Quantum Physics


Quantum Harmonies: Modern Physics and Music

The universe is built on harmonies. The Pythagoreans had it right when they married mathematics, music, and the cosmos. Just as mathematical patterns underlie the musical scales and intervals most pleasing to the ear, they also describe the probability waves at the heart of quantum theory.

More than 2500 years ago, according to ancient sources, Pythagoras applied his discoveries in music theory to the behavior of the celestial objects. Pluck a string, and the pitch of the note it produces is related to the length of the string. When the lengths of two strings are a simple ratio—1/2, 2/3, and so on—the notes together sound harmonious. Pythagoras believed that the universe itself hummed with its own harmony—beautiful, divine, and inaudible to human ears. He characterized the intervals between successive orbits, such as those of Mercury and Venus, as either tones or half-tones (the smallest intervals in the musical scale), adding up to seven whole tones that form a perfectly harmonious natural order.

When the French physicist Louis de Broglie proposed the wave nature of electrons and other matter particles, he may very well have had musical harmonics in mind. De Broglie showed how the different energy levels of Niels Bohr’s atomic model emerged naturally by describing electrons as standing waves of various frequencies, thereby generalizing the wave theory of light to material particles. Just as a guitar string can be plucked in certain ways to produce particular sounds, electrons in de Broglie’s scheme are forced to oscillate in particular patterns, corresponding to certain frequencies and energy levels.

Image: Flickr user Matt M., adapted under a Creative Commons license.

Austrian physicist Erwin Schrödinger developed de Broglie’s idea further with his famous wave equation, yielding three-dimensional pulsations known as spherical harmonics. Spherical harmonics differ from standing wave patterns because they describe a wider assortment of shapes—spheres, barbells, and so forth—that offer a richer description of electron behavior.

However, as shown by German physicist Max Born, it is not the electrons themselves that display wave patterns, as de Broglie and Schrödinger believed, but rather the probability distributions indicating, for example, their likeliest positions. While neither Schrödinger nor Einstein were comfortable with Born’s statistical interpretation, it has persisted as the standard view.

Superstring theory, a hypothetical attempt to unite the fundamental forces—the gravitational, electroweak and strong forces—applies the idea of harmonics on a far smaller scale than atomic physics, on the order of the Planck length, about 10-35 meters (compared to about 10-10 meters for atoms). It replaces point particles with vibrating strands of energy. Various modes of vibration determine the particles’ properties, explaining the diversity of the particle zoo through the complexity of the oscillations and the geometry of the higher-dimensional space in which they are embedded.

So if physicists are tuned in to the music of the universe, are musicians returning the favor? Tears for Fears singer, songwriter, and guitarist Roland Orzabal was inspired to take on the philosophical conundrums of quantum mechanics in the early 1990s, when he began to devour popular science books.

“I became fascinated with where science was headed and all the reality-challenging concepts it was throwing up,” recalled Orzabal. “Wonderful thought experiments such as Schrödinger’s Cat have an almost poetic, visual quality to them, which, as a songwriter, I found inspirational, so much so that I managed to play with the concept in a song of the same name.”

Orzabal was also inspired by Einstein’s famous dismissal of the randomness of quantum mechanics. “’God does not play dice’ is a gift to any songwriter,” said Orzabal, and it inspired a second science-themed song, “God’s Mistake”—though to Orzabal, that mistake is the unpredictable outcome of love, not of a physics experiment.

Max Born also embraced the uncertainty at the heart of quantum physics. “I cannot understand how you can combine an entirely mechanistic universe with the freedom of the ethical individual,” Born wrote to Einstein. “To me a deterministic world is quite abhorrent—this is a primary feeling.” Probabilistic quantum mechanics, Orzabal suggests in verse and Born in his letter, doesn’t seem unnatural in the face of a world in which passion and conflict are unforeseeable as well. On the contrary, Einstein’s clockwork ideal appears out of step with tumultuous reality.

Orzabal writes for concert halls, not classrooms; he’s wrestling with the fundamental nature of the universe in the way that comes most naturally to him—music. But other musicians use their art as a science teaching tool. Haverford physicist Walter Smith, who maintains a library of musical physics parodies on his excellent webpage PhysicsSongs.org, points out the educational value of songs related to physics. “Songs about physics can help students to remember critical concepts and formulas, but perhaps more importantly they communicate the lesson that physics can be fun,” says Smith. From satirist Tom Lehrer’s rapid-fire rundown of the periodic table to the celebrated physicist James Clerk Maxwell’s somewhat less celebrated forays into song, physics and music have a long and lively friendship.

