As the universe expands, it is continually subjected to energy shifts, or “quantum fluctuations,” that send out little pulses of “sound” into the fabric of spacetime. In fact, the universe is thought to have sprung from just such an energy shift.
A recent paper in the journal Physical Review Letters reports a new mathematical tool that should allow one to use these sounds to help reveal the shape of the universe.
The authors reconsider an old question in spectral geometry that asks, roughly, to what extent can the shape of a thing be known from the sound of its acoustic vibrations?
The researchers approached this problem by breaking it down into small workable pieces, according to author Tejal Bhamre, a Princeton University graduate student in the Department of Physics.
To understand the authors’ method, consider a vase. If one taps a vase with a spoon, it will make a sound that is characteristic of its shape. Similarly, the technique Bhamre and her coauthors developed could, in principle, determine the shape of spacetime from the perpetual ringing caused by quantum fluctuations.
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at least in the case of the Euclidean signature, is the discipline of spectral geometry.