The same, yet different

I had kind of a strange experience yesterday. I was biking to class, which is a pretty routine thing for me, and all of a sudden I got the feeling of being lost. Now if you know me you'll know that I'm terrible with directions, but come on. I've been living at my new place for about 3 weeks now and I bike to Ångström pretty much every day. I should know where I'm going. And yet, somehow, I just didn't recognize the street properly. I wasn't lost, of course, and once I got over my brief confusion I continued on my way to class. It wasn't until I saw a cloud of dust blowing around in the Ångström parking lot that I realized what was different: the streets were dry.

I know this may not sound like much of a revelation, but this was the first time I had seen my path to school without it being damp or snowy. It's been sunny and warm the past few days, so I'm going to go ahead and get my hopes up that this is a sign of winter ending. That, and the fact that even if I have class until 17.00 these days it's still light outside when I get home, which is a novelty after the darkness!

But enough about the weather. The class I was cycling to yesterday (and today) was the last component in my Quantum Field Theory course: a crash course on the Higgs boson! I had actually done something similar to this before, but that was before I had the tools to really appreciate what exactly I was doing.

Now, I've found in the past that typically when a course has some kind of added component, especially when it's taught by someone else (I'm looking at you, labs), I haven't overly enjoyed it, so I was a little bit sceptical about the crash course. However, it actually turned out to be really cool! Basically we spent two afternoons motivating the need for the Higgs mechanism, and then working out some of the details of how it works and how to test it. In fact, I'm currently procrastinating that assignment by writing this post, so I better at least say something about the material to compensate for that.

Basically quantum field theories (which are how we describe particles that can interact) are governed by an expression called the Lagrangian. Experience tells us that these expressions should have certain symmetries. For example, if you look at an interaction from another viewpoint, you should still get the same results, which means the Lagrangian should have a rotational symmetry. Another type of symmetry that we typically require is called a gauge symmetry. Now, the Lagrangian also encodes what the masses of the various particles in our theory should be. However, when we write these "mass terms" in, we often lose our gauge symmetry, which is unacceptable. The Higgs mechanism provides a neat solution. I would be tempted to call it a mathematical trick if it didn't have such serious physical consequences.

The Higgs mechanism allows you to rewrite the Lagrangian to "hide" your mass terms such that they only appear later on, leaving our Lagrangian with the desired symmetry. However, as is often the case in physics, simplifying one thing causes another to get more complicated. In this case, the "price" we have to pay to simplify our Lagrangian is that the theory becomes more complex: we have to add another particle, the Higgs boson. This is why I wouldn't just call it a trick, since it requires the existence of an actual measurable phenomenon, so it is empirically falsifiable. Luckily for us, the discovery of the Higgs boson was announced on July 4th 2011 2012 by CERN (which is a very cool place if you ever get to visit!). So my crash course is really useful to describe real life, and as such I better get back to work on my assignment. Wish me luck!

edit: Thanks to Danu for correcting the date on the Higgs boson discovery!