Olbers' Paradox Calculator

The paradox was discussed by various thinkers long before Olbers. Thomas Digges (1576), Johannes Kepler (1610), Edmund Halley (1720), and Jean-Philippe de Cheseaux (1744) all considered the problem. Olbers discussed it in 1823, giving it widespread attention. Edgar Allan Poe suggested a finite age resolution in his prose poem Eureka (1848).

If the universe is about 13.8 billion years old, we can only receive light from stars within our light horizon. No matter how many stars exist beyond this distance, their light has not had time to reach us. The volume of the observable universe contains a finite amount of starlight, insufficient to brighten the entire sky to solar surface brightness.

Cosmic expansion redshifts distant starlight to longer wavelengths, reducing each photon's energy. Starlight from galaxies billions of light-years away is stretched from visible to infrared or even microwave wavelengths by the time it reaches us. This dramatically reduces the intensity of the received radiation. The expansion effect is arguably more important than the finite age in resolving the paradox.

Yes. The CMB is the redshifted thermal radiation from the surface of last scattering (the early hot universe). In a sense, every line of sight does terminate on glowing matter — the CMB — but this radiation has been redshifted from about 3,000 K visible light to 2.73 K microwave radiation over 13.8 billion years. In the microwave band, the sky is indeed uniformly bright — just as Olbers might have expected, but at a much lower energy.

Current estimates suggest about 10^22 to 10^24 stars in the observable universe (roughly 200 billion trillion stars). This comes from estimating about 2 trillion galaxies in the observable universe, each containing on average hundreds of billions of stars. The uncertainty spans orders of magnitude due to the difficulties of counting faint, distant, and obscured galaxies.

A static universe with finite age would be somewhat brighter than ours, because there is no redshifting to reduce photon energy. However, if stars formed relatively recently and the universe had no beginning-state radiation (unlike our Big Bang), a relatively young universe could still have insufficient integrated starlight to make the sky bright. The combination of finite age and expansion makes our sky dark.

It tells us the universe cannot be simultaneously infinite, static, eternal, and uniformly filled with stars. The paradox was historically used to argue for a finite universe. We now know the correct resolution involves the finite age and the expansion. It is a beautiful example of how a simple observational fact — the dark night sky — constrains fundamental cosmological properties.

If every line of sight terminated on a stellar surface in an infinite, static, eternal universe, the sky brightness would equal that of the average stellar surface. Using the Sun as typical, every point of the sky would be about as bright as the surface of the Sun (about 2x10^7 W/m^2/sr). Earth would receive as much radiation from the dark sky as it does from the Sun today — making the surface temperature around 6,000 K. Life as we know it would be impossible.

Yes. A gravitational version asks why the universe has not collapsed under its own gravity (resolved by expansion and dark energy). A thermodynamic version asks why the universe is not in thermal equilibrium (resolved by its young finite age and low entropy initial state). These related paradoxes all point to the same resolution: the universe had a beginning and is evolving away from it.