We are living in a universe where
particles are interacting every single time.
See this book I got here? The electrons in
my hands are actually repelling the
electrons of the book. Really? If that
doesn't convince you, we can make a cloud
chamber from dry ice and see these
amazing patterns of particles
interacting with other particles. You ask
what's behind all that? Quantum Field
Theory. Okay, let's start with the word
"quantum". Quantum can be closely associated
with probability like rolling a dice. Now, if
this dice is the interaction for example,
when electrons repel and we throw this
dice in an electron-electron field. The
Quantum Field Theory will tell us what
happens when the fields interact with a
certain probability. Hmm. Does that mean
there are a lot of possibilities as to
how electrons repel? Not just repel
because of their negative charges? Yes
and no. Electrons repel not just due to their charges. That's a classical view. In a
quantum view, they repel because of
exchanging virtual photons. What? Let's
use Feynman diagrams to visualize that.
When electrons happen to be near each
other, a virtual photon is emitted by one
electron and the other electron absorbs
it. Hence, the repulsion. Easy as it sounds
right? Well, remember. I did emphasize other possibilities going on when electrons
repel. That means, aside from this diagram, there are other diagrams too. Noooo.
To solve that, we need to find which diagram among others is most probable so we can
approximate. A theory called perturbation
will help us find that and let's use
this paper as an analogy. Suppose that I
put a value of this whole paper as one.
Folding it once becomes one-half. Twice
becomes one-fourth, and so on. But as we
go on to fold it many times, the number
contributes less to the value of the
whole paper. So, one-half becomes the best approximate to one. Like folds in the
paper, diagrams have vertices - the area
electrons absorb emit photons.
How many vertices a diagram has is also
how much is its probability to happen.
Specifically, one vertex contributes
approximately 1 over 137.
That's the fine-structure constant
Two vertices contribute to the constant
squared and the others follow the same
pattern. But since there are no one
vertex diagrams, we can now approximate the two vertex diagram as the most
probable interaction when electrons
repel. But wait, there's an exception to using
perturbation. Diagrams called loops
actually add up to contribute a bigger
probability. Meaning, we need to include
them in our approximation. But when
scientists did that, it led to an
infinity. This required them to use a
mathematical technique called
renormalization. It's very complicated
but the idea is that we get rid of the
infinities by introducing a "cut-off" so we
can have finite values. Now the importance of these values goes back to this book, the
cloud chamber, and exceptionally the
whole universe. They describe how quantum
fields function in the microscopic world
and the only thing we see in our daily
lives, that is in a macroscopic world, are the ones with the highest probability.
