Music Theory and Quantum Mechanics

Note trans. : This is another translation of an article from Ethan Hein's blog (Ethan is an associate professor of 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, for example, can offer. His other materials in our translation can be found here: 1 (on the techniques of visualizing music), 2 (on the basics of converting analog sound to digital).

In high school, you probably saw a similar picture:
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This figure shows a stylized nucleus with red protons and blue neutrons, surrounded by three gray electrons. This pretty standard picture. It can make a good logo. Unfortunately, it is absolutely wrong. Subatomic particles are to a certain extent similar to small glass balls, but the degree of this similarity is extremely small. The electrons really move around the nucleus, but the movement does not occur along an elliptical path, 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 is much easier to do.

Quantum particles are waves

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

Protons and electrons are attracted to each other as a magnet is attracted to the refrigerator. If electrons really looked like small satellites moving around a planet, they could rotate at any distance from the nucleus and could easily fall into the nucleus and collide with protons. But this is not happening. 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 displayed in a random order on the screen. Try to imagine this “static” around the nucleus of the atom, and you will get a much better picture of what is happening than give images with satellites orbiting around the planets.

When electrons are in orbit around an atom or molecule, their pattern of motion is not accidental, unlike white noise on a TV screen. When electrons move along an orbit of atoms, their energy fields are organized into a structure similar to rolling ripples. You can explore this pattern with the help of the interactive visualization of the subatomic world from Paul Falsted - look for the hydrogen atom simulator at the end of the “Quantum Mechanics” section.

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 . Electron harmonics have three dimensions in contrast to one-dimensional harmonics of strings, but they are based on the same principle. These harmonics determine the structure and interaction of the electron wave, just as the harmonics of the string form the basis of chords and scales. The harmonics of the electron field are called orbitals .

The whole physical world consists of electron harmonics.

This screenshot of the Felsted quantum harmonic oscillation applet shows the first harmonic of the electron field around the H2 molecule, two hydrogen atoms, each of which consists of one proton and one electron. This is the “electronic” equivalent of the harmonic of a guitar string on the 12th fret. The blue drop indicates the position of one electron, the red drop indicates the position of another electron. At higher energy levels, orbitals take on more complex forms. This is a direct analogy of more complex musical intervals, which can be obtained from the higher harmonics of the 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 atomic orbitals interact. If the most distant cells are unoccupied, they can be filled with electrons from other atoms, linking the atoms into molecules. All liquid and solid materials retain their structure due to the exchange of electrons between orbitals.

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



This six-sided structure of ice appears because of how the oxygen and hydrogen orbitals line up. You can observe how this hexagon structure is repeated at the macro level in the form of snowflakes and hoarfrost.

If you heat the ice to the melting point, you essentially photons the surface of the ice, knocking electrons out of the orbitals so that they can move more freely from atom to atom. Atoms continue to remain connected, but not so rigidly, and the structure of their connection becomes less “strict”.



If you continue the process of photon “shelling,” then completely break the bonds between the molecules, which will begin to freely and independently move in the state we call steam. If you fire pairs of photons, then break the molecules, thereby separating the electrons from the nucleus in the form of a plasma. An even greater energy pulse 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, atomic nuclei and molecules are vibrating energy fields, each of which has its own specific wave form and harmonic.

When I get bored, I like to imagine that everything around me, all matter and energy, are resonating energy fields that form consonances just as sounds add up to chords. Who said science can't be fun?

Learning through music

Albert Einstein told reporters that he often "talks in terms of musical architecture." Einstein was a keen violin lover and stood at the foundations of quantum mechanics. Perhaps these two facts are related.

Did Einstein draw obvious 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 used to say that we should not even try to visualize the true nature of electrons. She was right that she did not try to humiliate herself to primitive explanations or to lead us on the wrong path, but she gave up too soon. She didn’t 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, first of all I will try to make sure that they come across in practice with musical harmonics. I would show them that to play higher harmonics requires more energy, and how these higher harmonics allow you to create a richer musical palette. And if then we return to chemistry, then children will understand it much easier.