Music Theory and Quantum Mechanics

Note perev. : This is another translation of an article from Ethan Hein's blog (Ethan is an associate professor in music technology at the University of New York). In this article, he reflects on the connection between the theory of music and quantum mechanics and proves that the traditional graphic visualization of the microworld is in many ways inferior to the analogies that a guitarist or violinist can offer. Read his other materials in our translation here: 1 (on techniques for visualizing music), 2 (on the basics of converting analog sound to digital).

In high school, you probably saw a similar picture:

This figure depicts a stylized nucleus with red protons and blue neutrons, surrounded by three gray electrons. This is a nice standard picture. It can make a good logo. Unfortunately, she is absolutely wrong. Subatomic particles are somewhat similar to small glass balls, but the degree of this similarity is extremely small. Electrons really move around the nucleus, but this movement does not follow an elliptical trajectory, as if they were small satellites orbiting around a planet. The true nature of electrons in an atom is much more unusual and interesting. And images can hardly convey the essence of quantum particles. Using music theory, this is much easier.

Quantum particles are waves

The problem with pictures in textbooks like the image above is that because of them, you begin to perceive particles as “things.” But they are not things. They appear and disappear, like fast flashes - this is more like our ideas about energy. What we call “particles” are actually clots of energy fields.

Protons and electrons are attracted to each other as a magnet is attracted to the refrigerator. If the electrons really looked like small satellites moving around the planet, they could rotate at any distance from the nucleus and could easily fall into the nucleus and collide with protons. But this does not happen. Electrons always self-organize into extremely specific spatial structures around the nucleus. This fact seemed a mystery until scientists began to consider electrons as probabilistic waves in an energy field.

A good analogue of how particles actually behave is television white noise, which consists of a huge number of electrons that are randomly displayed on the screen. Try to imagine this “statics” around the nucleus of an atom, and you will get a much better picture of what is happening than images from satellites orbiting planets give.

When electrons are in orbit around an atom or molecule, their pattern of movement is not random, unlike white noise on a TV screen. When electrons move in the orbit of atoms, their energy fields are organized into a structure similar to rolling ripples. You can study this pattern using interactive visualization of the subatomic world by Paul Falstead - look for the simulator at the end of the “Quantum Mechanics” sectionhydrogen atom.

But what does all this have to do with music theory? The vibrations of the electron field around the atom act like harmonic vibrations. Electrons have harmonics, just like guitar strings . Harmonics of electrons have three dimensions, in contrast to the one-dimensional harmonics of strings, but they are based on the same principle. These harmonics determine the structure and interactions of the electronic wave, just like the harmonics of the string form the basis of chords and scales. Harmonics of the electron field are called orbitals .

The whole physical world consists of harmonics of electrons

This screenshot applet for quantum harmonic oscillations Felsteda shows a first harmonic of the electronic field around the molecule H2, two hydrogen atoms, each of which is composed of one proton and one electron. This is the “electronic” equivalent of the harmonic of a guitar string at the 12th fret. A blue drop indicates the position of one electron, a red drop indicates the position of another electron. At higher energy levels, the orbitals take on more complex forms. This is a direct analogy to more complex musical intervals that can be obtained from the higher harmonics of a guitar string.

Orbitals can be represented as a system of small cells, each of which can occupy only one electron. These cells are split in pairs, and the electrons "prefer" to live in neighboring cells. The structure of all objects and chemical elements is determined by how the external orbitals of atoms interact. If the most distant cells are unoccupied, they can be filled with electrons of other atoms, linking atoms into molecules. All liquid and solid materials retain their structure due to the exchange of electrons between orbitals.

The molecular structure of ice created by Masakatsu Matsumoto is shown below . Red balls are oxygen atoms. Blue ones are hydrogen atoms. Yellow rods are bonds - they are created by electrons that exchange the most distant orbitals of oxygen and hydrogen atoms.



This hexagonal ice structure appears due to the way the oxygen and hydrogen orbitals line up. You can observe how this hexagonal structure repeats at the macro level in the form of snowflakes and hoarfrost.

If you heat the ice to its melting point, you essentially bombard the ice surface with photons, knocking electrons out of the orbitals so that they can move more freely from atom to atom. Atoms continue to be bound, but not so rigidly, and the structure of their connection becomes less "strict".



If you continue the process of photon “shelling”, you will completely break the bonds between the molecules, which will begin to move freely and independently in a state that we call vapor. If you bombard steam with photons, you will break the molecules, thereby separating the electrons from the nucleus in the form of a plasma. An even larger energy impulse will break the nucleus into protons and neutrons, and the protons and neutrons themselves will split into components: upper and lower quarks. Quarks, protons, neutrons, nuclei of atoms and molecules are vibrating energy fields, each of which has its own special waveform and harmonic.

When I get bored, I like to imagine that everything around me, all matter and energy are resonant energy fields that form harmonies like sounds add up to chords. Who says science cannot be fun?

Learning through music

Albert Einstein told reporters that he often "reasoned in terms of musical architecture." Einstein was an enthusiastic violin player and stood at the foundation of quantum mechanics. Perhaps these two facts are related.

Did Einstein draw explicit parallels between musical and quantum harmonics? We probably will never know about this, but such a connection exists, and future scientists will be able to benefit from it. The concept of electronic orbitals is still not fully developed. When I was in high school, my (beautiful) chemistry teacher said that we should not even try to visualize the true nature of electrons. She was right that she did not try to humiliate herself with primitive explanations or lead us on the wrong path, but she gave up too soon. True, she did not have the opportunity to use powerful interactive computer visualization, but our school had an excellent music class. If I ever have the opportunity to teach children chemistry, I will first try to make sure that in practice they came across musical harmonics. I would show them that to reproduce higher harmonics requires more energy, and how these higher harmonics can create a richer musical palette. And if later we return to chemistry, then it will become much easier for children to understand it.