Every electron in the universe is exactly identical to every other electron. It's not just that we can't tell them apart, nature itself can not tell the difference (this has observable consequences in physics). Not only that, the description of a positron moving forward in time is identical to the description of an electron moving backward in time.

This led Richard P. Feynman to suggest that there is only one electron in the universe moving back and forth in time, so the reason that all electrons are indistinguishable is that they are in fact all the same electron.

(I should note that Feynman did not mean this terribly seriously, but it illustrates as forcefully as anyone can that electrons are completely identical.)

The big cheese isn't getting it right. If we accept the one electron model, we can explain any number of sightings of that electron. Note that this electron obeys some very weird dynamics: for instance, successive measurements obey the Pauli exclusion principle, there are several localisations for the electron, etc. And, of course, there is only the one positron...

I'm not sure how mass is explained (when building a model of the entire universe, as opposed to locally-measured mass), since presumably we could observe (assuming really good experiments) gravity generated by electron mass.

But the point is that the dynamics will work. So if you still believe in operative definitions in physics, you've got real problems (metaphysically speaking): you cannot give any operative definition that will force the existence of more than one measurable electron, and (Occam's razor!) one electron is the simplest hypothesis explaining all the observed electrons.

If there were actually only one electron, weaving forward and backwards through time, what would happen if you could somehow catch this 'tron and not let anyone else use it? Would the universe cease to exist? Would it unravel, starting at the point you got greedy and spreading through time until nothing had never existed in the first place? Of course, that the universe seems to still exist suggests that doing such a thing might be impossible (because given the amount of past and future the universe is likely to have, pretty much anything that can be done, will be done).

Still, were I a more motivated mad scientist I would build a doomsday device around this concept and threaten to activate it unless my demands were met: "Bow to my will, or I will not only destroy the universe, but I will arrange it so the universe never existed in the first place! Not only will you never use an electron again... things will change so you never had the use of any electrons... ...what? You're not scared? Look, all your stuff is made up of electrons. No, you won't still have fond memories of your stuff, becuase it never would have existed in the first place. Yes... your new iPod is made up of electrons too. Think about it: I will destroy your iPod before it was even made! So you'd better... <whatever>"

Mind you, demonstrating the effectiveness of such a device would be hard, since it too would cease to exist as soon as it was activated, and would never have existed in the first place. Hey... wait a second, if the device never existed then it would never have been activated, and thus the device would still exist... so it could then be activated... at which point it would cease to exist... oh, nevermind...

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