Nocturna: Olbers' Paradox

Cosmology & the Sky arc, page 142 of 193. Back to The Pixelated Physics Universe

Who they are

Nocturna wraps herself in the night sky and asks the oldest question in astronomy: why is it dark?

Nocturna is a character of the Cosmology & the Sky arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

The physics

If the universe were infinite, eternal and evenly filled with stars, every line of sight would end on a star and the night sky would blaze. A thin shell of radius r holds a number of stars growing as r², while each star's light falls as 1/r², so every shell adds the same brightness. The way out: the universe has a finite age, t₀ ≈ 13.8 billion years, so light from beyond a certain distance has not reached us, and redshift dims what does arrive.

$$ \begin{gathered} dN_{\star} \propto r^{2}\,dr, \qquad F_{\star} \propto \frac{1}{r^{2}} \ \Rightarrow\ dF_{\text{shell}} \propto dr \\ t_0 \approx 13.8\ \text{billion years} \end{gathered} $$

Symbol Meaning SI unit
$r$ distance from the observer to the shell m
$dr$ shell thickness m
$dN_{\star}$ number of stars in the shell 1
$F_{\star}$ light received from one star W/m²
$t_0$ age of the universe, about 4.35 × 10¹⁷ s s

Honest caveat: Dust does not work: over time it would heat up and glow.

Sources

Crossovers

Nocturna meets The Silence Beyond (Cosmic Horizon / Observable Limit). Nocturna asks why the night is dark. The Silence Beyond gives part of the answer: the universe has a finite age, so light from beyond the horizon has not reached us. Expansion and redshift dim the rest.

Nocturna meets Fermia (Fermi Paradox). Nocturna's paradox about the dark sky has an answer. Fermia's paradox about a silent galaxy does not. One is solved physics; the other is still an open question.

Wear the lore

Concept keywords: Olbers' Paradox, Nocturna, Cosmology & the Sky, physics lore, Pixelated Physics