## Time Travel in “Primer”

November 12, 2008

So instead of working on exams for the last few days, I’ve been watching a lot of films. I’ve just watched “Primer” again, after having watched it a few years back. It’s an excellent, almost Heinleinesque, time travel movie, albeit quite low budget (and you can watch it here for free!) I’m not entirely sure its consistent, but its fun all the same.

Time travel in this film is fairly limited. You switch on the machine and wait for the number of hours you want to go back to, get in the machine, wait that number of hours again, and you’ll come out the time you started. For example, suppose you switch the machine on at 12pm, and you want to go back four hours, you climb into the machine at 4pm, wait -4 hours (4 hours personal time) and get out at 12pm again. If you wait for longer you just bounce back and forth between 12pm and 4pm (e.g. if you wait 5 hours personal time you get out at 1pm, etc…)

Just a few points of clarification. Time travel in Primer, unlike, say, in Heinlein’s stories, is continuous. Informally, this means that when God drew the time travellers trajectory, her pencil never left the four-dimensional page.

[Digression. Note, that this definition is *not* the same as saying that for each time traveller the function from personal time to location in fourspace is continuous: we must distinguish three kinds of temporal distance. (i) temporal displacement: if I meet my time travelling self I have a displacement of zero from him (ii) temporal distance: if I meet my time travelling self who, this time tomorrow, gets in a time machine and zips continuously to 3008AD and back to today in a space of an hour, his distance from me is 6000 years and (iii) personal time: in the last case my time travelling self has a personal time difference of one day and an hour.

I’m imagining the map from your personal timeline to your location can be discontinuous while your worm is perfectly continuous. E.g. suppose over the next hour I undergo a strange experience: for each x < 60, x minutes into the hour I can’t remember the first x minutes, but I can remember the future last x minutes of the hour in reverse order. After the hour is over I experience everything normally again. It seems plausible that you could fill enough details into this story so that it constituted a discontinuity in my personal time, even though my worm is continuous throughout.

Also, I’m imagining that a continuous time traveller could live an infinite amount of personal time while having only a finite distance and displacement from her birth (after 1/2 an hour she’s aged 1 year, after 3/4 of an hour she’s aged 2 years, etc…). Similarly, a continuous time traveller can have a finite amount of displacement and have had an infinite amount of distance from her birth (imagine the sine wave that diminishes in amplitude according to the sequence 1/2, 1/3, 1/4, 1/5 etc… the line cannot be assigned a finite length, but will still be continuous.) Finally, you can have an infinite (or at least unbounded) amount of distance and displacement from your birth while only a finite amount of personal time has passed. Imagine you’re in an accelerating time machine: in the first half hour of personal time you travel to 4000AD, in the next quarter of an hour you’re at 8000AD, in the next sixteenth 16000AD etc… Actually, I think this is another example where the personal time to location function will have to be discontinuous while your worm is continuous.

Ok that was longer than expected! End digression.]

Anyway. One cool thing about the film, which I think was intended, was that when they came out of the machine for the first time they couldn’t write properly. The only way I could make sense of the bouncing back and forth process involved rotation in time, which would mean they would come out left handed, if they went in right handed. (The arrows represent the direction of personal time.)

[Analogy: in twospace you can rotate a ‘p’ onto a ‘q’ going into the third dimension.]

Another weird thing: in the 12pm to 4pm example I gave above, if you decided to wait 4n hours personal time before getting out, you would expect to have n colocated copies of yourself in the time machine (since the machine doesn’t move.) This seems to be quite different from continuous time travel as I had always previously thought about it (where you would go in large arcs to avoid hitting yourself.)

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