Olbers'
Paradox: Why is the sky dark at night?
- Previously explored by
Digges (1576),
Kepler (1620),
Halley (1721), and
de Cheseaux (1744)
- Publicized by Wilhelm Olbers (1826) as a paradox of nature
- Solution proposed by Edgar Allen Poe (1848)
- Imagine that the universe is static, infinite in size, eternal in age,
and uniformly filled with stars. As we look out along any line of sight, we
must eventually see a star. Distant stars will appear much fainter than
nearby stars; their flux will follow the inverse square law and fall off as
the square of the distance. However, the number of stars will increase, with
the square of the distance, and so there will be far more of them.
| Flux per star | ~ | 1 / R2 |
| Number of stars | ~ | R2 |
| Total Flux | ~ | R2 / R2 ~ 1 |
These two effects cancel, and so along any line of sight the aggregate
light from distant stars should shine a brightly as do nearby stars. The
night sky should thus be brightly lit up, in all directions.
- Given this, why doesn't the night sky shine uniformly, as bright as the
nearby stars?
- If the universe has a finite age, then enough time may not have passed
for the light from the most distant stars to reach us yet.
- If the universe is expanding in size, then the light from distant stars
will be cosmologically redshifted to longer wavelengths (thus appearing to be
longer wavelength, lower energy light).