# Pendulum Waves and the Beginnings of Quantum Physics

It may not be the “most beautiful video ever”, but it’s quite pleasing nevertheless. I find it fascinating that there is an illusion of connection between the pendulums: they are swinging independently of each other, so the oscillation of one isn’t affecting any of the others, but they still appear to be in tandem.

I titled this blog “Galileo’s Pendulum” partly so I could use the phrase I thought of (“the pendulum is mightier than the sword”), but also in reference to Galileo’s importance in the history of science. However, I never really have drawn attention to the name of the blog in a post or explained what “Galileo’s pendulum” is all about, so this seems as good an opportunity as any. Galileo found that the amount of time a pendulum takes to swing — its period of oscillation — is related to its length. A short pendulum has a short period, while a long pendulum will take a much greater amount of time to complete a single swing.

In this video, the pendulums are all of different lengths, running from short to long, though note the lengths don’t increase in a straight-line fashion — there’s a subtle curve if you look at the position of the pendulum bobs early in the video. The pendulums begin together, but because they have different periods of oscillation, they quickly fall out of sync — but because of the specific relationship between the lengths of the pendulum strings, they create fascinating wave patterns.

Beyond Galileo, independent oscillators like this actually play a very important role in the history of physics. Specifically, Max Planck found he could explain thermal radiation by assuming light comes in bundles of energy we now call photons; Albert Einstein extended this idea by treating every atom in a material as — you guessed it — an independent oscillator! Even though each pendulum in the video is acting independently, their collective behavior results in waves; even though each atom in Einstein’s model of a solid is vibrating independently, their collective behavior gives rise to the distinctive spectrum of stars. Galileo’s pendulum led, via a long and winding road, to the beginnings of quantum mechanics and our modern understanding of materials. We can see hints of this even in this simple video, so maybe it’s the most beautiful video ever after all.

### 7 responses to “Pendulum Waves and the Beginnings of Quantum Physics”

1. […] Pendulum Waves and the Beginnings of Quantum Mechanics: how that cool pendulum-wave video that has been making the rounds connects to photons. […]

2. […] version of quantum mechanics (the type most people have heard about, and the type I’ve written about most) uses the same time. However, it’s important to remember that the non-relativistic version of […]

3. […] Here’s what I had to say about it at the time. To summarize, I pointed out that the patterns we see are emergent, based on the relative lengths of the pendulum strings. They aren’t interacting with each other, but the fact that the lengths of the strings are mathematically related to each other creates the beautiful waveforms. In other words, despite there being no direct interaction, there is a kind of indirect relationship that is intriguing. A similar insight led Max Planck and Albert Einstein to the beginnings of quantum mechanics; in this post, I’ll start from a modern understanding of quantum oscillators and work backwards to show how these pendulum waves connect to all sorts of interesting phenomena. Two equivalent positions for the nitrogen atom (labeled N) in an ammonia molecule. The hydrogen atoms (marked H) are in the same places in both images. […]

4. Thanks! This really helped me complete my homework. We did a similar test, that resulted in the same way. This website has great, educational information. Maybe you could make some posts more ‘kid friendly?’, just a suggestion. Thanks again! :)

1. I’m glad you found my page useful! What kind of assignment was it?

I wouldn’t mind making some more kid-friendly content; what kinds of subjects are you interested in?

5. […] earlier blog posts, I’ve discussed how unconnected oscillators can appear to link up, creating patterns and giving rise to phenomena such as lasers and the spectra of stars. […]

6. This was a great page I stumbled upon! Thanks for the information, it was very nicely put.