*Uncertainty is a Nice Motif*

2023-08-06

This is my attempt to connect quantum physics and music. I realize that I am very much out of my depth writing this, so here’s a disclaimer: I study media arts, not physics. Take this with a grain of salt.

Both music and quantum mechanics deal in uncertainty. In music, short sounds correlate well with many different frequencies, so the precise frequency content is ‘uncertain’. In quantum physics, there is uncertainty between the position and momentum of particles, as described by their corresponding wave functions. Turns out that time-frequency uncertainty and position-momentum uncertainty are manifestations of the same principle, and apply to any Fourier transform pairs. When I realized this, some of the magic of quantum uncertainty faded.

Uncertainty alone doesn’t explain the stochastic nature of quantum mechanics, though. In quantum computing, the measured value of a qubit is probabilistic. When I first learned about this, I came up with what I thought was a fairly clever and simple explanation: the universe may be running at a higher sampling rate than we are able to observe. The probabilistic nature of the outcome would then be the result of sampling a function that is changing faster than nyquist. As far as I understand, this would be considered a hidden variable theory. There would be some underlying state of the particle which we cannot measure but which determines the outcome of the measurement.

Bell’s Inequality shows that any valid hidden variable explanation for the wave function must be non-local. This means that the hidden variable which determines the measured state of the particle must be coordinated between particles over great distances and faster than the speed of light. If you’re curious, the proof of this is more-or-less straitforward. Try googling the CHSH game. Since most people believe that faster-than-light communication is not possible, most people rule out non-local hidden variable theories as well.

That’s to say, my theory was a bit half-baked. Though, its nice to think that the backend of the universe could be constructed with long strings that vibrate faster than the speed of light.

This all got me interested in other explanations of quantum mechanics and led me to the many worlds interpretation. In many worlds, a qubit in superposition belongs to two separate worlds. The stochasticity in our measurements no longer comes from a hidden variable, but instead from not knowing which world we are observing from. Instead of being uncertain about a particles movement, we are uncertain about our place in the universe.

Anyways, I’m uncertain that any of this is correct at all, so I’m gonna end here. Perhaps I’ll come back to quantum in the future.