When the uncertainty principle goes up to 11…

Sagan/Slayer t-shirt design by Monsters of Grok

I’m a middle-aged professor of physics and I love heavy metal.

There, I’ve said it.

I know that the mere mention of heavy metal – the music, that is, not one of those dubiously defined toxic elements in the periodic table – is likely to provoke a disdainful wrinkling of the nose among the more, let’s say, cultured readers of physicsfocus. But before you run to the hills, or depart en masse for BBC iPlayer and the more sedate sounds of Radio 3, first let me explain just why I am so heavily into metal and all its myriad sub-genres(including thrash, death, power, progressive, and – forgive me – hair metal), and why the Heisenberg uncertainty principle is fundamentally connected with the ‘crunch’ of a metal guitar riff.

The best metal is incredibly harmonically rich. The music of Black Sabbath and Metallica, to name but two metal giants, echoes and channels the sheer heaviness of the work of classical composers such as Wagner, Rachmaninoff, and Paganini. Indeed, one of the most accomplished metal guitarists there is, Yngwie Malmsteen, frequently cites Paganini’s work as a formative influence on his playing. And a British band who were a major inspiration for the fledgling Metallica, Diamond Head, ripped off paid homage to Holst’s Planets Suite – specifically, Mars: Bringer of War – on their seminal track Am I Evil? Other examples of classical ‘crossover’ abound in the metal oeuvre.

In addition to being harmonically sophisticated, however, particular ‘breeds’ of metal are also rhythmically complex. Thrash metal, and the closely related industrial metal and ‘djent’ sub-genres, in particular, are based around exceptionally tight and syncopated rhythm guitar riffs where extensive use is made of palm muting to damp the strings. The video below includes a few examples of the use of heavy string muting in a number of archetypal metal riffs.


Bands like Meshuggah and Fear Factory have honed the level of syncopation to a very fine art where even the vocals become percussive and are locked in sync with machine-like guitar ‘chugs’ in challenging time signatures. It’s this rhythmic complexity – and the type of guitar style that’s required to produce it – which underpins the link between heavy metal and the Heisenberg uncertainty principle.

Unfortunately, the uncertainty principle continues to be explained — at least in many pop sci accounts (see here for example) — in terms of the disturbance that a measurement causes to a quantum system. This rather frustratingly fails to put across the fundamental essence of the uncertainty principle and can be somewhat misleading for students.

The uncertainty principle is simply an unavoidable and natural consequence of imbuing matter with wavelike characteristics. A wave can equally well be described in the time or in the frequency domain. These are conjugate variables and we can switch between the two descriptions of the wave using the wonderfully elegant Fourier transformation process. (An erstwhile colleague at Nottingham described the Fourier transformation of data as “what physicists always do when they can’t think of anything better”. I agree, and am guilty as charged! But there’s a very good reason why physicists fall back on Fourier analysis time and time again…) Any sound engineer or producer is also familiar with the results of Fourier transforming audio waves (although they may not refer to the process in quite those terms): a spectrum analyser provides a visualisation of Fourier components, while a graphic equalizer allows the relative amplitudes of those components to be modified.

The uncertainty principle arises from a very simple relationship between the two different representations of a waveform on the time and frequency axes: the shorter the signal is, the wider its frequency spectrum must be. Put more simply: narrow in time, wide in frequency. The width of the spectrum is simply a ‘proxy’ for our uncertainty in defining a specific frequency for the waveform. This, of course, translates to other pairs of variables including, in particular, position and momentum, giving rise to the standard form of the uncertainty principle which 1st year physics undergraduates are most familiar with.

Metal guitar lends itself rather well to a demonstration of the uncertainty principle in action. An undamped string left to its own devices on a highly amplified guitar produces a distorted note which sustains for some time:

The waveform is shown below on the left. On the right hand side is the frequency spectrum for the fundamental (i.e. first harmonic) of the guitar string. Note that the spectrum is essentially a single spike at the frequency of the fundamental. (Of course, there are many other frequency components but we don’t need to worry about those – I’ve zoomed in on a narrow portion of the spectrum containing just a single harmonic).

If the string is now muted to get the signature ‘crunch’/’chug’ of the metal riff, the waveform dies out on a very much shorter time-scale:

This time-limited signal has a correspondingly wider frequency spectrum, i.e. our effective uncertainty in determining the frequency of the fundamental is much greater. (The intensity of the peak in the frequency spectrum will also decrease but I’ve scaled it up to allow for better comparison of its width with that of the original narrow peak).

This natural broadening of the spectrum of a time-limited signal represents the very essence of the uncertainty principle. And as was also aptly demonstrated by the IOP Schools lectures a few years back, what better way to demonstrate fundamental physics principles than via a heavily distorted guitar dialled all the way up to 11?

As I was finishing this post I found out that New College here in Nottingham will offer a degree in heavy metal from September 2013. It’s of course already attracted more than its fair share of opprobrium, widely mocked as a “Mickey Mouse” degree, but an undergraduate module or two on the physics of heavy metal strikes me as a very good idea indeed. It’d be an intriguing and left-field route into teaching topics such as vibrations and waves, signal processing, Fourier analysis, ordinary and partial differential equations, and feedback (non-linear dynamics).

I wonder if New College Nottingham is in need of an external examiner for its course..?

Philip Moriarty

Philip Moriarty

Philip Moriarty is a Professor of Physics at the University of Nottingham. His research interests lie in what has occasionally been described as “extreme nanotech” in that he works alongside a talented bunch of nanoscientists to prod, poke, push, pick, and pull individual atoms and molecules in order to explore forces and interactions down to the single chemical bond limit. Moriarty also has a keen and long-standing interest in science communication and public engagement. He is a member of the Sixty Symbols team that was awarded the Institute of Physics Kelvin prize in 2016 for “innovative and effective promotion of the public understanding of physics”. While he doesn't share his infamous namesake's fascination with the binomial theorem, Moriarty enjoys exploring the maths-music-physics interface including, in particular, the deep and fundamental links that exist between quantum mechanics and heavy metal music (a theme discussed at length in his book, “When the Uncertainty Principle Goes to 11”). He blogs at https://muircheartblog.wordpress.com.
Philip Moriarty
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