One Electron Universe

The one-electron universe hypothesis, commonly associated with Richard Feynman when he mentioned it in his Nobel lecture, postulates that there exists only a single electron in the universe, propagating through space and time in such a way as to appear in many places simultaneously.

There’s an idea that suggests all the universe’s electrons are actually one particle forever traveling backwards and forwards in time. It’s a simple, elegant idea that solves some of physics’s biggest mysteries. There’s only onetiny problem. It seems to be complete nonsense.

This is the story of that bizarre thought experiment and John Archibald Wheeler, the brilliant, largely unsung physicist who came up with it.

The Indistinguishable Problem

Like so much of the quantum world, electrons are strange. What’s worse, they’re all strange in exactly the same way. Every electron is identical to every other electron. They all have the same mass, the same electric charge, and the same spin. Electrons are just one of the indistinguishable particles – other examples include photons, neutrinos, protons, neutrons, and indeed most of the subatomic particles.

This isn’t a trivial point, either. Not only is it impossible to tell electrons apart based on their physical properties, it’s essentially impossible to tell them apart at all. This is because determining specific electrons by their position would require measuring their trajectories with exact precision, and the laws of quantum mechanics forbid this. Between measurements, electrons in the quantum world are probabilistic, defined by wave functions that give the odds of finding that particle in any given position. When the wave functions of multiple electrons overlap, it becomes officially impossible to determine which of the electrons was the one that was originally measured.

This is all well-established quantum theory, backed up by nearly a century of experimental work. But it doesn’t answer the deeper question – why are all the electrons identical? They most assuredly are, but there’s no actual reason why they should be. For many scientists, a question like this traipses over into philosophy, at least at current level of knowledge. As far as most of physics is concerned, indistinguishable particles are indistinguishable simply because that’s the way the universe is. No further explanation can be advanced, and so far one hasn’t really been needed.

The One Electron Universe

The one electron universe is, among other things, one of the very few attempts to explain why all electrons are identical. It has its roots in an entirely different form of symmetry between particles, that of an electron and its antimatter counterpart, the positron. The two particles have the same mass, the same spin, the same everything except for its charge. Leaving the charge aside, the electron and the positron are, well, indistinguishable, and in 1940 that gave a Princeton physicist named John Wheeler an idea.

Wheeler’s idea is often associated with his doctoral student, the legendary physicist Richard Feynman. That’s probably because Feynman gave the idea its most famous airing in his 1965 Nobel Lecture. Here’s his account:

I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, “Feynman, I know why all electrons have the same charge and the same mass.” “Why?” “Because, they are all the same electron!” And, then he explained on the telephone, “suppose that the world lines which we were ordinarily considering before in time and space – instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future we have the wrong sign to the proper time – to the proper four velocities – and that’s equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron.”

Wheeler had keyed into a basic if bizarre point of particle physics: the direction in which time flowed doesn’t seem to matter much at all, and the arrow of time is, in most cases, completely reversible. (It’s a bit more complex than that, but this is a topic for another time.) The upshot is that, with a few simple equations, Wheeler could transform an electron moving forward in time to one traveling backwards, and the only observable change would be the particle’s charge, which would flip from negative to positive. In other words, an electron would become a positron.

As Wheeler pointed out, each electron traces out a unique path through spacetime, which is its world line. He simply connected all the forward-traveling electrons and backwards-traveling positrons into a single gigantic world line, imagining a particle tracing its way back and forth through the history of the universe to become every electron and positron we had ever observed. And that was why all electrons were indistinguishable.

Prepare To Feel Very, Very Old

The implications of this would be absolutely tremendous. Current estimates suggest there’s about 10⁸⁰ atoms in the observable universe, so let’s use that same figure for the number of electrons. (Actually, since the vast majority of those are one-electron hydrogen atoms anyway, that isn’t much of a stretch.) The universe is already nearly 14 billion years old, but it will last far, far longer than that, although the ultimate age of the universe depends on which theory of its final fate you subscribe to.

Since we’re really only going for a rough estimate anyway, let’s just use 4.6*10²⁶ years, which is the lower limit for the lifetime of an electron before it decays (assuming it actually decays, which isn’t a certainty). So then, if the one electron universe is correct, that single particle has traveled through the universe 10⁸⁰ times, with each journey taking 460 septillion years, and you can double that for all its return trips as a backwards-going positron.

That means, by the end of its journey, the electron is 2*4.6*10²⁴*10⁸⁰ years old, or just about 10¹⁰⁵ years old. That’s ten-thousand googol years old. That also means that 99.99% of the electrons in your body, and indeed everywhere in the universe, have already been traveling for over a googol years…assuming this is true, of course. I don’t know about you, but I suddenly feel weirdly ancient.

The Trouble with Observation

It’s going too far to call the idea of a one electron universe a full-fledged theory, or really anything close too it – it’s more of a gloriously unconventional thought experiment. But that doesn’t change the fact that, from a strictly theoretical perspective, there’s absolutely nothing wrong with it. Sure, your intuition probably tells you that this is very, very unlikely, but classical world intuition doesn’t mean anything in the quantum world.

After all, we now take it as read that it’s impossible to know the velocity and the position of a particle at the same time, that particles are generally speaking just as happy traveling backwards in time as they are forward, that particles can be entangled so that measuring one will instantaneously affect the other, no matter how far apart they are. These are all deeply weird, yet they’re all absolutely true. So why not a single time-traveling electron for the entire universe?

The single electron universe falls down on experimental grounds, not theoretical ones. You might have spotted the problem – for a single electron to account for all electrons in the universe, it needs to travel backwards through the universe exactly as many times as it travels forwards. That means, in this model, that there should be exactly as many positrons as there are electrons. We know that that simply isn’t the case, and that matter completely and utterly dominates antimatter, which means the one electron universe can’t be true.

To be clear, Wheeler never pretended otherwise. As Feynman recalled in his lecture, Wheeler was aware of this problem from the outset and, probably half-joking, offered a rather unlikely way to explain the positron shortage:

“But, Professor”, I said, “there aren’t as many positrons as electrons.” “Well, maybe they are hidden in the protons or something”, he said.

In his memoir, Geons, Black Holes & Quantum Foam, Wheeler made it clear that this “positrons in protons” idea was not meant to be taken seriously:

I knew, of course, that, at least in our corner of the universe, there are lots more electrons than positrons, but I still found it an exciting idea to think of trajectories in spacetime that could go unrestricted in any direction — forward in time, backward in time, up, down, left, or right.

Wheeler did leave himself a tiny loophole there, pointing out that we know electrons far outnumber positrons “at least in our corner of the universe”, which leaves open the theoretical possibility that elsewhere in the cosmos there might be all the positrons needed to make up this vast local discrepancy. That, however, goes against the cosmological principle, which is the general assumption that the universe is essentially the same all over and we don’t occupy a special or unusual position in it. Technically, that doesn’t have to be true, but there’s 500 years of physics backing it up, and there would need to be some truly extraordinary reasons for physicists to consider abandoning it.