So, before I start I have a confession to make (this thing does feel like a confessional, doesn’t it?). I am one of the mysterious (former?) friends who tempted David into this misadventure, only to get cold feet at the last minute. I guess that after participating in many discussions on blogs, I still don’t have a clear idea what they are good for, but there is definitely a potential… So, I’ll start with the occasional post and we shall see where it goes.
Continuing my confession, I started teaching again this last week. This semester I am teaching a course introducing quantum field theory to beginning graduate students. I see the world (OK, my tiny little world) as being divided into two kinds of people. There are those who think quantum mechanics, the kind that deals with particles like electrons and their wavefunctions, is our fundamental description of the world. Then there are those who know better…So, my aim is to convert as many people as possible to view quantum fields as the fundamental entity of our (current description of) nature, and everything else as a derived concept. Along the way I am hoping to disabuse students of such confusing notions as relativistic quantum mechanics and second quantization…So, you see, I have my hands full, how can I possibly afford the time to blog?
The history of fields is fascinating, I’d really like to know more about that history. One way to think about them is as a device to restore locality to our description of the world, one that includes long-range forces such as the gravitational pull between the sun and the earth. It is counter-intuitive to think about the sun acting on the earth from so far away, we are used to being skeptical about such non-local effects (think about bending spoons across the room, without touching them). So, to feel more comfortable we can invent an intermediate medium which exists everywhere, and call it the gravitational field. The story goes then as follows: the sun distorts the medium, the distortion is felt everywhere, in particular we feel that distortion as a gravitational pull. So, everyone is happy, sanity is restored to our worldview, and most importantly we don’t have to take Uri Geller too seriously.
Except now we have a new entity, an infinitely complicated object, something like an elastic medium existing everywhere around us. It can do what we want- avoid thinking about action at a distance- but it can do so many other things, it is infinitely more intersting than just good old pointlike particles…So, when we consider exciting fields in all kinds of interesting ways, they really come into their own. We can have travelling waves propagating across space, they can have different profiles, we can even localize them, so they look like localized bundles of energy moving around, bouncing off each other like billiard balls.
Kind of like particles, actually, makes you wonder about those particles…