Say a pair is created in space, they move around for five seconds, and annihilate each other. You could also explain that as a single electron in a loop – electron moves forwards in time for five seconds, changes direction (becomes a positron), moves back in time for five seconds, changes direction, the cycle repeats.
You can extend that to a set of two of electrons/positron pairs. Assuming each electron is created and destroyed with different positrons, you can again explain the system in terms of a single electron that changes direction four times. Add a few more in and you have a whole universe with one electron.
(That assumption may be a big one, which is where things fall down, but it's not nonsense. Also, bear in mind that the while idea of "moving" back in time is a helpful analogy, it's not very precise and shouldn't be taken too literally)
In fact, if you consider that a lot of particles would have presumably been created in the big bang, at which point they would conveniently be in the same location in our other three dimensions as well, it's certainly conceivable that you could have a single particle pinballing back and forth as you (and I guess Wheeler) describe.
Of course, still far from a certainty, but a neat idea.
P.S. I acknowledge that I have absolutely no real-world basis for this idea, just a thought.
An extrapolation from the one-electron-universe hypothesis is that the entire universe exists within a single point - this is why constants are constant across the universe, why matter is the same everywhere, why particles share properties, how tunnelling works, etc. - we just perceive it as being uncompacted from our reference frame, whatever or wherever that may be. Elements of some SUSY theories touch on this too - that there is only one string, that the universe is a projection from higher dimensions "curled up" in a planck-scale point....
Frankly, we can't know, and I'm not sure that we ever really can, due to the limitations of our faculties, and the rooting of our "reality" in how this particular collection of molecular machinery interacts with other physicality around it.
There are lots of things we can't know, but it's like toothpaste; if we posit certain things as fixed, if our observations mean anything, something else has to vary.
...how is that like toothpaste?
I don't disagree with what you're saying, but... toothpaste?
The idea is that what we see as an annihilation of an positron and an electron is just electron changing direction on the time axis.
Thanks - you have now rendered me incapable of doing anything productive for the rest of the work day as I stare out the window contemplating that concept.