I don’t want to supersede the Wikipedia which indeed does a great job, as always. I just wanted to say that I’m enjoying very much the fifth season of Lost, much more then the others. Now I can really feel the story making progress, and there are time travels! Too bad they last only a few episodes.

Nevertheless, Lost depiction of time travels is not my favorite. Let’s review it for the ones who do not waste time on TV series. Survivors split in two, one group left the island, the other remained; after turning a giant rudder on the island, the second group experiences changing of time: for thirty minutes they are in 2004, FLASH, for other 2 minutes they are in 1968 and so on. This endures until another spin of the rudder, but at the end they’re no more in the “present”, they are about 30 years before. What is important is that they “cannot change what happened”: for example, they can’t manage to kill someone that they knew survived till 2004.

This ultimately ends up in this: what they are living in the seventies has already happened — there’s no free will for them in the past. When they were in the present, they never met they’re future their selves, but that’s just fortuity.

Another interesting things to observe is the following situation. To fix ideas, call “blue survivor” the one living in the present and “red survivor” the one living in the past, as in the figure. Assume the survivor write his diary; it will account the facts happened during the ‘70, ‘80, ‘90, ‘00 to the blue survivor, then again, in the ‘70, ‘80, … to the red survivor. Then in 2003, the red survivor could mail the diary to the blue survivor. Now, blue survivor could read the diary and he will be forced to do all the things written in the diary: no free will. And not only for the red survivor, but also for the blue one who is living his present [¹]!

The conclusion is that if time travels as in Lost are (or will be) feasible, then the whole time-line, from time zero to time infinity is fixed: all events are predetermined, all action are already there waiting to be done. This is a legitimate way to overcome time paradoxes (and absolute confusion) as seen in Heroes, for example. In Heroes, there is a confusion between the “one time-line” and the “multiple time-line [²]” approaches. What are the differences in the two approaches?

If we insist in having only one time-line, then the red survivor can act on the blue survivor, and the state of the blue survivor have influence on the state of the red survivor; this is the famous grandfather paradox: can I go back in time and kill my grandfather (before he had my father)? With Lost time travels, I can go back in time but no matter how hard I try, I cannot kill him. With Heroes time travels, maybe I can, but anyway a incomprehensible mess happens. A formalization of Lost approach is the so called Novikov self-consistency principle: I can change actions, but the probability that the final state of the system is different from the first time is zero.

The other approach, of multiple time-lines, or of parallel universes, implies that when you decide to kill you grandfather, the choice you made create a branch in the time-line, so the grandfather killer is not really yours, but the one of your copy in the new time-line, and the grandson never generated is the copy, not you. In the new time-line, your copy do not exists anymore, but you, in your time-line, keep existing.

Anyway, the motivation of this post is not just Lost fifth season. Recently I viewed (three times — tough they were not enough) the movie Primer which happened to treat time travels. The movie is a mess (but a good one this time), and leaves some interpretation on the story and the travels theory to the watchers. The movie’s time machine work in this way:

• activate the machine (that is a box);
• after, say, six hours, get in the machine;
• wait six hours in the machine;
• exit from the machine;

after you exit, you end up at the same time you activated the machine in the first place. In the movie, they turn on the machine with a timer because they don’t know what will happen if they meet their future selves.

Even if this kind of time machine would suggest a multiple time-line approach [³], my favorite interpretation is different: to me there is just one time-line, but when you exit from the machine “in the past”, you erase all the events happened after, that remains only in your brain as memories. Sure, in the movie we see that almost all events happen in the same way they happened the first time, but this is quite obvious: almost nothing changed (this could be a different point of view of the Novikov principle). You could even kill yourself, and this is not a paradox since unlike in the Lost approach, the red survivor can act on the blue one, but the state of the blue does not influence anymore the red one. There are no connection between the blue and the red survivors. The red one could even force the blue one not to enter the box anymore, and after that you will live with your copy for the rest of your life, as two separate people. In the movie this event is considered by the characters, but never actually tried.

I’m not a physicist and this chat made that clear. Indeed, probably my interpretation is not physically acceptable (the main point: what causes something to exit from the box?), but I think is fascinating for two observation. The first is that what we are living now may be erased if someone had activated a box, but we won’t remember anything. In some sense, almost like in The Matrix: you cannot sense that you are in a virtual reality. The second observation is that for the time traveling one, the effect is to create true memories of events never happened. This is virtual reality pushed to the limit!