When the uncertainty principle goes up to 11…

sagan

First published at physicsfocus.

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).

Uncertainty-to-11-sustain

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).

Uncertainty-to-11-chug

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..?

Image: Sagan/Slayer t-shirt design by Monsters of Grok

15 Responses to When the uncertainty principle goes up to 11…

    1. John Duffield says:

      Interesting stuff, Phil. I suppose you know all about the “Optical Fourier Transform”, like on Steven Lehar’s web page, about half way down. A lens converts an extended-entity wave into dots on a screen, effectively performing a real-time non-mathematical Fourier transform. I can’t help wondering if something similar is going on in the double-slit experiment. A photon goes through both slits, as per Steinberg et al’s plot in In Praise of Weakness. But when you detect it, you get a dot on the screen. And if you detect it at one slit, the photon is transformed into a dot that goes through that slit only.

    1. Firstly – it feels good to finally know I’m not the only physics-loving metalhead (or should that be metal-loving physicshead). I thought you were supposed to appreciate art history and Mahler, so I tend to keep it quiet! Thanks very much for this video, and the novel way of looking at the uncertainty principle.

      Secondly, a thought occured – when palm muting, I often find that if one rests too hard on the string, a noticeable change in frequency can occur, because you’re effectively changing the length of the standing wave. Is that not a possible alternate cause for the effect?

        • Hi, Mike.

          That’s a wonderfully perceptive comment! I worried about this too and made sure that I was not changing the pitch. It’s one of the reasons that I tuned back up from “drop A” tuning in the video. The key thing is that the peak position of the fundamental stays at the same frequency – it just becomes broader.

          All the best,

          Philip

            • Of course! If you were to change the length, the frequency would have changed. The proof that the wavelength is the same is the unchanging fundamental. Brilliant 🙂

              I wonder if there’s some way to relate the uncertainty in frequency/wavelength to the width of the damper…

              Thanks for the reply,

              Mike

    1. Ian Liberman says:

      As creator of Pressman`s Rock Trivia and an obsessed metal fan, who is very much into physics and cosmology as a hobby, I can not remember when I have enjoyed a article as much as I have yours. Your use of the guitar string played at its loudest to demonstrate Heisenberg`s Uncertainty Principal,using time and frequency instead of position and momentum to demonstrate the cycle of the waveform. This is demonstrated by the uncertainty residing in “narrow in time, wide in frequency” and also vica versa, when you play the one string along with the illustrating graph and applying it to HUP .You also peaked my interest in how you illustrate how the fourier transformation of data is used for analysis. Thanks for an excellent learning experience with metal overtones.

    1. Kelly says:

      I absolutely loved this post and the analysis of metal from a physics perspective. I am a biologist as well as a very vocal metalhead, and a classically trained percussionist. I have never seen anything remotely strange about my love for metal and classical music and sometimes have a hard time explaining to people why I am the way I am, but this post, as well as some others I’ve seen recently make me feel better that metalheads are getting out there and talking about why we love this technically and lyrically amazing music as much as we do (I write this as I am listening to Swallow the Sun…). Hopefully there will come a day when I don’t get dirty looks for being proud of the death, doom and black metal I listen to, and I will no longer have to explain how I can have Beethoven following Behemoth on my iPod. Thanks again to all metalheads supporting the genre.

    1. Richard Codling says:

      Very interesting article! I got into physics through taking guitars and effects apart and eventually built up to making my own little valve amp so this brings it all back round nicely.

      I attended an interview to become a trainee physics teacher and as part of my interview I had to give a five-minute presentation about an aspect of physics that interested me. I chose the elctric guitar and highlighted what could be cross-referenced to what part of any given course, mostly experiments I wanted to try myself! I got a place on the course but ended up in the health service instead for various reasons.

      I notice you can see the decay envelope of your noise gate on the raw waveform of the ‘crunch’ D too does that affect the frequency composition? DId you try with and without?

      Right better be off, my new band have a gig in 8 weeks and we need some material… http://www.facebook.com/LiveBurial

        • Hi, Richard.

          Great comment. The noise gate will indeed affect the overall shape of the frequency spectrum, but the general principle remains – narrow in time, wider in frequency. An exponentially decaying sinusoidal signal (as for the traditional damped, driven oscillator) when Fourier transformed to frequency space, will have a Lorentzian frequency spectrum. (The resonance curve familiar from A-level physics).

          Other types of decay of the signal will change the shape of the frequency spectrum (e.g. an abrupt switch-off of the signal would be the equivalent of the top-hat function known to undergrads, and this would produce a sinc function in Fourier space).

          I was being entirely serious in the last paragraph of the post – metal guitar sounds could be used as a very effective and entertaining way of explaining Fourier transforms.

          I look forward to hearing some MP3s from your band – please post a link when you upload them!

          All the very best,

          Philip

    1. Great stuff Philip. I never dreamed I’d see the day when Heisenberg and hair metal were mentioned in the same article. On the other hand, Heisenberg would be a great name for a German industrial metal band.

      This reminds me how, when a German researcher developed an algorithm for classifying music according to characteristics such as timbre and rhythmic variation rather than genre, the system couldn’t really distinguish classical music from heavy metal: http://www.nature.com/news/2006/060717/full/news060717-16.html. One can, for example, draw some analogies between the rhythmic tricks of Led Zeppelin and Stravinsky, although the refined audiences to whom I sometimes talk about music cognition don’t always seem to appreciate hearing Black Dog.

      If you’re interested in seeing the two genres (and others) merged (lord, if not Lord, save us from Deep Purple’s Concerto for Group and Orchestra), check out Glenn Branca (http://www.youtube.com/watch?v=xdLhRB4dJJI) or Towering Inferno. TI’s album Kaddish has been described as a mixture of “East European folk singing, Rabbinical chants, klezmer fiddling, sampled voices (including Hitler’s), heavy metal guitar and industrial synthesizer”. It would be hard to improve on that recipe (which also brings us back to Heisenberg…).

        • Thanks for those fantastic links, Philip. Wonderful to know that a quantitative analysis of timbre and rhythm fails to distinguish reliably between metal and classical music!

          That Branca composition is… disturbing. I thought that Robert Fripp was ‘out there’ but Branca is on an entirely different plane – actually, in an entirely different universe. I can’t say that I enjoyed it but I certainly found it compelling.

          “…lord, if not Lord, save us…” Nice.

          Philip

    1. What an awesome site those links go to. Shows what I always suspected, which is that Bartok anticipated Slayer.

      This is risking getting off-topic now, but I couldn’t help thinking of one of my favourite YouTube videos:

      https://www.youtube.com/watch?v=9pS5xzOWbwo

      I love the way the demure little Japanese girl sits down to delight her audience with a beautiful performance, totally rocks out, then gives a petite little bow to polite applause. She’s even more extraordinary here:

        • It’s absolutely amazing, isn’t it? I watched that many moons ago during a tea-break in a long night of experiments which weren’t going particularly well and it cheered me up immensely!

    1. Mark Fromhold says:

      Philip,

      As you know, I’m also a middle-aged Professor of Physics but I also love folk music. So you see, it could be worse…

        • Hi, Mark.

          A bit of folk now and then is nothing to be ashamed of! Christy Moore, both solo and as a member of Planxty, is certainly lurking on my iPod. I’m also partial to the folk-prog-rock of Jethro Tull.

          Philip

Author: Philip Moriarty

Physicist. Rush fan. Father of three. (Not Rush fans. Yet.) Rants not restricted to the key of E minor...

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