Quantum Octave...

Image Source: Technology Review

Topics: Hilbert Space, Modern Physics, Quantum Mechanics, Superposition

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TECHNOLOGY REVIEW: One of the features of 20th century art is its increasing level of abstraction from cubism and surrealism in the early years to abstract expressionism and mathematical photography later. So an interesting question is what further abstractions can we look forward to in the 21st century?

Today we get an answer thanks to the work of Karl Svozil, a theoretical physicist at the University of Technology in Vienna and his pal Volkmar Putz. These guys have mapped out a way of representing music using the strange features of quantum theory. The resulting art is the quantum equivalent of music and demonstrates many of the bizarre properties of the quantum world.

Svozil and Putz begin by discussing just how it might be possible to represent a note or octave of notes in quantum form and by developing the mathematical tools for handling quantum music.

They begin by thinking of the seven notes in a quantum octave as independent events whose probabilities add up to one. In this scenario, quantum music can be represented by a mathematical structure known as a seven-dimensional Hilbert space.

A pure quantum musical state would then be made up of a linear combination of the seven notes with a specific probability associated with each. And a quantum melody would be the evolution of such a state over time.

An audience listening to such a melody would have a bizarre experience. In the classical world, every member of the audience hears the same sequence of notes. But when a quantum musical state is observed, it can collapse into any one of the notes that make it up. The note that is formed is entirely random but the probability that it occurs depends on the precise linear makeup of the state.

And since this process is random for all observer, the resulting note will not be the same for each member of the audience.

Abstract:

We consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.

Physics arXiv: Quantum music
Volkmar Putz, Karl Svozil