As pointed out by the other commenters, Cruithne doesn't orbit the Earth, but orbits the Sun with the in 1:1 resonance with the Earth. Its orbit is highly elliptical: at perihelion it's closer than Mercury, and aphelion further than Mars. Much of the time it's actually on the other side of the Sun to us. Here's a couple of gifs of its orbit:
The yellow kidney bean orbit depicted only takes a year, but it doesn't actually form a loop, and the kidney bean moves gradually away from the Earth around the blue circle. When it goes almost all the way around, it's going to start going back in the opposite direction. 770 years is the time it takes for the yellow orbit to traverse the blue orbit once in each direction.
Not only does it not orbit the earth in any physically meaningful sense - it doesn't even trace a shape that goes around the earth, which is annoying because I'm pretty sure I've told people that it did.
Well, assume that time loops back onto itself. Then the electron goes forward most of the time and you see multiple copies. ( This is of course ridiculous, everybody knows that all electrons are just pointers to one const particle structure. )
Obtaining multiple electrons by forcing a single one to bounce back and forth all the way across the time line a zillion times seems like a major design smell. That would be the worst hack ever, or at least the worst one before Facebook devs hacked Dalvik just to get their app to run on Android: http://jaxenter.com/facebooks-completely-insane-dalvik-hack-... ;)
Perhaps our universe is one created by a junior, or an intern, and this "creative" workaround got mocked on TheDailyWTF somewhere.
Well, it's immutable. So why would it be a problem with bouncing it around?
It's like a symbol in Ruby -- all instances of, say, :electron point to the same point in memory, they're just used all over the place. The sharing isn't problematic because you can't change :electron.
Why would you want to use 'electron' instead where every time you use it, you put another instance of it into memory?
Well I imagine it isn't optimized for readability :)
If the point is to have a jillion of electrons, each at the right time and place (for the observer), I assume a rather complicated mechanism must have been put in place to "tie the knot" just right - I mean to "navigate" the time-travelling electron just so it never fails to appear wherever, whenever it's expected.
In that case there'd be no need to convert back-and-forth between electrons/positrons or forward/reverse time at all. The only requirement would be that the observed Universe is a fixed-point of this loop.
Well, I won't pretend that I know how it's supposed to work, but even if the loop was closed, the electron (and the loop itself) still must have come to existence out of nowhere somehow, so it doesn't remove this ontological problem :)
I'm not really talking about an ontological problem though, I'm saying that an electron appearing on its own is a physical impossibility. Electrons must appear or disappear alongside a positron partner, which means that the idea of "local asymmetry" can't solve the symmetry problem.