The time-energy uncertainty principle is really a time-frequency uncertainty principle in disguise

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

Categorization

• XREF: Connects the book’s core time-frequency theme directly to quantum mechanics, echoing the reader’s own background knowledge of Heisenberg. — connects to: The uncertainty principle relates resonance width to decay time; Every wave-like quantity has an uncertainty principle tying its Fourier transform pair — Eric J. Heller, Why You Hear What You Hear- An…, 433; Position and velocity are Fourier transform pairs, hence obey an uncertainty principle (+2 more)
• DEFINE: Clarifies the structural identity between quantum uncertainty and time-frequency resolution limits.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 434

Broader Connections

• Every wave-like quantity has an uncertainty principle tying its Fourier transform pair #expands (0.95) — Eric J. Heller, Why You Hear What You Hear- An…, 433
• Time and frequency resolution cannot both be improved simultaneously #expands (0.90) — Toole, Floyd E, Sound reproduction- the acoustics and…, 951
• Position and velocity are Fourier transform pairs, hence obey an uncertainty principle #exemplifies (0.85)
• Frequency measured in Hertz is dimensionally inverse seconds #corroborates (0.80)