Beauty in Physics and Paul Dirac — Models and Morality

I like to listen to audiobook biographies of physicists. The frustrating thing is that I’m always confronted with how much physics I’ve forgotten since I studied it in undergrad.

Recently I listened to a biography of Paul Dirac. Before listening I definitely knew his name, but the only specific thing I could have connected him with was the Dirac Delta Function.

One of the best memories I have from college was going with a couple of my friends to the office hours of our favorite physics professor and having him teach us about the Dirac Delta function. The Dirac Delta function is a very weird and beautiful function.

Imagine a spike on a graph that is infinitely tall and infinitely thin, but somehow has an area of 1.

Imagine being told that this function:

Contains deep insights about the universe
Is hated by pure mathematicians (1), but us physicists who want results know better
Will save you hours of work on your homework
Is not necessarily something that will be covered in lecture, but you guys can handle it

Imagine being told all this by a radiant and brilliant theoretical quantum physicist whose only goal is to get you excited about physics.

It’s just a little bit of an exaggeration to say that’s the day I decided to become a physics major.

When Dirac did physics, he sometimes seemed more focused on the aesthetic beauty of his models than their truth. He said “it is more important to have beauty in one's equations than to have them fit experiment.”

I’ve usually been pretty skeptical of this argument. It’s seemed to me that because beauty is so subjective, it’s better for us to look for truth in science than for beauty.

I learned in reading that Dirac also came up with the notion of a magnetic monopole (2). No magnetic monopoles have ever been verified. If they exist at all, some theories predict there may only be one in the entire universe.

In another class, our favorite professor explained to us that somewhere in a lab in California, was a sensor meant to detect magnetic monopoles. One day, shortly after being set up, the sensor registered a spike. Since then, it has never registered anything.

Most likely the machine malfunctioned that day. But just maybe that was the one day when the one magnetic monopole in the cosmos happened to wander through California.

Part of the fun of studying physics is learning beautiful arcane notation.

In quantum mechanics the most fun bit of notation is bra-ket notation, which is things like this:

Learning bra-ket notation felt like gaining the ability to understand a foreign script that quantum wizards use to describe nature’s secrets.

I hadn’t known Dirac came up with bra-ket notation too (3).

Dirac had faith that sometimes the beauty of an equation could tell us something that experiment could not.

Dirac came up with 3 of the most inspiring physics concepts I encountered during undergrad. Moments like learning about possible existence of magnetic monopoles are what made me want to keep studying physics.

I now think the search for beauty is intertwined with the search for truth. You need to have the beauty in order to keep you motivated to find the truth. And we’re lucky enough to live in a world that when you find one, the other is often not far.

Footnotes:

1. In fact, they like to say things like that it’s technically a “distribution”, not a “function”

2. We all know magnets always have a north end and a south end. But what if you had a magnetic particle that was all north and no south? That’s the basic idea of a magnetic monopole.

3. He also came up with the Dirac Equation. I never made it far enough in physics to learn it, but my physicist friend tells me that it is very beautiful – it compactly describes every electron in the universe