The Universe on a T-Shirt

Recently I was asked what the equation on my t-shirt meant and I was ashamed at myself because the best answer I could give was that it described a bunch of particles… and I’m a physics major. So as a diligent man of science I decided to set out on a 2-hour journey across the Interweb to find out what this equation really meant. Sadly, there were no mentions of 42. But I did find this thing called the Standard Model. It’s the theory of ‘almost’ everything, the holy grail of modern physics as some physicists like to call it. That equation up there is a mathematical explanation of the Standard Model. It describes the behaviour of the Universe and everything within it. And it fits on a t-shirt. Woah.

Specifically, it’s called the Standard Model Lagrangian, or in other words, a scary formula. Don’t worry, I’m not a fan of big words either. A Lagrangian (luh-grawn-gee-uhn) is just a nice way of writing an equation so that we know what it’s doing at any given time. That’s what the L stands for.

The first line tells us about three of the four fundamental forces in the Universe, the electromagnetic and the strong and weak nuclear forces (suck it gravity!). How can a bunch of symbols tell us these things you may ask? Well in particle physics, forces and particles are represented by fields in space and time. The Fμν represents the electromagnetic field and also includes a field description of the strong and weak force.

The second line tells us how these forces act on the fundamental particles of matter known as quarks and leptons, both of which are types of fermions, represented by the fermion field (ψ) in the equation. You might be familiar with protons, neutrons and electrons which make up atoms, the building blocks of the universe. But protons and electrons are made up of quarks while an electron is just a type of lepton!

The third line involves both the fermion field (ψ) and the Higgs field (ϕ). It describes how fermions get their mass from the Higgs boson, a particle that was discovered in 2013, 50 years after it was theorised to exist! The fourth line describes how the Higgs field (ϕ) and boson act when they are changed or manipulated.

Take a close look at the equation again and you’ll see some weird-looking D’s in the second and fourth line. They describe the movements of the fermion and Higgs fields. They also represent parts of the electromagnetic, strong and weak force which means that each of those D’s also describe how the fermion and Higgs fields interact with the fundamental forces of nature!

Hopefully, you can see that the gravitational force is not in the Standard Model Lagrangian. That’s because we still don’t know where gravity fits into the grand scheme of things. Physicists are still trying to bridge the divide between particle physics, what happens at the tiny scale, and general relativity, which describes gravity and what happens at the huge scale. Some physicists think that we might soon discover the ‘graviton’, a hypothetical particle that is responsible for the gravitational force while others are placing their bets on string theory and other weird and wonderful ideas.

The way the equation is written is an homage to the advances made during the 20^th century in a field which hardly anyone knew anything about. With chalk in hand, physicists like Einstein, Bohr, Planck, Schrödinger, Dirac, Feynman and so many more spent lifetimes in front of blackboards trying to find the elusive theory of everything. The equation on my t-shirt represents the furthest we have come to answering the universe’s greatest mysteries. Now, whenever someone comes up to me and asks me what this equation means, I can at least do some justice to some of the greatest minds that ever lived.

Nicholas Kondal

Further reading to blow your mind:

http://iopscience.iop.org/article/10.1088/1361-6552/aa5b25/pdf

http://www.symmetrymagazine.org/standard-model/

It’s amazing how those 4 lines can explain how pretty much everything in the universe behaves. But I must confess… the above equation is an abbreviated version of the actual equation. Below is the Standard Model Lagrangian in all its glory. Enjoy.

Click to access sml.pdf

http://www.symmetrymagazine.org/article/the-deconstructed-standard-model-equation