Behold.
The foundation of the universe.
The ideas that govern the microscopic world.
It’s quantum field theory time.
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Hey Crazies.
I know you’ve wanted quantum field theory for a while now.
Well, it’s finally time, but let’s ease into this with a closer look at light.
We’ve got two different models for light: The EM wave model
and the photon particle model.
Both of which seem unconnected.
Spoiler Alert: They’re not.
Having ideas be separate is great when you’re trying to be practical,
but deeper understanding comes from seeing how things are the same.
Even though Henry from MinutePhysics has called me pedantic for this philosophy,
I’m going to stand by it anyway.
Neither of these models is a part of the other.
Like I said, they seem unconnected.
The only possibility is that there’s a deeper idea that explains both of them.
That deeper idea is the quantum field.
But let’s ask a simpler question first.
What is a field?
I did a video on this before, but that was back in the early days,
so let’s go over this again.
A field is a quantity or measurement assigned to all points in space.
That’s it. Nothing more. Nothing less.
But quantities come in many different varieties, kind of like my clones.
There are scalar quantities, which are just single numbers.
A scalar field would be something like voltage or electric potential.
A single number assigned to every point in space.
There are also vector quantities, which are numbers with direction.
A vector field would be something like an electric field.
A number and arrow assigned to every point in space.
There are even tensor quantities, with many levels of detail.
A tensor field would be something like the Riemann spacetime curvature.
A collection of 256 numbers assigned to each event in spacetime.
Light is called an electromagnetic wave because it’s a wave in the electromagnetic field.
When I show you a wave like this, the blue and orange arrows don’t have a
size in space.
Only the white line does.
The arrows are measured in whatever units are appropriate for the field.
A field that existed before the wave passed through it.
I’ve always just kept the picture simple by not showing you the field.
Every field has an equilibrium.
In the middle of empty space with nothing around,
the equilibrium for the EM field is zero everywhere.
When the light passes through, the field is disturbed and those numbers change.
After the light passes through, the field returns to normal.
The point I’m trying to make is that zero-values don’t mean the field isn’t there.
Zero is still something.
The field is always there.
Well, at least on paper.
The physical existence of a field is still up for debate.
So is that electromagnetic field a quantum field?
Eh, not really. At least, not the one I just showed you.
Oh.
Come to think of it, that electromagnetic field is actually two fields.
A blue arrow for the electric field and an orange arrow for the magnetic field.
But when we talk about them, we group them together as one thing.
You might say we unify them.
That’s what a unified theory is: Showing that two different things are just
different parts of the same thing.
In this case, the electromagnetic field.
This is a tensor that has electric parts and magnetic parts.
Instead of having two different vector fields, we just have one tensor field.
But tensors aren’t always very convenient.
Hmmm, let’s take this one step deeper.
The electric and magnetic vector fields can be written as
changes in electric and magnetic potentials.
That’s brings our tensor of 16 numbers down to just a vector with 4.
It contains all the same information and, honestly, it’s much closer to reality.
Wait a minute!!
Potential is almost potential energy, so I think we’re onto something here.
We’ve stepped down from the electromagnetic field to an energy field.
Energy is something quantum particles can have.
A quantum field is just a field of quantum properties.
A quantum measurement like energy assigned to every point in space,
but this is where things get a little wonky.
Quantum properties are intertwined with each other through the wave function
and, if we imagine that quantum properties are part of fundamental fields
then they’re no longer attached to particles.
There are 17 different types of particles with unique properties.
Some of those properties are fixed.
Others, like spin orientation, have some wiggle-room.
If we start treating their properties like fields instead
then we’re going to need, like, 100s of fields.
So many fields, my brain hurts!
Alright, maybe we can group them together like we did for the EM field.
Let’s focus on some basic quantum numbers: Spin, Electric Charge, and Color Charge.
Color charge is how we tell gluons apart from photons, commenters.
If we group using those properties, the field-count drops way down.
Different spins and charges require separate fields, so
we’ve got 6 Leptons, 6 Quarks each with 3 possible color-charges,
8 color-charge combinations for Gluons.
Yep, all separate.
1 Photon, 3 Weak Bosons, and 1 Higgs.
If each one gets its own field, that’s a grand total of 37 fields,
which is the best we can do without a semester-long course in particle physics.
Wait, then what’s a particle?
Perfect timing!
You’re, like, my best clone ever.
I’m so proud of you.
Really?!
So these fields exist everywhere, across all space and time.
But that doesn’t mean particles are everywhere.
There’s only a particle when a quantum field get excited.
For example, this is the photon field with no photons in sight.
Here in empty space, the field-energy hovers around zero
with just some quantum uncertainty keeping it from being exactly zero.
It’s called the Vacuum State: The ground state of the field.
Suddenly, an electron and a positron crash into each other.
They annihilate and their energy is added to the photon field.
The result is two photons, two non-zero places in the photon field.
But then, the same can be said about the electron and positron.
They were just places in the electron field with an energy hovering above zero
and their interaction shoved their energy into a different field: The photon field.
It’s just energy moving from one field to another.
Welcome to Quantum Electrodynamics: The study of how the electron field and the
photon field interact.
It’s an example of something called a Quantum Field Theory.
A model that governs how quantum fields interact.
So to summarize: A quantum field is a set of quantum properties
assigned to every point in space.
Each one existing alongside the others, allowing them to interact.
and any energy in a field higher than its vacuum state
will be seen as a particle carrying the properties of that field.
Whoa!
As usual, if you have any questions, please ask in the comments.
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By the way, I meant it when I said photons don’t experience space or time.
In our frame of reference they do, of course, but they don’t in their own.
For a photon, all of space is one point and all of time is one moment.
And, on that note, thanks for watching!