way (observe it or enter it, and as you noted nothing would leave, either). Sort of a pocket universe, no?

As far as I know, yes, this is correct. It would have to live behind a so-called "trapped surface" like the inside of a black hole.

I would expect any kind of time travel at all--even that involving a wormhole and a billiard ball--to involve chaotic effects that would percolate outwards from the original event... Feel free to correct my hideous misperceptions...

Well, I don't know about "correct" since that would imply that I have actual knowledge instead of just some slightly better-informed ramblings. But I'll say this much: I don't think you'd see the "chaotic effects" for the reasons we'd be discussing above. My conjecture is that any region of space which contains closed timelike curves would necessarily have to be isolated behind an impenetrable curtain.

I suspect the commonly-held confusion arises because in relativity there are two kinds of time: coordinate time, the so-called "fourth dimension" that mixes with space coordinates under Lorentz transformations, and proper time, which is what we experience as that "going-forward" sensation and is what a clock actually measures. Whenever you carve out a world-line in spacetime, the conventional choice of parameter along that world line is proper time.

I contend that in order for a theory to have any kind of predictive power, i.e., in order to have a self-consistent theory in which any kinds of physical effects can be studied and reproduced, the conditions must be such as to allow a global solution of the field equations of that theory on spacetime. The classical physics way of coping is to specify some boundary conditions at an instant of coordinate time in some convenient reference frame, and then evolve those conditions forward with the field equations. (NB: there is no real mention of "proper time" when you do this, because the "events" and "observers" are all part of the 4-D field configuration.) Assuming no closed timelike curves exist, it's enough to do this only in the far past; the future will be whatever comes from that evolution. Coordinate time and proper time essentially always flow in the same direction.

Now suppose we have a universe in which closed timelike curves exist. The boundary conditions here are different -- they are periodic! And this will give rise to (in essence gravitational) forces which will keep the test particles orbiting around in perpetuity. Proper time could technically be said to increase without bound for any given test particle, but in fact nothing would ever change over various cycles of the loop as things would by definition have to come back to their original configuration.