Truncalis: Asymptotic Series QED
Nuclear & Particle Physics arc, page 184 of 193. Back to The Pixelated Physics Universe
Who they are
Truncalis has one line, and says it often: “More terms. worse answer.”
Truncalis is a character of the Nuclear & Particle Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
QED perturbation series is (generally argued to be) asymptotic, not convergent: adding terms improves the answer only up to an optimal order (heuristically ~1/α ≈ 137), after which it worsens.
$$ \begin{gathered} n_{\text{opt}} \sim \frac{1}{\alpha} \approx 137 \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $n_{\text{opt}}$ | heuristic optimal truncation order | — |
| $\alpha$ | fine-structure constant | — |
Sources
Crossovers
Truncalis meets Perturbelle (Perturbation Theory). Perturbelle keeps only the first-order shift ⟨n|V|n⟩. Truncalis warns that in QED, adding more and more orders improves the answer only up to a point, because the series is generally argued to be asymptotic.
Truncalis meets Counterterra (Renormalization). Counterterra makes each order of the series finite. Truncalis knows that the series as a whole may still diverge. Finite terms do not guarantee a convergent sum.
Wear the lore
Concept keywords: Asymptotic Series QED, Truncalis, Nuclear & Particle Physics, physics lore, Pixelated Physics