It's 1928.

Over the past quarter century, the greatest geniuses of the modern era discovered the two keys to the fundamental nature of reality.

Einstein's theory of special and general relativity had changed forever the way we think about motion, space, and time.

And the emerging field of quantum mechanics had radically altered our understanding of the fundamental building blocks of the universe.

Yet, this year, 1928, one brilliant insight would bring these theories together and unveil the quantum fabric of reality.

It would also predict the existence of anti-matter.

20 00:00:50,750 --> 00:00:53,400 By the late 1920s, Einstein and Planck had already shown that light is a particle, as well as a wave.

And Louis de Broglie had shown that all matter has this dual wave-particle nature.

Bohr, Heisenberg, Born, Pauli, and others pieced together a mathematical description for the weird nature of subatomic particles.

Then, in 1926, Erwin Schrodinger wrote down his famous equation, the Schrodinger equation, which breathed life into this emerging model.

It describes how these matter waves, represented as wave functions, change over time, and allowed physicists to predict the evolution of quantum systems, such as the strange interference pattern in the famous double-slit experiment.

Yet, everyone knew there was a problem.

First and most obvious, the Schrodinger equation is totally incompatible with Einstein's relativity.

In relativity, the dimensions of space and time are intrinsically connected and they float into each other as frames of reference change.

But the Schrodinger equation tracks the evolution of a particle's wave function according to one and only one clock, typically the clock in the reference frame of the observer.

Relativity tells us that the passage of time depends on velocity.

So the Schrodinger equation only works for slow-moving objects.

That's a problem.

Subatomic particles are often moving at close to the speed of light.

The other problem with the Schrodinger equation is that it describes particles as simple wave functions, distributions of possible positions and momenta that have no internal properties.

Yet, we now know that many elementary particles have an internal property called spin.

That doesn't mean that they're actually rotating.

But spin does result in a sort of quantum angular momentum.

For example, an electron's spin causes them to align themselves with magnetic fields, just like a rotating electric charge would.

The axis of spin can point in different directions; for example, up or down.

The discovery of quantum spin starts with an Austrian physicist named Wolfgang Pauli.

Pauli realized that to explain electron energy levels in atoms, those electrons must obey a rule that we call the Pauli exclusion principle.

It states that no electron can occupy the same quantum state as another electron.

In fact, it applies to all particles called fermions.

In the case of electrons in atoms, it suggests that we should only find one electron per atomic orbital, if we count each orbital as a quantum state.

However, we actually observe two electrons per orbital.

And so Pauli realized there must exist a hidden quantum state.

Pauli introduced what we call a new degree of freedom internal to electrons, one that could take on one of two values.

Let's call those values up and down.

That would allow two separate electrons, one up, one down, to occupy the same atomic energy level, without occupying the same quantum state and therefore violating the Pauli exclusion principle.

Other physicists soon figured out that this new quantum state represented spin and the up and down degrees of freedom were the direction of pointing of the angular momentum axis.

We now call these two component wave functions, spinors.

Now, it's OK to ignore spin in the old Schrodinger equation and get approximate answers.

But when a magnetic field is present, spin direction becomes very important.

So for fast moving electrons and for electrons in electromagnetic fields, the Schrodinger equation gives the wrong answers.

The problem consumed a brilliant British physicist, Paul Dirac.

He wanted a fully relativistic version of the Schrodinger equation that worked for electrons.

In a way, he started with relativity.

He wrote down Einstein's famous equation, E equals mc squared, but in its full form, including momentum.

He then used quantum mechanical expressions for energy and momentum.

The result was a huge mess.

But Dirac stumbled upon a single simple idea that caused the resulting horrendous mathematics to collapse into an incredibly simple, beautiful equation.

That simplification required Dirac to expand the internal workings of the electron even further.

Instead of having a two-component spinor, up and down, as in Pauli's theory, he needed four components.

Now, he had no idea what those two additional mysterious components might mean.

But the resulting equation was so simple and elegant that somehow Dirac knew that he was onto something.

