Motion Captured: Grokking

July 1, 2015


This series has been a grab bag of nice results in physics that can be illustrated with relatively simple animations (or cat videos). There was no particular theme intended and the list of topics was generated completely by my interests and ability to write short(ish) javascript code. Nevertheless I will pretend that I am much more methodical than I really am and try to provide some kind of unifying philosophy for the series.

There was a competition in 1993 to produce a one page explanation of what the Higgs boson is and why politicians should care. You can see the winning entries here. I like the cocktail party one myself. A famous person, perhaps the director of a prestigious Danish research institute, arrives at a cocktail party. Due to his fame and intense personal magnetism he attracts a large group of admirers who crowd around and slow him down. The crowd here is supposed to be analogous to the Higgs field and the famous scientist is an electron. Now imagine not the man himself but a rumour of his arrival. The initiator of the rumour gathers listeners that cluster around him, those listeners pass it on themselves creating more clusters as they spread it. Here the rumour is the Higgs boson.

The concept of ‘spontaneous symmetry breaking’ is crucial to understanding the Higgs. The analogies that help you understand this are about balls perched on sombreros, hot magnets or pencils balanced on their tips. An unstable pencil is equally likely to fall down in any direction but it must choose only one and thus ‘break the symmetry’. Likewise the ball rolls down the hat in some direction and the magnetic field ends up pointing a particular way. An arbitrary direction is chosen out of an infinity of possible ones. The mathematics of quantum field theory and group theory have to be our ultimate guides in the subatomic world but the analogies still remain useful for our emotional understanding of symmetry breaking. There is a nice word for this: “grok” – to understand something completely and intuitively.

If you want to be a particle physicist you should know how to do accurate calculations. I was told by a lecturer once “Rudy, if the secret police shake you awake in the middle of the night you must be able to calculate the one loop Higgs mass correction”. But you should also develop some ‘physical intuition’. This is an idea about how the results of a calculation will go, or should go, without necessarily doing it. We can even develop physical intuition about systems that are physically impossible to experience, a famous example being the Feynman diagram. You have probably seen the little doodles covering the blackboards at CP3. These drawings are indispensable not only for calculating what happens in particle collision experiments but also as the visual language that is used to discuss particle physics. It’s much easier to draw a squiggle on the blackboard and puzzle about it than it is to stare at the equivalent multi-dimensional integral. Feynman diagrams help you to grok quantum field theory and understand what subatomic particles are really doing.

Computers are definitely indispensable for calculation but are still underused when it comes to gaining a deeper conceptual understanding. But compared to blackboard drawings computer animations have an extra, easily comprehensible dimension: time. Have a look at this animation. There is a field (the dots) in a special potential (the springs) which, as I explain there, allows spontaneous symmetry breaking to occur. You start almost at equilibrium (by pressing the random button) and then watch it go. The red dots clump in just the same way as at the cocktail party. Similarly I can tell you all about sensitive dependence on initial conditions or you can try playing with a double pendulum yourself, without worrying about air resistance, strings and wobbling out of the plane. The theory of critical phenomena and phase transitions is beautiful and you can see what ‘structure on all scales’ means without scalding yourself by staring into your kettle. The central limit theorem is crucial to much of science and you can learn to trust it by watching a ball randomly bounce off pegs.

If nothing else I hope these animations have helped you to understand an idea or two a little better. Perhaps they can act as a bridge for your intuition, between hand-waving explanations about cocktail parties on one side and formal mathematics on the other. Perhaps a time evolving Feynman diagram will be useful as you create some future theory of physics. Perhaps they will inspire you to make your own animations. There’s something very satisfying about seeing code you wrote from scratch create a beautiful picture or move in ways you didn’t imagine.

I started these short articles last year as a physicist in Denmark, posted them from exotic locales like Bali and Brighton and I now find myself a biologist in England. Not to exclude the possibility of ever making another one, but most of my time nowadays is spent thinking about DNA, so the pace of posting will slow dramatically. You might occasionally find something nice here. In the mean time, don’t spend too long playing Tetris (s and d to rotate, p pauses and unpauses, arrow keys to move, down to slam, click the left pane to start or restart, try clicking the ‘Fixed’ box…).