Time Travel Paradoxes
I posted this on a mailing list recently and thought my LJ friends might be interested. It's cut because it's a l-o-o-o-o-n-g discussion.
Clasic Time Travel
Assuming a "classical" physical universe , there are all sorts problems associated with the idea of Time Travel.
What I find interesting is that most people have a "common-sense" view of time and time travel. That view is much like H.G. Wells, in that it is a dimension independent of space, even though it seems that we can only travel in one direction along it.
Wells, who wrote his famous story before Einstein's special and general relativity theories, supposed that (for the sake of the story) you could somehow disassociate your physical existence and jump to a point along that time dimension. Before then, most time travel stories were of the "Rip van Winkle" variety -- featuring one-way travel into the distant (and not so distant) future.
It's not just a matter of "turning back the clock" because say, 10 seconds ago, doesn't just exist 10 units back a dimension of time, but also in at least three other dimensions as well. We exist on the Earth with is rotating, and in turn rotates around the Sun. that in turn is in an orbit around the Milky Way Galaxy, which itself is heading on a collision course with the Andromeda Galaxy (don't worry, we won't hit until a few billion years more). At any point in time we are in constant movement in the spatial dimensions. Any time machine that moved you back 10 seconds in time, would also have to move you the same in the spatial dimensions as well.
After Wells' story, other authors followed up on the idea, without really questioning the theoretical basis on which it drew. Remember, that Wells' ideas were pre-relativity. Post-relativity is another matter, as time is seen as being part of space-time. You can't extract just one dimension from the others, because they are all the same thing.
The speed of light became a "limit" because nothing could travel faster than it. This is not an arbitrary limit -- we can "imagine" faster velocities -- but a physical one. If nothing can exceed the speed of light then that means there are certain times & places in the "future" that are realistically, impossible for us to reach. Likewise, we can only have started within a certain subset of space-time in the "past", to be able reach our present.
Confused? I've read a book called "E=mc^2" by David Bodanis (which is partly what inspired the topic) and his old website goes into more detail about the equation and relativity. In particular, he has a page on "light cones" that clarifies this idea.
So, for us and most of the space-time universe, it's a matter of "you can't get there from here". Travel to the past would theoretically involve faster-than-light travel, something which, so far has yet to be observed or be theoretically possible.
Storyline Paradox
There's another paradox, which was put to me as this:
"Lets assume that time travel is possible and you go back in history and tell yourself a story or something. Something you haven't heard anywhere else and never will. Then you, of course, eventually go back in history and tell yourself the story. You have to. You have already done that. (What might happen if you didn't, is a big question on itself.) ; The question is, who originally invented the story?"
This is what might be called an "empty loop". Something is supposed to have come from nothing. Our common-sense idea of how things work would tend to reject this idea as somehow inherently wrong, and hence the paradox.
The best study and treatment that I've read of empty loops is by Polish author Stanislaw Lem. Not only did he analyse why they'd be impossible, but he's also written at least one story that exploits the idea!
Here's some links to what he's written:
"The Time-Travel Story and Related Matters of SF Structuring for analysis"
and...
Ijon Tichy series of Books.
(in one story, the protagonist is trapped in a region of space where time is non-linear, and encounters more than one version of himself) Fiasco ...where Time Travel is involved in one story.
Basically though, the idea is that the empty loop violates the third law of thermodynamics -- "The Entropy of an Isolated System always Increases". The question then becomes whether
a) the laws of thermodynamics are accurate?; and
b) even if they are, are the players in a time-travel situation in an "Isolated System"?
It's pretty difficult to argue against the three laws (the other two are "Energy Can Be neither Created nor Destroyed" and "The Entropy of a Perfect Crystal at Absolute Zero is Zero" -- see them explained at Edited Guide Entry at http://www.bbc.co.uk/h2g2/guide/A467714) because no one's ever found convincing evidence that disproves them. When things didn't add up, theory came forward (like E=mc^2) that put the data into context.
So are the players/actors in a time-travel situation in an "Isolated System"? If we took the events of only one time period, maybe not, but if we take the events of the whole event, yes.
Consider the "telling yourself a story" idea. While we can imagine this situation, we can also see how it wouldn't work in reality. How is the story transmitted? Either it gets passed on socially (using speech, vision, et cetera) or via hard copy (on paper, on a disk, et cetera).
If it's socially, then it's subject to entropy in the form of the subject's memory. Even with a eidetic memory some details would inevitably be different from what was told the younger self. If it's by hard copy, then we have two possibilities.
First, the object involved existed before the time travel event and continued to exist after it as well. Suppose the story is written on paper. the "later self" writes the story on a conveniently placed scrap of paper, goes back in time, gives it to the "earlier self" who remembers enough to write it again later. The scrap of paper is left in the past, at least from the perspective of the "later self" and only passes through the loop once. It might be later destroyed or perhaps kept in a safe so that the later self copies it word for word to a "conveniently placed scrap of paper". In this instance, the paper exists twice while it is being copied, and the older version stays in the future.
The second take of course is when the lazy "later self" decides that they can't be bothered copying out the story, and so uses the original. In that case, the paper exists on an endless loop, or so it would appear. But it would still be subject to the 2nd law of thermodynamics. Even the most careful person cannot help but damage it in even the smallest of ways when its handled. The paper must therefore slowly deteriorate, because the same damage is constantly being done to it! (see Time Travel Paradoxes for another example).
Head spinning yet? All it means is that we can imagine the impossible. Just because we can imagine something doesn't mean that it can be "true" in the sense that it could or does exist.
Alternate Worlds
The third take on time travel ignores the limits of relativity and the laws of thermodynamics. What if time travel were actually travel to "alternate worlds"?
The standard time travel paradox, or going back to "change history" implies that there was only one past, or one source, for an available present. A good discussion of this can be found at Time Travel Paradoxes (as referenced above).
Time is looked at like a tree, and our present is just one branch of many possible ones. By going back to change things, we prune one branch and create another. The issue is, having altered our own past, why or how would we do such an action in the first place?
Authors of time travel stories have attempted to provide a number of explanations for this. Here's some of them:
- Alternate Past
The protagonist doesn't travel back to their own past, but in fact to an identical (to that point) parallel time stream. When things are altered here, it doesn't change their own time-line, but the parallel one's. e.g. "Rebel in Time" by Harrison. - Personal Timelines;
The protagonist exists only in their own personal timelines, intact with memories of who they are and what they've done. Everything else changes. e.g. "The Sound of Thunder" by Bradbury. - Fate, or the "elastic" quality of time ;
No matter what the protagonist does, time "bends" so that the same overall result occurs. e.g. An episode of the "Outer Limits" in which a time traveller manages to kill Hitler as a baby, but the nanny substitutes another baby (who becomes Hitler) instead. - Fate, or the "destiny" of time
No matter how badly the protagonist tries, they can't change the ;past, or the future! "Terminator 3" comes to mind.
There are other variations too, which I'm sure people can suggest. Just remember that the above discussion is concerned with time-travel within Einstein style space-time. When Einstein was theorising, there was no talk of alternate universes (except for ideas of indeterminacy, vis "Schrodinger's Cat", also see the Wikipedia article on this especially ).
Consider this: many time--travel stories aren't really about the
subject, but about identity. "Who am I" is a central theme.
Some other links: