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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,