Physicists and Fugues: A Well-Tempered Pairing

by Ashutosh Jogalekar

Sergei Rachmaninoff and John Wheeler were both masters of their art, equally at home with details and wild speculation, both seeing their disciplines as holistic ones encompassing all of human experience and the universe

As someone who has been interested in both classical music and the history of physics for a long time, I have been intrigued by comparison of the styles between the two art forms. I use the term “art form” for physics styles deliberately since most of the best physics that has been done represents high art.

Just like with classical music, physics has been populated by architects and dreamers, careful workmen and inspired explorers, bursts of geniuses and sustained acts of creativity. It is worth spending some time discussing what the word “style” might even mean in a supposedly objective, quantitative field like physics where truth is divined through precise measurements and austere theories. The word style simply means a way of thinking, calculation and experiment, an idiosyncratic method that lends itself individually or collectively to figuring out the facts of nature. The fact is that there is no one style of doing physics, just like there is no one style of doing classical music. Physics has blossomed when it has benefited from an unpredictable diversity of styles; it has stagnated when a particular style hardened into the status quo. And just like classical music goes through periods of convention and experimentation, deaths and rebirths, so has physics.

If we take the three great eras of classical music – baroque, classical and romantic – and the leading composers pioneering these styles, it’s instructive to find parallels with the styles of some great physicists of yore. Johann Sebastian Bach who is my favorite classical musician was known for his precise, almost mathematical fugues, variations and concertos.

Listening to Bach is almost always a religious, transcendental experience for me – I consider the Goldberg Variations the most transcendental piece of music ever conceived. Somehow Bach manages to bridge the gap between making his music utterly precise and rational and yet a journey into the mind of a God of the highest spiritual qualities whose ineffable manifestations beggar belief.

Who among the pantheon of physicists could mirror this inspired rationality of Bach? We need to find someone who spans a large body of work, whose mind was steeped in rational abstraction and yet who demonstrated what Einstein once called, in the context of Niels Bohr’s work on atomic physics, the “highest form of musicality in the sphere of thought.” Enrico Fermi and Hans Bethe could both be candidates because of the sheer amount of the work they accomplished and its expansiveness, but none other than Paul Dirac seems to me to fit the perfect Bachian mold. Dirac’s theories were so precisely elucidated that, in Freeman Dyson’s words, studying them was like seeing “perfectly formed sculptures falling from the sky”. The Goldberg Variations certainly seem to fit that image for me; so do the English Suites. Bach spoke to God through his creations; Dirac spoke to the God of mathematics through his. In Bach’s universe, no piece of music made sense unless it spoke to the glories of God; in Dirac’s universe, no piece of physics made sense unless it was expressed in beautiful mathematics. In both Bach and Dirac’s work we see the human mind treading the line between rationality and faith almost perfectly.

What about Einstein? Just like Dirac and Bach, Einstein had an uncanny feel for the workings of nature, not through the mysterious formulas of mathematics but through an almost tactile feel for reality, one so strong that it could leave him feeling that “something had snapped inside him”. Throughout his career Einstein made very diverse contributions to physics, ranging from relativity and the photoelectric effect to the laser and quantum entanglement. His virtuosity in imagining thought experiments was unparalleled, and in the deep recesses of this imagination a comparison to Wolfgang Amadeus Mozart might be obvious, especially since Mozart was the amateur violinist’s favorite composer. But the comparison is in fact deceptive. Mozart was a non-pareil genius and virtuoso, but the major body of his work in fact consisted of refining and consolidating the existing art forms of his time rather than creating revolutionary new forms the way Einstein did.

