Quantum Diaries

I don’t know the original source, but there’s an image that has gone semi-viral over the past year which challenges the reader to identify several brand names based on their logos versus plant names based on their leaves. (Here’s a version at Adbusters.) The point is to contrast consumerism to the outdoors-y/science-y education that kids would get if they just played outside.

This isn’t the place to discuss consumerism, but I don’t agree with idea that the ability to identify plant names carries any actual educational value. Here’s my revision to the image:

On the right we’ve encoded all of the particles in the Standard Model in a notation based on representation theory. In fact, this is almost all of the information you need to know to write down all of the Feynman rules in the Standard Model (more on this below).

Tables that the one above are a compact way to describe the particle content of a model because the information in the table specifies all of the properties of each particle. And that’s the point: whether we name a particle the “truth quark” or the “top quark” doesn’t matter—what matters is the physics behind these names, and that’s captured succinctly in the table. Science isn’t about classification, it’s about understanding. I leave you with this quote from Feynman (which you can watch in his own words here):

You can know the name of a bird in all the languages of the world, but when you’re finished, you’ll know absolutely nothing whatever about the bird… So let’s look at the bird and see what it’s doing — that’s what counts. I learned very early the difference between knowing the name of something and knowing something.

Addendum: naming those particles

For those who want to know, the particles in the table are, from top down:

1. The left-handed quark doublet, containing the left-handed up quark and left-handed down quark
2. The anti-right-handed-up quark
3. The anti-right-handed-down quark
4. The left-handed lepton doublet, containing the left-handed electron and left-handed neutrino
5. The anti-right-handed electron (a.k.a the right-handed positron)
6. The anti-right-handed neutrino
7. The Standard Model Higgs

SU(3), SU(2), and U(1) refer to the strong force, weak force, and hypercharge. Upon electroweak symmetry breaking, the weak force and hypercharge combine into electromagnetism and the heavy W and Z bosons. Here’s how to read the funny notation:

1. Under SU(3): particles with a box come in three colors (red, green, blue). Particles with a barred box come in three anti-colors (anti-red, anti-green, anti-blue). Particles with a ‘1’ are not colored.
2. Under SU(2): particles with a box have two components, an upper and a lower component. That is to say, a box means that there are actually two particles being represented. More on this below. Particles with a ‘1’ do not carry weak charge and do not talk to the W boson.
3. Under U(1): this is the “hypercharge” of the particle.
4. The electric charge of a particle is given by adding to the hypercharge +1/2 if it’s the upper component of an SU(2) box, -1/2 if it’s the lower component of an SU(2) box, or 0 if it is not an SU(2) box (just ‘1’).

As a consistency check, you can convince yourself that both the left- and right-handed neutrinos carry zero electric charge. Note, also, the fact that we’ve written out left-handed and right-handed particles differently. This is a reflection of the fact that the Standard Model is a chiral theory.

Finally, I said above that the table of particles almost specifies the structure of the Standard Model completely, the additional pieces of information required are:

1. Which of the above particles are fermions and which are scalars (the gauge bosons are implied)
2. Write down the most general ‘renormalizable’ theory (we write only the simplest interaction vertices)
3. Specify the pattern of electroweak symmetry breaking (the Higgs)
4. Specify the flavor symmetries (three of each type of matter  particle)

From this one can write the complete mathematical expressions for the Standard Model. One then just has to fill in the observed numerical values to be able to calculate concrete predictions for actual processes.