Quantum Listenings -- Amateur Sonification of Vacuum and other Noises

TL;DR

Explores complementarity between visual and auditory representations for understanding physical phenomena, outlining methods to map atomic and molecular observables to sound and to compare audio renderings with visuals. It presents concrete sonic mappings, including a hydrogenic 'quantum chord', nonlinear AFM oscillator dynamics, and Bose gas energy fluctuations, along with guidance on spectral synthesis of thermal, quantum, and white noise. The work demonstrates how sound can reveal structures in quantum and nanoscale systems that are not immediately evident visually, offering educational and exploratory tools and suggesting avenues for conveying coherence via stereo audio. Overall, it positions sonification as a practical, accessible complement to visual data in interpreting complex physical phenomena and noisy quantum systems.

Abstract

The sensory perceptions of vision and sound may be considered as complementary doorways towards interpreting and understanding physical phenomena. We provide a few selected samples where scientific data of systems usually not directly accessible to humans may be listened to. The examples are chosen close to the regime where quantum mechanics is applicable. Visual and auditory renderings are compared with some connections to music, illustrating in particular a kind of fractal complexity along the time axis.

Figures (13)

• Figure 1: Example of an acoustic waveform (two stereo channels are shown). These 210 ms represent the 2nd eighth note (see insert, g$^1 \approx 392\,{\rm Hz}$, i.e. period 2.55 ms) of Beethoven's 5th Symphony, 1st Movement (c minor, op. 67) live-in-Ramallah. Audio file: https://gitup.uni-potsdam.de/henkel/sonification_cd25/-/blob/main/Public_mp3s/Beethoven5_2nd-8th.mp3.
• Figure 2: Harmonics of D ($\approx 73\,{\rm Hz}$) up to the eighth (three octaves). In the usual tuning, the 6th harmonic appears at a$^1 = 440\,{\rm Hz}$. The 7th harmonic appears approximately a quarter tone below c$^2 = 523\,{\rm Hz}$, i.e., at $\approx 508\,{\rm Hz}$ (accidental $\flat$), cf. audio file https://gitup.uni-potsdam.de/henkel/sonification_cd25/-/blob/main/Public_mp3s/obertonreihe.mp3. (In diatonic tuning, D would appear at $440/6 = 73.333\,{\rm Hz}$, in well-tempered tuning, at $2^{-7/12} \, 440/4 = 73.416\,{\rm Hz}$.)
• Figure 3: Sonified duet of $\pi$ over ${\rm e}$. The digits of $\pi$ in base twelve are encoded into the well-tempered half-tones from f$^1$ to e$^2$, while ${\rm e}$'s digits in base five are mapped to a pentatonic scale. The only manual edits were applied to duration: the first note and the digit 0 getting longer durations. For a longer version, see Fig. 11 in the Appendix and audio file https://gitup.uni-potsdam.de/henkel/sonification_cd25/-/blob/main/Public_mp3s/pi_over_e_classical.mp3.
• Figure 4: Frequencies corresponding to the binding energies of the Hydrogen atom mapped to a piano keyboard. Note the beautiful features of "atomic harmony" Sommerfeld_Atombau: the levels $n = 2, 3$ are separated by two fifths (ratio $(2/3)^2$) and $3, 4$ by two fourths ($(3/4)^2$). (The slight offset of the levels $n = 3, 6$ with respect to the keys is actually due to the well-tempered tuning assumed here where fifths and fourths are not "pure".) The audio file https://gitup.uni-potsdam.de/henkel/sonification_cd25/-/blob/main/Public_mp3s/hydrogen_keys.mp3 renders the frequencies approximately on a well-tempered keyboard, including quarter tones.
• Figure 5: Analysis of nonlinear oscillations upon approaching a cantilever to a solid surface. In each of the four panels, one finds at top left: trajectory, top right: phase space protrait, bottom left: effective potential including a harmonic contribution from the piezo-control, bottom right: power spectrum (Fourier transform) of the vibration. The oscillation occurs at a fixed energy about $15\,k_BT$ above the potential minimum (horizontal line). The vertical line in the spectra marks the eigenfrequency $\Omega/2\pi \approx 140\,{\rm kHz}$. In the acoustic version (https://gitup.uni-potsdam.de/henkel/sonification_cd25/-/blob/main/Public_mp3s/listen_approach_curve.mp3), the time series has been re-scaled to that $\Omega/2\pi$ corresponds to roughly $400\,{\rm Hz}$.