The uncertainty principle relates resonance width to decay time

Evidence

A famous Fourier transform pair involves quantum mechanics. Nature left the framers of quantum theory no choice: matter, mass, you and I, everything is ultimately a wave. The position of a particle (which is really a wave) and its velocity (momentum) are Fourier transform pairs, and are therefore subject to an uncertainty principle. This has the shocking consequence that the more certain we are about the position of a particle, the less we know about its velocity! The reverse is true too: the more we know about velocity, the less we know about position. This is known as the Heisenberg uncertainty principle. It reads ΔxΔυ ≥ ħ/2m, where m is the mass of the particle, Δx is the uncertainty in its position, Δυ is the uncertainty in its velocity, and ħ is known as Planck’s constant, which is a known number. Another example of a quantum uncertainty principle involves time and energy. In quantum mechanics, it takes a lot of time to pin down the energy of the system precisely. If we’ve followed a system for only a short time, then we are not very certain about its energy. That uncertainty principle reads ΔE Δt ≥ ħ/2. Thus time and energy are Fourier transform pairs, as are position and velocity. The Einstein quantum relation E = ħ(2πf) relates the energy with frequency, most often the frequency of light emitted or absorbed in a quantum transition that changes the energy. Thus the time-energy uncertainty principle is really another time-frequency uncertainty principle in disguise. — Eric J. Heller, Why You Hear What You Hear- An…, 434 (#expands, via linked claim)

Time and frequency are the Fourier transform pair that concern us in this book. There are many other examples of Fourier transform pairs: quantities that are related by a Fourier transform. Anything that behaves as a wave has an uncertainty principle connecting Fourier transform pairs. — Eric J. Heller, Why You Hear What You Hear- An…, 433 (#expands, via linked claim)

Categorization

• XREF: connects to: The time-energy uncertainty principle is really a time-frequency uncertainty principle in disguise — Eric J. Heller, Why You Hear What You Hear- An…, 434; Every wave-like quantity has an uncertainty principle tying its Fourier transform pair — Eric J. Heller, Why You Hear What You Hear- An…, 433; Attenuating a resonance’s spectral bump necessarily reduces its ringing (+3 more)

Broader Connections

• The time-energy uncertainty principle is really a time-frequency uncertainty principle in disguise #expands (0.90) — Eric J. Heller, Why You Hear What You Hear- An…, 434
• Every wave-like quantity has an uncertainty principle tying its Fourier transform pair #expands (0.80) — Eric J. Heller, Why You Hear What You Hear- An…, 433
• Attenuating a resonance’s spectral bump necessarily reduces its ringing #corroborates (0.75)
• Room modal bandwidths depend on decay time, not frequency #corroborates (0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2012
• Quantum uncertainty drives the early universe’s non-uniformity. #epitomizes (0.70) — Hawking, Stephen, A Brief History of Time, 247