Since today is Halloween, I really wanted to write a post talking about the spookiest particles in physics, ghosts.
The problem is, in order to explain ghosts I’d have to explain something called gauge symmetry. And gauge symmetry is quite possibly the hardest topic in modern physics to explain to a general audience.
Deep down, gauge symmetry is the idea that irrelevant extra parts of how we represent things in physics should stay irrelevant. While that sounds obvious, it’s far from obvious how you can go from that to predicting new particles like the Higgs boson.
Explaining this is tough! Tough enough that I haven’t thought of a good way to do it yet.
Which is why I was fairly stoked when a fellow postdoc pointed out a recent popular physics article by Juan Maldacena, explaining gauge symmetry.
Juan Maldacena is a Big Deal. He’s the guy who figured out the AdS/CFT correspondence, showing that string theory (in a particular hyperbola-shaped space called AdS) and everybody’s favorite N=4 super Yang-Mills theory are secretly the same, a discovery which led to a Big Blue Dot on Paperscape. So naturally, I was excited to see what he had to say.
The core analogy he makes is with currencies in different countries. Just like gauge symmetry, currencies aren’t measuring anything “real”: they’re arbitrary conventions put in place because we don’t have a good way of just buying things based on pure “value”. However, also like gauge symmetry, then can have real-life consequences, as different currency exchange rates can lead to currency speculation, letting some people make money and others lose money. In Maldacena’s analogy the Higgs field works like a precious metal, making differences in exchange rates manifest as different prices of precious metals in different countries.
It’s a solid analogy, and one that is quite close to the real mathematics of the problem (as the paper’s Appendix goes into detail to show). However, I have some reservations, both about the paper as a whole and about the core analogy.
In general, Maldacena doesn’t do a very good job of writing something publicly accessible. There’s a lot of stilted, academic language, and a lot of use of “we” to do things other than lead the reader through a thought experiment. There’s also a sprinkling of terms that I don’t think the average person will understand; for example, I doubt the average college student knows flux as anything other than a zany card game.
Regarding the analogy itself, I think Maldacena has fallen into the common physicist trap of making an analogy that explains things really well…if you already know the math.
This is a problem I see pretty frequently. I keep picking on this article, and I apologize for doing so, but it’s got a great example of this when it describes supersymmetry as involving “a whole new class of number that can be thought of as the square roots of zero”. That’s a really great analogy…if you’re a student learning about the math behind supersymmetry. If you’re not, it doesn’t tell you anything about what supersymmetry does, or how it works, or why anyone might study it. It relates something unfamiliar to something unfamiliar.
I’m worried that Maldacena is doing that in this paper. His setup is mathematically rigorous, but doesn’t say much about the why of things: why do physicists use something like this economic model to understand these forces? How does this lead to what we observe around us in the real world? What’s actually going on, physically? What do particles have to do with dimensionless constants? (If you’re curious about that last one, I like to think I have a good explanation here.)
It’s not that Maldacena ignores these questions, he definitely puts effort into answering them. The problem is that his analogy itself doesn’t really address them. They’re the trickiest part, the part that people need help picturing and framing, the part that would benefit the most from a good analogy. Instead, the core imagery of the piece is wasted on details that don’t really do much for a non-expert.
Maybe I’m wrong about this, and I welcome comments from non-physicists. Do you feel like Maldacena’s account gives you a satisfying idea of what gauge symmetry is?