If you've studied any physics you know that like charges repel and opposite charges attract.

But why?

It's as though this thing - electric charge - is as fundamental a property of an object as its mass.

It just sort of ... exists.

Well it turns out if you dig deep enough, the fundamental-ness of charge unravels, and in many things, including mass itself, unravel with it.

Although many mysteries remain in physics, at least our understanding of electricity and magnetism seems pretty complete.

The math that describes it - Maxwell's equations or quantum electrodynamics - seem to wrap it up nicely.

Except that all of electromagnetism is powered by a single property: electric charge.

And neither Maxwell’s equations nor QED say a thing about what electric charge really is.

It seems to just be a property that particles can have or not have - as fundamental as mass.

Like we’ve got to the exasperated end of a child’s train of but why?

But why?”, where the only answer is: "just because."

The idea of “fundamental” feels like the physics version of “just because”.

But actually, in the case of electric charge we have at least one or two more “but why’s” with which we can annoy the universe.

Today we're going to ask them, and the answers will take us through the birth of Particle Physics, and, in fact, through the birth of the universe itself.

As with much of modern physics, this story begins with Werner Heisenberg, whose epiphanies birthed quantum mechanics.

At some point, Heisenberg turned his remarkable intellect to the newly discovered neutron.

He was suspicious of its similarity to the proton - they’re practically twins in the atomic nucleus, occurring with similar numbers and almost the same mass, with the only major difference being our mysterious friend - electric charge.

The neutron seemed like a chargeless, or neutral proton, hence the name.

Heisenberg wondered if the two particles were in fact just different states of a single particle which he called the nucleon.

At this point we already knew of particles that had internal states.

For example electrons have this thing called spin - a quantum analogy to angular momentum.

Spin can take on discrete values; in the electrons it can be +1/2 or -1/2, loosely corresponding to the spin axis being aligned or anti-aligned with your measurement device, which we’ll call “up” and “down” states.

And spin is conserved - flip an electron’s spin and the difference has to be transferred by a photon.

So if the protons and neutrons are just two states of the same particle, Heisenberg reasoned that they may be differentiated by a property analogous to spin, governed by analogous mathematics.

Thus, in 1932 Heisenberg proposed a new fundamental property of matter: Isospin, a contraction of isotopic or isobaric spin, depending on who you ask.

In this theory the proton would be the “up” state with isospin 1/2, and the neutron would be the down state with isospin -1/2.

By introducing this new conserved quantity, Heisenberg started to make sense of the relationship between protons and neutrons.

For example, with this choice of their relative isospins, it made sense why nuclei prefered to have roughly equal numbers of protons and neutrons, and at the same time allowed precise predictions of the outcome of collisions between these particles.

But for isospin to really do its job, it needed to explain the most obvious difference between protons and neutrons - which is to say electric charge.

Charge would have to depend on isospin, which could mean that charge is not a fundamental property after all.

Fast forward a few decades.

Our particle colliders advanced, leading to the discovery of weird new particles.

So many of them, in fact, that physicists struggled to make sense of this so-called particle zoo.

But there were some clues.

For example, some of these particles had very similar masses but very different electric charges, which I hope reminds you of the proton and neutron.

So maybe each of these groups were really a single particle in different states - with different isospins.

The case for isospin was solidifying.

But what exactly was the connection between isospin and electric charge?

Well that mystery was solved independently by Kazuhiko Nishijima and Murray Gell-Mann.

Peering into the depths of the particle zoo, they noticed another pattern.

There seemed to be a family of particles that were only created in pairs.

Similar to how the electron and positron are only created in pairs in order to conserve electric charge.

But these new particles weren’t doing this to conserve charge, nor isospin, nor any other known property.

This suggested a brand new conserved quantity, which was altogether strange.

In the same way that isospin followed the same mathematics as regular quantum spin, this new property seemed to obey the math for our old friend electric charge.

They called it Hypercharge.

Nishijima and Gell-Mann discovered an even deeper pattern.

Electric charge, isospin and hypercharge were intimately connected across all particles.

In fact, it seemed that electric charge was just isospin plus half of hypercharge.

To be pedantic, that’s the z-component of isospin, but we’ll put that complication aside for now.

The conservation of fundamental properties defines which interactions are possible and which are impossible.

Charge alone couldn’t explain the patterns of interactions and particle types observed in the particle zoo.

However hypercharge and isospin seemed to do a much better job - suggesting that these may in fact be more fundamental than charge.

But there remained a mystery.

Not every combination of isospin and hypercharge were possible.

It was Murray Gell-Mann who first noticed this.

Plotting particles according to their isospin and hypercharge revealed peculiar geometric patterns.

For example some groups of eight particles formed hexagons, and one group of ten particles formed a triangle.

Except that the triangle was missing the bottom corner.

