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Richard Feynman called it

the jewel of physics

Of all of our mathematical descriptions of the universe,

this one has produced the most stunningly precise results

I'm talking about quantum electrodynamics - the first true quantum field theory

Quantum mechanics is perhaps

the most unintuitive theory ever devised

And yet it's also the most successful in terms of sheer predictive power

Simply by following the math of quantum mechanics, incredible discoveries have been made.

It's wild success tells us that the mathematical description provided by quantum mechanics

reflects deep truths about reality

and by far the most successful,

most predictive formulation of quantum mechanics

is Quantum Field Theory

It's the best description we have of the fundamental workings of reality.

And the first part of quantum field theory that

was derived, Quantum Electrodynamics

is the most precise, most accurate of all.

Quantum field theory,

QFT

describes all elementary particles as vibrational nodes

in fundamental fields that exist at all points

in space and time through the universe

quantum electrodynamics - QED

provides this description for one such field:

the electromagnetic field.

the pillars of QED are the description of

the behavior of the EM field,

and the description of the behavior of the electron

by the Dirac equation.

We covered the Dirac equation last time,

and you really should watch that episode first if you haven't already.

Now, before we start thinking about

vibrating quantum fields,

or even fields at all, let's talk about vibrations.

knows that a stretched string vibrates

with a certain frequency, when plucked.

It also vibrates with an amplitude that depends on

how hard you pluck it. A larger amplitude

and/or a larger frequency means the

vibration carries more energy. At any point in time,

every point on a vibrating string, is displaced by

some distance from its relaxed (or equilibrium) position.

and that displacement changes over time,

as the string oscillates back and forth.

Guitar strings are 1-dimensional,

but we can expand the analogy to any number of dimensions.

In 2D, we have a membrane. Like a drum skin.

Everywhere on the surface of a vibrating drum skin,

there is a displacement from the flat equilibrium state

in the up-down direction.

The 3D analogy is harder to imagine.

Every point in space, has some displacement

in some imaginary extra direction.

Analogous to, but not the same as a 4th dimension.

For example, in a 3D room full of air,

sound waves are oscillations in air density.

That air density has an equilibrium value,

which is just the average density,

but in every point in the room,

a soundwave can cause air density to oscillate:

to higher and lower values.

We describe air density as a field,

because it has some value everywhere in the space of the room;

and that's all a field is,

some property that has some value throughout the space.

Ok,

let's go----quantum.

And let's go back to the string.

If this were a

quantum mechanical guitar string,

there's need to be a minimum amplitude

for the vibration that depended on its frequency.

No vibrations with amplitude smaller than that minimum could exist.

And every larger vibration

would have to be a whole number,

an integer multiple of the smallest amplitude.

This is exactly how light behaves.

tells you that you can only have one fermion, so electron, quark,