Broadling: Natural Linewidth
Quantum Foundations arc, page 24 of 193. Back to The Pixelated Physics Universe
Who they are
Broadling has one line, and says it often: “Short talk. broad line.”
Broadling is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Natural linewidth: a state with lifetime τ has energy width Γ = ħ/τ (Lorentzian line).
$$ \begin{gathered} \Gamma = \frac{\hbar}{\tau} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\Gamma$ | natural energy width | J |
| $\hbar$ | reduced Planck constant | J·s |
| $\tau$ | lifetime | s |
Sources
Crossovers
Broadling meets Δ-X (Heisenberg Runner / Uncertainty Principle). Δ-X trades position for momentum. Broadling makes the same kind of trade with time and energy: a state that lives only for a time τ has an energy width Γ = ħ/τ. Neither of them can get a sharp value of both quantities at once.
Broadling meets Densara (Fermi's Golden Rule). Densara sets the decay rate Γ. Broadling turns that rate into an energy width, ħ times the rate. A fast transition makes a broad spectral line.
Broadling meets Flipwarden (21 cm Hydrogen Spin-Flip Line). Broadling's rule makes Flipwarden's line extraordinarily sharp. The hydrogen spin-flip state lives about ten million years, so the 21 cm line's natural width is tiny. Its observed width comes from the gas's motion.
Wear the lore
Concept keywords: Natural Linewidth, Broadling, Quantum Foundations, physics lore, Pixelated Physics