No big deal - Gell-Mann just hypothesized an undiscovered particle - the omega baryon - with the right isospin and hypercharge to fill that hole.

Sort of like how Mendeleev had used holes in the Periodic Table to predict the existence of unknown elements.

And when the omega was discovered by experimentalists, Gell-Mann got his Nobel prize.

Isospin and hypercharge seemed to be “deeper” than electric charge.

But the geometric relationship between these two new properties hinted that there may exist even deeper physics yet; even more fundamental rules which explained why they should be constrained in these ways.

Again, it was Gell-Mann who figured this out.

He recognized that these patterns were actually representations of a mathematical symmetry known as SU(3).

Unfortunately we can’t get into the gory details of symmetry groups in this episode, but in short, Gell-Mann realized that he could make sense of the geometric symmetry if nucleons themselves were not elementary particles, but rather made up of smaller components, which he dubbed quarks.

He showed that isospin and hypercharge were just emergent properties that reflected the different types of quarks that make up one of these particles.

Starting with experiments at the Stanford Linear Accelerator Center in 1968, the reality of quarks quickly became conclusive.

So after all this hard thinking it turns out that isospin and hypercharge were as much mathematical abstractions as was electric charge.

There must be something deeper - something that lives in the hearts of these quarks and other elementary particles - that governs these differences between particle groups, and that also governs electric charge.

The quark model for nucleons led to a description of the strong nuclear force via this SU(3) stuff to give us quantum chromodynamics.

But that’s a story for another time.

It may seem like the strong force led us astray - but actually it points to the answer.

For one thing, the early approaches of Heisenberg and Gell-Mann and others are exactly what we need - it's just that they were applied to the wrong force of nature.

And it's by unraveling one of the forces of nature that we can explain electric charge - but it's not the strong force, it's not even electromagnetism.

The secrets of electric charge are actually hiding in the last, most obscure of the quantum forces - the weak force.

It’s also the weirdest force of all, and we need to consider two of its weirdest properties.

First, the weak force can transform particles into other particles - something no other force can do.

Second, it only works on left-handed particles.

That second really does sound weird, and it is - but it's the thing that's going to connect all of this back to quantum spin, which is sort of where we started.

One consequence of quantum spin is this thing called chirality, which is sort of the projection of spin in the direction that a particle is moving.

It's more complicated, obviously, but that'll do for now.

Particles can have right-handed chirality if their spin is clockwise relative to their momentum vector and left-handed chirality if it's counter-clockwise.

Only particles with left-handed chirality feel the weak force.

For example, the electron has both a right- and left-handed component.

Only the left-handed component can emit one of the weak-force carrier particles - the W boson - and in doing so transform into a neutrino.

Remember that Heisenberg imagined that the proton and neutron were differentiated by this new conserved quantity, isospin.

We can play the same trick with the electron and neutrino.

So it turns out that the new conserved quantity behaves eerily similarly to isospin.

We're going to call it weak isospin.

Only left-handed particles have it, and so it has an intimate connection to the quantum spin.

Weak isospin is effectively the charge of the weak force, carried by these W bosons.

To fully explain weak interactions we need a second charge - this one carried by the Z boson.

It acts more like electric charge, so we'll be imaginative and call it weak hypercharge.

And here's the weird thing: weak isospin and weak hypercharge are mixed in exactly the same way as Gell-Mann’s versions of these quantities.

Which is to say, electric charge equals weak isospin plus half weak hypercharge.

And we know these weak versions of isospin and hypercharge must be fundamental because they are properties of elementary particles that can't be broken into smaller pieces.

Particles like the electron, the neutrino, and even the quark.

That's right, quarks feel the weak force and obey the same rule for their electric charge.

It turns out that our old strong-force versions of isospin and hypercharge in the composite particles of the particle zoo emerge from their different quark content, but are driven by these more "real" weak-force quantities.

Let me summarize where we've got to: the charge that drives electromagnetism is governed by the charges that drive the weak force.

So does that mean that electric charge is not really fundamental?

We need to question what fundamental really means.

What we’ve learned is that electromagnetism and the weak force are deeply connected.

Or, should I say, were connected.

These two forces were once united in what we call the electroweak force, whose charges were the same weak isospin and hypercharge that we just discovered.

Something happened to that force in the very early universe to force these charges to only take on a specific combination of values - the combination that we now observe as electric charge.

That event - the breaking of electroweak symmetry - created the weak and electromagnetic forces as we know them today.

So we now know that electric charge is a sort of shadow of the ancient fields from the birth of the universe.

Very soon we’ll follow this thread deeper to fully understand why these fields separated, and how, in this process, the Higgs field was also created.

Which, by the way, grants mass to elementary particles - yet another supposedly “fundamental” property”.

But is it any more fundamental that the dubiously fundamental electric charge?

And if mass isn't fundamental, then what is?

We’ll find out soon as we continue to unravel the tangled symmetries of spacetime.