[MUSIC PLAYING] Sometimes, seemingly crazy ideas in physics lead to the most profound advances-- for example, the idea that every electron in the 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 his 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.

When the electron is moving backwards in time, it's a positron, the anti-matter 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 anti-matter 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 anti-matter into his path integral formulation and the following spacetime 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 Wheeler-- that 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 a 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 a segment of that worldline if we take a slice through space time 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 point, there can be multiple instances of the same electron.

Think about it as though you are flying over a giant S-bend in a river.

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 to the power of 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 currents changes.

Well, moving charged particles also produce a current-- an electric currents.

The direction, or sign, of that current depends on the direction of motion, but also on the sign of the charge.

For example, if a negatively charged electron is moving to the left, it 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 the same opposite signed minus I current.

So you get the same flipped sign whether you reverse the direction of the 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 reverse time.

That doesn't mean that time actually goes backwards, just that if you reverse the ticking of the clock in the particles 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's 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 the parity, reverse time-- a particle should end up back where it started.

But if you just flip the charge and in parity-- so do a CP transformation-- you still have to reverse time again to get back where you started.

So that means CP transformations leave an object time-reversed.

So that's equivalent to a T transformation.

But a charge flip just turns a particle into its anti-matter counterpart.

A parity inversion still leaves it as anti-matter.

CP transformations alone turn matter into mirror-reflected anti-matter.

So T transformations must do the same thing.

In the sense of these fundamental symmetries, anti-matter is time-reversed matter.

We already saw how expressing anti-matter as time-reversed matter is extremely useful in simplifying quantum field theory 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 in time.

If we draw a Feynman diagram for the whole 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 are the same electron.

Now, there are some 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, when 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, though, 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 as oscillations, as 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.

And the notion is nonetheless 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 tangled knot in the one single thread weaving back and forth across the reaches of spacetime.