The One-Electron Universe (Script) (Patreon)

One-Electron Universe & Feynman Diagram Challenge Answer

Sometimes seemingly crazy ideas in physics lead to the most profound advances. For example, the idea that every electron in the entire universe is really the one same electron, traveling forwards and backwards in time.

In the spring of 1940, the great physicist John Archibald Wheeler had a flash of insight. He picked up the phone and called Richard Feynman. The fateful conversation began, “Feynman, I know why all electrons have the same charge and the same mass." "Why?" asked Wheeler’s former graduate student. "Because, they are all the same electron!" Wheeler went on to describe the One-Electron Universe idea: that there exists only one electron, and that electron traverses time in both directions. It bounces in time, eventually traversing the entire past and future history of the universe in both directions, and interacting with itself countless times on each pass. In this way it fills the universe with the appearance of countless electrons. And when the electron is moving backwards in time it is a positron; the antimatter counterpart of the electron.

Whether or not we should take Wheeler’s idea seriously is debatable. However Richard Feynman did take at least one aspect very seriously: the mathematical equivalence of antimatter as time-reversed matter. In fact it was Swiss physicist Ernst Stueckelberg who first proposed this idea in the 1930s. But Wheeler’s One-Electron Universe idea  inspired Feynman to build this representation of antimatter into his path integral formulation and the following space-time interpretation of quantum mechanics, which won him the 1965 Nobel Prize in Physics. 

The One-Electron Universe was motivated by an odd fact about electrons that had troubled him: they are all identical. Exactly the same charge, exactly the same mass, exactly the same everything. There was no satisfying explanation for this. Wheeler’s notion was that if electrons behave as though they are identical, perhaps they truly are – to the point of being identically the same entity. Let’s think about the electron as its worldline. It exists as the line traced by its passage through space and time, rather than as a point-like particle at one instant in time. The point-like electron is just the segment of that worldline if we take a slice through spacetime at one instant in time.

The direction of an electron’s worldline can shift as the electron is scattered by photons. But what if it were possible to deflect an electron back the way it came, temporally. If an electron can reverse its course in time then its worldline looks like a zigzag. At any one time there can be multiple incidences of the same electron. Think about it as though you are flying over a giant S-bend in a river. If you can only see the straight parts of the flow, that one river looks like three rivers. That one electron, zigzagging back and forth 10^80 times looks like all of the electrons in the universe.

This winding river analogy is actually pretty useful. If you were observant, you might notice that between zigs and zags of the river the direction of the current changes. Well, moving charged particles also produce a current – an electric current. The direction or “sign” of that current depends on the direction of motion, but also the sign of the charge. For example, if a negatively charged electron moving to the left produces some current, “I”, then an electron moving to the right produces the same strength of current but with the opposite sign: “minus-I”. And a positively charged positron moving to the left also produces that same opposite-signed minus-I current. So you get the same flipped sign whether you reverse the direction of motion of the electron OR if you give it the opposite charge by turning it into a positron. But reversing a particle’s motion is mathematically the same as watching it in reversed time. That doesn’t mean that time actually goes backwards; just that if you reverse the ticking of the clock in the particle’s coordinate frame its direction of motion appears reversed, which has the same effect as flipping its charge.

Actually, it’s slightly more complicated than that. In a quantum field theory that is consistent with Einstein’s special relativity, all particles must be symmetric under what we call CPT transformation. “C” is charge conjugation – so flipping the sign of the charge. “T” is time reversal – changing the direction of the coordinate clock,. “P” is parity inversion, which can be thought of as reflecting the particle like in a mirror. So if you make all of these changes at the same time – flip the charge, invert parity, and reverse time - a particle should end up back where it started. But if you just flip the charge and invert parity, so do a CP transformation, you still have to reverse time again to get back where you started. That means CP transformations leave an object time-reversed. But that charge transformation just turns the particle into its antimatter counterpart. The parity inversion leaves it as antimatter.  In the sense of these fundamental symmetries, antimatter IS time-reversed matter.

We already saw how expressing antimatter as time-reversed matter is extremely useful in simplifying QFT calculations because it massively cuts down the number of Feynman diagrams you need. For example, this one diagram for electron and photon scattering represents both the double-deflection of an electron, or of a photon producing an electron-positron pair before the positron annihilates with the first electron. That virtual particle in the middle may be an electron traveling forwards or backwards in time; the latter is a positron.

So how does this work with Wheeler’s one-electron hypothesis? We can think of the annihilation of an electron and positron as just the electron being deflected back in time. Similarly, the creation of a particle pair is the electron being scattered forward in time. If we draw a Feynman diagram for whole the universe, we can have only one electron undergo countless scattering events; some of which change its course through time. At some point in the middle of the diagram we see many, many electrons. Wheeler’s idea was that they’re the same electron.

Now there are big problems with the one-electron universe idea. The biggest is that we should see equal numbers of electrons and positrons at any time. After all, after that first electron makes it to the end of time, it needs to travel back again as a positron in order to have any more electrons. But clearly there are more forward-propagating electrons than positrons. Wheeler suggested, perhaps half-jokingly, that all of the positrons may be hiding in protons. Ultimately he didn’t pursue this idea particularly seriously.

It’s certainly not widely accepted that there’s only one electron in this universe, nor whether that’s even a meaningful statement. We now think of electrons are oscillations - waves in the more fundamental electron field. It doesn’t really make sense to think of an electron as a thing that carries an identifying label. However the insight was a critical step in Feynman’s later work However the notion is rather poetic; imagine that every electron – indeed every particle - in our bodies – in everyone’s bodies - is the same particle, separated from itself by countless passages across the cosmos and across all of time. That makes each of us a tangle knot in the one single thread, weaving back and forth across the reaches of space time.

Hey everyone, now that we completely understand the fundamental nature of antimatter, let’s go back and look at the solution to the Feynman diagram challenge question. I asked you to draw all of the two-vertex and four-vertex diagrams for the interaction where electrons and positrons scatter off each other, using the simple rules that I laid out for building Feynman diagrams. Here are the two-vertex diagrams.

These are really interesting because the processes seem so very different. In one case we have a positron and an electron influencing each other’s momentum by exchanging a virtual photon, similar to electron-electron scattering. But in the second case, the electron and positron actually annihilate each other, produce a virtual photon, which then creates a “new” electron-positron pair. As long as the in-coming and out-going particles have the same momenta, these two are part of the same overall interaction. The four-vertex interactions look like this.

We randomly selected 5 correct answers. If you see your name below you’re a lucky winner and we have a space time t-shirt for you. Email us an pbsspacetime@gmail.com with your name, address, US t-shirt size (small, medium, large, etc). Also, let us know which t-shirt you want. That includes our brand knew shirt: the heat death of the universe is coming! In fact this shirt is available to anyone to purchase – link in the description. We also have a new shirt that’s exclusive to challenge winners and Patreon supporters – Astrochicken Von Neumann, conqueror of the galaxy.