No, rather than Mozart, the apt comparison for Einstein seems to be with Beethoven who for me is the closest a classical music composer gets to being a creative scientist of the highest caliber. One can listen to any number of Beethoven’s superlative creations – the 5th and the 9th, the late string quartets, and of course, the Grosse Fugue, one of the most radical works ever written – to understand the sheer, wild novelty that his mind exuded. Any of these could bear a fair comparison to Einstein’s devastating realization that gravity is the curvature of spacetime. Yes, yes, now that one thinks about it, one can see the two unruly manes nodding in unison. There are also the more standard-issue compositions of Beethoven like the Emperor Concerto, compositions which accomplish a more Mozartian consolidation of existing styles and yet which simply ooze joy, that could be considered tantamount to some of Einstein’s “minor” contributions, such as one of his first papers demonstrating the existence and size of molecules through an exploration of Brownian motion or his work extending Satyendranath Bose’s work to quantum statistics. The deceptively mundane and the outright profound – both dot the luxuriant landscape of Einstein and Beethoven’s great oeuvre like gems scattered in a garden of musical and scientific delights.

The Mozart-Beethoven comparison in fact manifests itself sharply in a memorable event of 20th century set squarely in its middle, one that marks the high watermark of the work of the old masters and the passing of the torch to a new generation. In 1948, in a conference set in the Pocono Mountains of mountains, the physics prodigy Julian Schwinger blew away and left exhausted a collection of some of the 20th century’s leading scientific minds, men like Fermi, Bethe, Bohr and Oppenheimer, by blazing through a six-hour talk that rewrote our understanding of the interaction between light and matter, the theoretical framework known as quantum electrodynamics. Comparisons with Mozart were immediately forthcoming.

Comparisons with Beethoven weren’t so forthcoming for the speaker who followed Schwinger, a brash, brilliant, unruly 25-year-old physicist from New York City named Richard Feynman who left his audience bewildered and annoyed rather than impressed. Feynman had formulated a radically novel view of quantum electrodynamics from scratch that involved novel entities: particles moving backwards and forwards through time, squiggly diagrams that would enable physicists to see past lengthy calculations and simply visualize what happens, a set of calculational tools that would transcend their original narrow realm of elementary particles. The vision was so radical that nobody could understand it. And yet, it was a vision that was to soon become part and parcel of the theoretical physicist’s toolkit, much like how the radical foundations that Beethoven laid became ingrained in all of subsequent classical music. If the hallmark of a great mind is that their radical vision soon becomes the establishment vision, then Feynman’s greatness mirrored Beethoven’s.

Just like painting and music, physics can be pointillist. There are physicists and musicians who rather than erecting complete edifices put together a partial but brilliant superstructure; a set of bricks in a novel configuration here, a dab of ideas there that points the way to something bigger. The physicists may not get every decimal point right and the musicians may not say the Bachian last word, every note in its precise place. But they show where the path lies and inspire others to follow it. In classical music you have Igor Stravinsky; in physics you have Robert Oppenheimer.

Oppenheimer’s 1930 ‘Note on the Theory of the Interaction of Field and Matter’ laid out a troubling discrepancy in quantum field theory that led to infinite values for interactions of subatomic particles. It was an impression, a dim view of a wild forest, a path chosen but not yet followed, leaving the journey for other physicists to chart out on their own; a journey that was completed in part by Schwinger and Feynman almost twenty years later. This was not so much an explanation as an invitation. More importantly, it was influence. A similar theme pervades the work of Stravinsky which was marked by stylistic diversity. While no Oppenheimer paper caused a “near riot” the way the first performance of ‘Rite of Spring’ is supposed to have, Stravinsky and Oppenheimer both share eminent status as being the inaugural geniuses of new movements; modernism in case of Stravinsky and quantum electrodynamics and later black holes in case of Oppenheimer. Neither man achieved the fame that men of the first rank like Einstein and Beethoven did, but in terms of influence they were second to none.

Speaking of Russian composers, what physicist could possibly parallel the artistic genius of Sergei Rachmaninoff? Like the great Russian novels, Rachmaninoff’s most famous compositions – the 1st and 2nd concerto, the 2nd and 3rd symphonies – seem to be overflowing with every kind of human emotion. When I listen to the 2nd symphony (and especially its 3rd movement) I feel like I am listening to the equivalent of ‘War and Peace’, an enormous saga with music to suit every mood, ever aspect of human existence, every story that’s ever told. In the 2nd symphony I see all of life. I feel all of life. In the German-speaking tradition, Mahler occupies a similar place; his 3rd symphony sometimes seems to contain all other symphonies ever written. Along with the other Russian greats, Prokofiev and Shostakovich, Rachmaninoff is intense sturm und drang, titanic emotion and feeling writ large. But Rachmaninoff was also the master of precision and technique – any listening of the 3rd concerto makes that superlative talent for getting the details right clear. To mirror Rachmaninoff, then, we need a physicist who combined audacious dreaming with superior technique, a fearlessness to experiment combined with complete mastery of the traditional resources, an equal ability just like Sergei Vasilyevich’s to rise to stratospheric levels and zoom in with laser beam focus when needed.