Even CERN’s Large Hadron Collider has gotten into the game. In 2008, most non-scientists knew very little about the LHC, except perhaps the irrational misconception that it might create a miniature black hole that would gobble up the Earth. Enter CERN physicist Kate McAlpine, who wrote and performed the “Large Hadron Rap,” a musical rundown of potential LHC discoveries.

“Particle physics is quite esoteric to most people, so I wanted to write lyrics that might give a basic understanding of what this big, expensive machine was for and why it was so exciting,” said McAlpine. “Rhyme is a great memory aid, so if you can get the words and rhythm to stick, understanding can follow even it doesn’t come right away. Many teachers and parents have been in touch to request rap videos for use in classes or tell me how much their children love the ‘Large Hadron Rap.’ I think the biggest thing that the ‘Large Hadron Rap’ might have done among young people is put science on their radar as something other than dissecting animals, mixing things in beakers, and rolling balls down inclined planes.” To date, the video has been watched more than 7.7 million times.

When science and current events cross paths, they may become the subject of folk music. My favorite example is Christine Lavin’s history of Pluto’s planetary status set to verse, entitled “Planet X.”

As Lavin recounted, “’Planet X’ was inspired by an article in USA Today about Pluto’s planetary status. Halfway through the article I knew there was a song inside the story bustin’ to get loose!”

Music resonates, it pulses, it leaps into our psyches. It offers a safe space for scientists and musicians alike to work through the paradoxes of modern physics, and it can be the spoonful of sugar that helps students learn—and enjoy—physics. Thousands of years after the age of Pythagoras, physicists are still discovering the harmonies of the universe.

Thanks so much to Roland Orzabal, Kate McAlpine, and Christine Lavin for their thoughtful comments. I have linked to more science-themed music videos on Twitter under the hashtag #ScienceSongSaturday.

Go Deeper
Editor’s picks for further reading

Pythagoras: His Life and Times
Discover Pythagoras in this in this 2010 reissue of Thomas Stanley’s 1687 classical survey.

Michigan Technological University: Physics of Music
Physicist B. H. Suits on the physics principles behind musical scales, instruments, and more.

NUVO: Quantum theory and classical music
Ontario-based conductor Edwin Outwater on the historical parallels between classical music and quantum theory.

Tell us what you think on Twitter, Facebook, or email.


Paul Halpern

    Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. A prolific author, he has written thirteen science books, including "Einstein's Dice and Schrödinger’s Cat: How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics" (Basic Books). His interests range from space, time and higher dimensions to cultural aspects of science. The recipient of a Guggenheim Fellowship, Fulbright Scholarship, and an Athenaeum Literary Award, he has appeared on the History Channel, the Discovery Channel, the PBS series "Future Quest," and "The Simpsons 20th Anniversary Special." Halpern's books include "Time Journeys," "Cosmic Wormholes," "The Cyclical Serpent," "Faraway Worlds," "The Great Beyond," "Brave New Universe," "What's Science Ever Done for Us?," "Collider," and most recently "Edge of the Universe: A Voyage to the Cosmic Horizon and Beyond" (Wiley 2012). More information about his writings can be found at phalpern.com.

    • SERAPH1212

      That Gravity is EXACTLY as described by Einstein, but not fully understood by him, is simply Refraction of the Wave Function of a ‘particle’ by adjacent Mass. Also collaborated by Lensing effect of Photons passing great mass. Photons being ‘open’ waves as different to the ‘closed’ waves of a ‘particle’. To equate to Einstein’s definition of Gravity, simply put, ‘Time dilation across the wave’ either ‘open’ or ‘closed’.

    • mpc755

      Aether has mass. Aether physically occupies three dimensional space. Aether is physically displaced by the particles of matter which exist in it and move through it.

      The Milky Way’s halo is not a clump of dark matter traveling along with the Milky Way. The Milky Way is moving through and displacing the aether.

      The Milky Way’s halo is the state of displacement of the aether. The Milky Way’s halo is the deformation of spacetime.

      A moving particle has an associated aether displacement wave. In a double slit experiment the particle travels through a single slit and the associated wave in the aether passes through both.