The resulting Dirac equation describes the spacetime evolution of this weird four-component particle-wave function, represented by the symbol psi.

It contains the marks of both quantum mechanics, in the Planck constant, and relativity, in the speed of light.

The Dirac equation perfectly predicts the motion of electrons at any speed, even in an electromagnetic field.

It was a major victory.

But it opened up even more questions than it answered.

To begin with, what on earth were those two extra degrees of freedom in the four-component electron?

The answer came from trying to calculate the energy of the electron using this equation.

It predicted something totally bizarre.

It allowed electrons to exist in states of negative energy.

If true, that would lead to some weird effects.

For example, a lone electron moving in an electromagnetic field could keep releasing energy as light infinitely, and sink lower and lower, to infinite negative energy states.

There was no bottom to the energy well.

Now, we know perfectly well that this doesn't happen.

Dirac came up with an idea to explain this.

We call it the Dirac sea.

Imagine an infinitely deep ocean of electrons that exists everywhere in the universe.

These electrons occupy all of the negative energy states, all the way from negative infinity, up to zero.

The only time we can actually interact with an electron is when one has a positive energy, which would leave it sitting on top of the sea.

This is where the Pauli exclusion principle comes back.

If the energy states of this imaginary ocean are all completely full, then that one extra electron can't lose any more energy.

It just floats on top of the sea.

The idea of the Dirac sea leads to its own weird predictions.

Remove one electron from the surface and it leaves a hole.

That hole should act like a particle all by itself.

It would be like an eddy on the surface of a pool of water.

It would move around.

It would have inertia, acting like it had the mass of the missing electron.

It would also act like it had the opposite electric charge to the electron, a positive charge.

And if a positive energy electron found one of these holes, it would fall in, annihilating both, and releasing all of the energy bound up in their masses.

Of course, there is something in our universe that acts exactly like holes in the Dirac sea.

It's called anti-matter.

And Dirac had just predicted its existence.

Now, the Dirac sea itself doesn't really exist.

But it was one of the first attempts to describe something very real, the idea of a quantum field.

We now know that every elementary particle has an associated field, that fills all of space.

These fields are more like membranes than infinitely deep oceans.

They have a very definite energy, usually zero.

And the elementary particles that we know and love are just regions where a field has a bit more energy.

That energy manifests as vibrations in the field.

Now, quantum field theory is a very deep topic.

And it'll be the subject of upcoming episodes.

But for now, let's get to the bottom of these holes.

Paul Dirac's negative energy solutions describe anti-matter, not holes in the Dirac sea.

Only a few years after Dirac wrote down his equation in 1928, the positron, the anti-matter electron, was spotted in cosmic rays by Carl Anderson.

Anti-matter is very real.

But what is it?

Well, it's a vibration in the same quantum field as its regular matter counterpart.

Anti-matter's existence is fundamentally tied to these weird four-component electrons that Dirac invented to make his equation work.

Those two extra components correspond to the up and down spins of the electron's anti-matter counterpart, two spin directions for the electron, two for the positron, a four component spinor.

In fact, the electron and the positron cannot exist without each other.

They are two sides of the same coin, positive and negative energy solutions of the same type of vibration in the electron field.

It's actually a tiny bit more complicated than that, and way more awesome.

But there will be time for all of that in the future.

So all elementary particles have a quantum field and all have an anti-matter counterpart.

Just as with the holes in the Dirac sea, anti-matter particles have the same mass as their counterparts, but opposite charge.

That mass is very real.

It's not negative mass despite this negative energy description.

When matter, anti-matter counterparts find each other, they annihilate, releasing an awful lot of very real energy.

A penny of anti-matter could be used to launch a good-sized rocket into orbit.

Dirac's incredible insight in combining quantum mechanics and relativity reveal an entire flip side of our universe, with its prediction of anti-matter.

It was also a key step in the discovery of quantum field and quantum field theory and the development of the standard model of particle physics, which have become our best description of the underlying workings of reality.

And that's a quantum rabbit hole that we'll jump into very soon, right here on "SpaceTime."