To me the choice seems clear: John Archibald Wheeler. Wheeler was often referred to as a magician among 20th century physicists. He was not just one of the 20th century’s most successful physicists, working out the mechanism of nuclear fission with Niels Bohr, working on the hydrogen bomb and jump-starting general relativity research in the United States, but also one of the most original and outlandish. When his most famous student, Richard Feynman, was asked about Wheeler’s crazy ideas later in life, he replied that Wheeler was always crazy. He was fond of pushing physical principles to the absolute limit in all their creativity and coining neologisms that stuck; among other things, he came up with “black hole” and “it from bit”, the latter signifying the fundamental importance of information, an insight that’s all too paramount in the age of quantum computing and artificial intelligence. The young Wheeler was known for his precise calculations on fission and the S-matrix. The later Wheeler was known for ideas so outlandish, ideas like the delayed choice experiment, that he explained them in speeches and essays rather than in papers. Together, just like Rachmaninoff’s 2nd symphony, Wheeler’s physics and ideas seemed to encompass all of nature, from the subatomic to the cosmic, from space and time to human existence.

There are other physicists and musicians who made small but decisive contributions. How many of us remember Gustav Holst for anything other than The Planets? Or Pachelbel for anything other than his Canon, a piece that has the distinction of having become important enough to be elevated to wedding and elevator music? Now contrast that with Emmy Noether who, while she made several important contributions, is known for one seminal contribution: her overriding, deep discovery of the connection between symmetry laws and conservation principles embodied in Noether’s Theorem. Another example of a Holst-like singular physicist is Roy Kerr whose discovery of an exact general solution for countless rotating black holes provided, according to Subrahmanyan Chandrasekhar, the most shattering experience of his entire career. These physicists, in zoological parlance, are frogs who make singular individual discoveries, even if they are not birds like Einstein or Dirac who are circling high above the landscape.

What do the evolving styles of music and physics tell us? Throughout the history of music in general and in classical music in particular, we see an element of rebellion, sometimes subtle and sometimes outright. From Gregorian chants to the transcendental yet somewhat staid music of Bach, on through the consolidating genius of Mozart and the Romantic explorations of Beethoven and Chopin, we begin to enter more experimental territory. The culmination comes in the 20th century with the Russian masters, with Prokofiev and Stravinsky and the atonal Schoenberg. Physics has seen similar parallels, especially in the application of mathematics. From the brilliant but conventional application of calculus and linear algebra by Maxwell and Heaviside and Jeans to the novel differential geometry developed by Riemann, Einstein and Grossmann, all the way to new topological methods introduced by physicists like Roger Penrose in their study of black holes and condensed matter physics, there has been an element of unruly splendor in physics, an enthusiastic embrace of stepping out of conventional territory, scoping out that territory and developing it to such an extent that it then becomes conventional territory, only to open the way for someone else to use it as a springboard to launch themselves on to the next frontier. In this sense, string theory, as divorced as it has become from experiment, continues the tradition of experimenting with new mathematical tools for solving tough problems in physics. The unified picture that emerges is one of both classical musicians and physicists being like explorers, never at rest, always defying conventional wisdom.

If there is one lesson that we should then draw from even a cursory comparison of classical music and physics styles, it’s the lesson of diversity. There will always be a place for new styles of classical music and physics because no one style encapsulates the paradigm. Like Niels Bohr’s complementarity, both classical and music will continue to benefit from styles that are new, even divergent and opposed; and yet both kinds will be essential to capturing human experience and the laws of nature.