      In a double slit experiment it is the aether that waves.

      • N8
        • mpc755

          The Michelson-Morley experiment looked for an absolutely stationary space the Earth moves through. The aether is not an absolutely stationary space. The aether is displaced by the particles of matter which exist in it and move through it.

          What is referred to as deformed spacetime is the state of displacement of the aether.

      • Len Goforth

        A halo is reflection of light bouncing off of particles. This does not necessarily mean that a halo is a deformation. Perhaps it is a formation, and it is deformed by spacetime.No matter however, because there are equations that pr5ove both are possible, and possible simultaneously.

        • mpc755

          The Milky Way’s halo is not light bouncing off of particles. The Milky Way’s halo is the state of displacement of the aether.

          ‘Milky Way’s halo more squished than spherical’

          “The Milky Way may look like a giant spiral in space, but in the world of invisible dark matter our galaxy is shaped like a giant, flattened beach ball, a new study has found.”

          The aether displaced by the matter the Milky Way consists of is pushing back and exerting inward pressure toward the Milky Way. This causes the spiral arms to be pushed toward the center of the Milky Way which causes the state of displacement of the aether to be in the form of a squished beach ball.

    • Todd

      Einstein also said that learning how the universe works is akin to attempting to deduce how a clock works without ever being able to open it. We will never be able to step outside the universe to study it with pure objectivity. With this in mind, theories about the makeup of fundamental particles will always seem to beg the question…ok, now what is “that” made of? Or, with superstrings – what is it that is vibrating? I wonder if we will ever be able to know the answer. Have we maybe reached the point where we should accept that the search for more and more fundamental particles is caught in an infinite regress? Are we spinning our wheels? I suppose we aren’t yet, maybe far from it, but it is interesting to think about. What direction would we take if we discovered that the universe has been leading us in circles?

      • gatorallin

        Always liked his quote… I have no special talent. I am only passionately curious. -Albert Einstein

        Orbiting circles. ….

        • Len Goforth

          More likely, orbiting ellipses. These are seen more frequently.

      • Jeffrey Werbock

        The phrase “fundamental particle” is an oxymoron; either it is fundamental, meaning, a quantum and therefore a singularity of energetic action, or it is a particle, which means it is a part of something else, presumably something larger. Confronted with the confounding paradox of photons behaving like a particle when in trajectory and like a wave when interacting with other energetic presences such as the outer shell of electrons surrounding the nucleus of atoms, they labeled it a “wavicle”. I would suggest referring to so-called fundamental particles, wholicles, because they are complete units of energy. That said, they do not really exist; everything is interconnected in a single wholeness and it is merely our perceptual bias which forces us to regard the spectrum of vibrations of all energies as if there were discrete units of energy which could exist apart from the unifying matrix. If that were the case, there would be no such thing as half life. Every atom of a given radioactive isotope would decay all at the same time, going by the quantum model which insists there can be no difference between atoms of a given isotope. Of course they do not decay all at the same time. That’s because there are no discrete units of energy, there is a web and everything is a priori interconnected. With that a priori interconnection, no “unit of energy” could interact with another.

        There are no vibrating strings. There is only the vibration, no “string” or any “thing” which moves. The concept of pure motion with no object moving is too abstract, too “eastern mysticism” an idea for western educated thinkers and scientists to be comfortable with, so we invent particles, strings, dimensions, time, and so on.

        • Todd

          “It is merely our perceptual bias which forces us to regard the spectrum of vibrations of all energies as if there were discrete units of energy which could exist apart from the unifying matrix.”. Thank you! I’ve been waiting a long time for someone to articulate this. So what we study is what we can know from our limited perspective and if nature presents us with “particles” then particles are what we have to work with…it doesn’t make sense to think about them as representative of some fundamental picture of reality.

      • Len Goforth

        I’ve read that the universe is always expanding; there is no center; it is curved; and that theer are about a dozen equations that prove, mathematically, that the possibilities of 4 or more dimensions is high. THAT alone is awe inspiring. To find out more might spoil the wonder.

        • Paul Halpern

          Yes, contemporary physics is wondrous indeed!

