How music is like the north pole of Saturn

Astronomers discovered this humungous hexagonal cloud pattern on the north pole of Saturn. Their best guess is that it's a standing wave in the planet's weather. Judge for yourself - it might be a couple seconds before the animation loads:

The atmosphere blows around and around, but the pattern stays the same, like an eddy in a river. A standing wave 'stays still' even if the medium is moving. The wave isn't a 'thing' so much as a pattern of interactions of things. When waves moving in opposite directions meet each other, some waves cancel each other; others reinforce each other. This is what the physicists call 'wave interference', even where the waves are reinforced and not canceled. Standing waves don't have to go around in a circle. Waves travelling along a string or air column reflect back when they reach an end. Standing waves in vibrating strings or columns of air settle into the harmonic series, which we hear as musical tones.

Much of what follows draws on the resonance section of Rod Nave's invaluable Hyperphysics site. Resonance is self-organizing. When you first pluck a guitar string, it begins to vibrate in a tumbling complexity of different modes. But the guitar has been careful designed to 'want' to vibrate at its resonant frequencies, and the nonmusical vibrations swiftly die out, while the musical ones reinforce themselves.

All m atter and energy behave in some ways like standing waves at the ultra-tiny scale. Science textbooks usually show subatomic particles as little marbles, a good enough approximation in some ways but fundamentally misleading. There's something vibrational and musical happening at the quarks and gluons level, something the physicists have been circling around since Einstein. All subatomic particles, and even entire atoms, have wavelike qualities. The mathematical techniques that quantum physicists use to understand the vibrations of protons and neutrons are largely the same ones that describe guitar strings. It came as no surprise to me that Einstein was an enthusiastic amateur musician.

A standing wave isn't a 'thing'. It's the emergent result of many things interacting. Some physicists think that space itself may not be a 'thing' either, that it's the emergent result of many small discrete interactions. From Lee Smolin's book Three Roads To Quantum Gravity:

[O]ur world cannot be understood as a collection of independent entities living in a fixed, static background of space and time. Instead, it is a network of relationships, the properties of every part of which are determined by its relationships to the other parts ... [T]he relations that make up the world are causal relations. This means that the world is not made of stuff, but of processes by which things happen. Elementary particles are not static objects just sitting there, but processes carrying little bits of information between events at which they interact, giving rise to new processes. They are much more like the elementary operations in a computer than the traditional picture of an eternal atom.

Look around and imagine that you see each object as a consequence of photons having just travelled from it to you. Each object you see is the result of a process by which information travelled to you in the shape of a collection of photons. The farther away the object is, the longer it took the photons to travel to you. So when you look around you do not see space - instead, you are looking back through the history of the universe. What you are seeing is a slice through the history of the world. Everything you see is a bit of information brought to you by a process which is a small part of that history.

The whole history of the world is then nothing but the story of huge numbers of these processes, whose relationships are continually evolving. We cannot understand the world we see around us as something static. We must see it as something created, and under continual recreation, by an enormous number of processes acting together.

Music is the same way. It's an algorithm for producing vibrations detectable by the human body and thereby affecting changes to our emotional state. No human bodies, no music, at least not of the human variety.

Smolin's book The Trouble With Physics includes a chapter entitled Surprises From The Real World. One such surprise is the cosmic background radiation. Space was extremely hot after the big bang, and while it's cooled off substantially since then, there's still a very faint glow left over, the cosmic background radiation. This radiation is almost perfectly uniform, but it fluctuates at the level of a few parts in a hundred thousand. Think of these ripples as sound waves echoing from the violent birth of the universe. Smolin interprets the peaks and valleys in the cosmic background angular power spectrum graph thus:

The matter filling the early universe was resonant, like the head of a drum or the body of a flute... The wavelengths of the resonant modes tell us how big the universe was when it first became transparent: that is, when the initial hot plasma devolved, or 'decoupled', into separate realms of matter and energy three hundred thousand years after the big bang.

The vibration of a guitar string is built up of harmonics. The fundamental note is produced by the string's vibration along its entire length. The first harmonic is the same pitch an octave higher, produced by the string's vibration in halves. The second harmonic, a fifth above the first, comes from the string's vibrations in thirds. There are progressively higher and quieter harmonics from the string's vibrations in quarters, fifths, sixths, sevenths, and so on. Here's the fifth harmonic of a vibrating string, the component of its vibration that divides the string into six equal parts.

I learned this fact because it provides a handy way to tune a guitar. It was a delightful surprise to discover that the concept extends deep into modern physics as well.

String harmonics are linear vibrations. Surfaces can vibrate too; think of drum heads and speaker cones. Here are vibrational modes of a 2D quantum field inside an infinite cylinder:

Imagine the drumhead or speaker cone to be vibrating along many such modes simultaneously. The sound you hear is the sum total of all the different harmonics. Similar wave mechanics happen in three dimensions too, and in higher dimensions too for all I know.

Harmonics are a great way to think about the energy states of particles in quantum physics. String theorists make the analogy literal, arguing that all properties of subatomic particles arise from the vibrational modes of fundamental vibrating strings of energy. Waves, oscillations, self-organizing cycles - once you're looking for them, you see them everywhere. It's too bad we as a society don't value participation in music more highly, we miss out on the most fun way to learn a lot of really difficult concepts.

© ethan hein 2007 | back to memebase | back to top