You may recall Ian Randall’s recent cryptic word search on the theme of quantum physics. As a scanning tunnelling microscopist, I particularly liked the clue “Ill gent, nun in a bad way? It’s barrier breaking (10)”. Sticking with the cryptic quantum theme, I’m now going to consider something else that’s hidden – this time in a piece of music I’ve composed as the soundtrack for Physics World (click the play button above to listen).

It’s a dimensionless constant – a “plain, beautiful number” as my colleague Laurence Eaves  once memorably described it. It fascinated and infuriated Wolfgang Pauli, who loved its physical significance and its apparent mystical ramifications (surprising given his famously caustic and cynical demeanour). Richard Feynman, as his wont, dubbed it “one of the greatest mysteries of physics – a magic number that comes to us with no understanding”.

I’m talking about 137, also known as “alpha” or the inverse of the fine structure constant. Pauli was so obsessed with 137 that he’d say, when he died, his first question to the Devil would be: “What is the meaning of the fine structure constant?” In a staggering coincidence, that terminal moment came in room number 137 of the hospital in which he was being treated for pancreatic cancer.

If you’re wondering why Pauli believed that 137, rather than 42, was the answer to life, the universe and everything, the historian Arthur Miller has written an entire book on the subject. Entitled 137: Jung, Pauli, and the Pursuit of a Scientific Obsession, it explores how psychoanalysis helped Pauli to understand his creative powers and cope with life. Be warned: the numerology and woo quotients are off the scale.

A beautiful number

So when I was recently asked if I’d like to write a physics-inspired jingle and theme tune for the Physics World podcast, that “plain, beautiful” number immediately sprang to mind. What better constant to encode in the notes, chords and arpeggios of a physics jingle than the number that has driven so many physicists to distraction since Arnold Sommerfeld originally introduced it in the 1920s?

It’s not the first time I’ve dabbled with fundamental constants as the basis of musical riffs and rhythms. As I described last year in “Shreddinger’s equation”, I once created a musical mashup of quantum physics and heavy metal. But this time I decided to forego my natural inclination to turn everything up to 11 (and beyond) and instead write a piece of music – 137 – inspired by synthpop music from the 1980s, the decade in which Physics World was born.

Just over four minutes long, at the musical core of 137 is a very simple arpeggiated chord comprising the notes D, F and C. These are the first, third and seventh notes, respectively, of a C natural minor scale, if we assign C to the number 0. (Technically, and for those versed in music theory, it’s a D Locrian mode if we use the more conventional approach and label the first note in a scale/mode as 1.)

Throughout the piece, the 137 motif appears repeatedly on different instruments. Although the primary instrument is the synthesizer, what appear to be synth sounds in 137 are sometimes instead heavily effected guitar harmonics. It’s a nod, if you like, to the standing wave resonances of the quantum-particle-in-a-box model so beloved of undergraduate physicists. Talking of which, the “whooshing” sound – at around 13 seconds in – is the evolution of a superposition state in an infinite potential well converted to sound.

Heavenly connections

Other incidences of 137 come in the drum pattern that appears for the first time at around 00:45, the tempo of the piece (137 beats per minute, naturally) and the fade-out at the end, which is a heavily processed bass guitar playing natural harmonics that follow the 1-3-7 pattern. I’m a big science-fiction fan and was keen for this to sound like a cryptic encoded message from an alien civilization.

Another sci-fi-inspired effect is the Shepard scale starting at 02:30 – the steadily rising pitch that seemingly never stops rising, extensively exploited by composer Hans Zimmer in his score for the 2014 movie Interstellar. I discuss just how this intriguing audio illusion works in the context of 137 in the May episode of the Physics World Stories podcast, which was the official premiere of the new music.

Of course, pedants will point out that the fine structure constant isn’t exactly the inverse of 137. They’re right. So I’ll let Pauli have the last word. In a joke I once saw posted by the US physicist Chad Orzel, Pauli’s died and gone to heaven where he asks God why the fine structure constant is only roughly equal to 1/137? “Ah, I’m glad you asked that,” God replies, creating a blackboard and writing equations to derive it.

After about 10 minutes, Pauli says “Oh, THERE’S Your mistake!”

• Find out more about the new Physics World podcast theme tune in the May 2024 edition of the Physics World Stories podcast, where Philip Moriarty talks to host Andrew Glester.