    • David Hykes

      My work since 1975. http://www.harmonicpresence.org

    • Jeffrey Werbock

      Most people on planet earth find tonalities pleasing which are not on the scale of so-called most harmonious intervals. The Pythagorean preference for most harmonious intervals is a tonal prejudice which dominates the western world, not the eastern world, which includes many microtones, deliberate dissonance which is used to intensify the listeners’ yearning for harmonious closure. Pianos and guitars are tuned to a very close approximation of that Pythagorean scale, not quite, it’s a compromise known as the tempered scale, and most of western civilization lives under the tonal tyranny of the tempered scale.

      Still, I can understand why the Pythagorean scale of most harmonious intervals appeals to the theoretical aspects of certain concepts from quantum physics, the notion that states of energy represented by the idea of “fundamental particles” exist in increments called quanta in which there can be no states in between, ie. one electron, one photon, one quark, etc. But the scale of vibrations does not obey quantum conditions. There is no limit to how the scale of vibrations can be divided by frequency and wavelength.

      • David Rosales

        Eastern music isn’t any more free. Talking about western classical music throughout history there is evolution and exploration within the tonality that we are taught in schools. Eastern music does not adhere to this specific system of constraints but to its own. Even the different Iranian and Hindu traditions bent to a large degree on what we call extemporization follow very strict conventions and a limited number of modes (albeit not the european church modes and as you said, including intervals not found in european common practice period music ) and a limited number of patterns which can then be combined in quasi endless ways by performers. In fact, I would claim that if anything, western classical music, from its origins in medieval church music, grew to be far more flexible and encompassing than any of the eastern traditions which remained fairly “folk” and thus naturally even more narrow minded. Also plenty of european and other western folk music does not live under the “tyranny” of tonality.
        Also, although theoretically there is no limit to the degree to which pitch may be bent, this statement becomes complete nonesense in the context of music, where we create music for the communication of emotions. For this to work at all, a certain degree of conventions must be maintained or evolved together with people’ beliefs and perceptions at large. A language of sorts, if you will. Second, human distinction of pitch isn’t nearly good enough for this non-converging, ad-infinitum pitch bending to even matter.

        Don’t bring misinformation in your bundle of new age bullshit.

        • Forrest Cahoon

          I think you’re reading a lot into Werblock’s post that isn’t there at all. The only thing I see that could have set you off is the use of the term “tonal tyranny”. It is true that Western music notation, and more significantly keyboard instruments such as the piano, are built around the twelve-tone equal tempered scale, and so the great majority of Western music — especially since the dominance of the keyboard — has been developed with these notes as the raw material. That’s in no way controversial.

          Furthermore, in his last paragraph he EXPLICITLY DISMISSES a literal connection between quantum physics and acoustic vibrations, and in so doing REJECTS the most typical line of “new age bullshit” out there, the Deepak Chopra “quantum everything” bit.

          Werblock provides far more information than disinformation. You provide a lot of good information too, but your tirade is totally misplaced. It’s simply not against anything he said.

      • R L Parent

        The Pythagorean’s also cane up with the idea, and name, of “Imaginary Numbers”, ie the square root of -1.

        • Forrest Cahoon

          Nope. The name was bestowed by Descartes, and the only clue we have regarding work on them prior to the 16th century is a passing reference in one of the works of Greek mathematician Hero of Alexandria in the 1st Century AD — some five hundred years after Pythagoras.

    • Len Goforth

      By Zeus, I say ’tis fascinating, but I prefer the ancient myths that named our constellations. These are fun to tell around a campfire.

    • http://www.physicsibook.com tonyfarley

      what a great article! Thank you.

      • Paul Halpern

        Many thanks!

    • R L Parent

      dont forget the song by The Clash (I think) about the comet that struck Jupiter 30 years or so ago. He tied that celestial event to romantic affairs….. well written prose.

    • seescaper

      Google “beyond the point particle, Milo Wolff” for a full discussion of space resonance

    • Crop_O

      I’m still trying to figure out the longest distance between 2 points.

    • LeRoy Whitman

      Remember that models are only models … and built on other “accepted” models (any of which may have flaws). We are not “discovering reality”; we are seeking to use metaphors in order to speak about reality. In this sense, then, while science has useful applications in instances, by the very nature of the task it does not produce “answers” – only tools. The user is greater. And we are the ones creating these “definitions” – for good or for ill. The scientific model is itself only one endeavor among many in life. Not only the metaphors we create, but our motivation in what we are looking are constraints on the whole of experience, and can inadvertently blind us, if we do not step back outside of our own machine or dynamic model.