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

or that the universe does not, in fact, care in any way

[amnesiadust.livejournal.com]

"The fact does not create in me / A sense of obligation."

The problem with time travel of the kind that people really want to exist is that if it were possible, reality would be in essence unpredictable. Most of the laws of physics have strictly local formulations as differential equations, and for the most part that's all we care about since most labs or situations can be covered by at most a few coordinate patches. The places where GR gets nasty is where one tries to stipulate global solutions to equations... which in general can only be done in a very few special cases. "Cosmic censorship" and related paradoxes are mostly about trying to specify conditions under which global solutions exist. The laws themselves are well known -- the devil is in the boundary conditions, which frequently are downright intractable.

I suppose I'm inclined to consider Polchinski's view on self-colliding billiard balls as the most sensible, assuming one can actually construct a macroscopic wormhole through which things could pass. To do this, though, it wouldn't be enough to solve the dynamics for one moment in "time" and then evolve forward; you would have to solve for the entire history of the spacetime region and its surroundings at once. It also isn't clear to me what the transition region would be like -- whether you could just put a few coordinate patches around a region with closed timelike curves in it, or whether you would literally have to solve the entire history of the universe at once. We might observe the effects as mysterious forces (gravitational or otherwise) associated with the boundaries around the region.

In fact, if a sub-region with closed timelike curves existed, we wouldn't be able to see it -- it wouldn't emit anything, because any photons or particles within the region would have to keep circulating around the curves!

Hmm. Back to the work I'm being paid to do -- but this is interesting. I'll have to cut and paste this onto the PWiki, if one of our 'Pelicans hasn't beaten me to it.

Re: or that the universe does not, in fact, care in any way

[jrtom.livejournal.com]

"The fact does not create in me / A sense of obligation."

Heh. So apropos.

In fact, if a sub-region with closed timelike curves existed, we wouldn't be able to see it -- it wouldn't emit anything, because any photons or particles within the region would have to keep circulating around the curves!

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?

The other problem--or perhaps this is simply an emergent phenomenon of the problem you noted, on a higher level--is that 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, even if it involved very small amounts of mass/energy. I suppose that it's possible that if you did this way out in intergalactic space (where the really hard vacuum hangs out), and if the amount of time "skipped" was small enough, the probability of having any broader effects might be very small...but I can't see how you'd get to zero, in which case things didn't happen the way they did somewhere else, too, etc.

Feel free to correct my hideous misperceptions (and to copy this wholesale to the wiki (mmm...wiki) if you like). :)

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.

paradox found, cont'd.

[amnesiadust.livejournal.com]

I guess the question is whether it is theoretically possible to create a sensible universe with mixed boundary conditions, in which objects can freely move in and out of a region containing closed timelike curves, and interact with objects which have world lines that only move forward in coordinate time. This is a very difficult question to answer, but my gut instincts say "bat, meet supernova." It would seem to me impossible to predict anything that would happen in such a universe, since (as has been pointed out) one would observe from that point anything that had ever, or could ever, go around the loop at once. It would simply be history (though a very confusing one), rather than an effect "percolat[ing] outwards". One's instinct is to abandon coordinate time flowing forward and to use proper time only as the measure of local physics, but since each observer in the region may have his/her own different proper time, there is no way to unify the descriptions of interactions between different observers. Maybe string theory has a different way of handling this, but it clearly will require reformatting our brains in order to get a clean install of the new physics.

Put another way: Whenever we use phrases like "before X went back in time and changed history", what we have implicitly done is to put another notion of time-moving-forward over top of the "coordinate time" which is now being bent and superseded. This sense of time is assumed to correspond to the proper time of the observer travelling backward in coordinate time, but no unique and natural such choice can be made, and any such choice would have to coincide for all conceivable time-travelling observers.

Does this make any sense at all? It makes sense to me in my head, but maybe I haven't explained my thought process very well. And no doubt there lurk in my reasoning assumptions which are being challenged by today's Deep Thinkers. Back to the work I'm getting paid to do in the meantime...