If the universe is infinite and filled with stars, every line of sight should hit a star. The night sky should be BLINDINGLY BRIGHT—as bright as the surface of the Sun! So why is it dark?
Imagine the universe is infinite, static, and uniformly filled with stars. Look in any direction. Your line of sight must eventually hit the surface of a star! If every point in the sky is a star surface, the entire sky should glow like the Sun.
You might think: "Distant stars are dimmer—surely that helps?" Let's check:
Every shell—near or far—contributes the same total light! With infinitely many shells, total brightness → INFINITY.
The universe is only ~13.8 billion years old. Light from stars beyond 13.8 billion light-years hasn't reached us yet. We can only see a finite "observable universe."
Stars burn for limited time. Even in an eternal universe, stars would need ~10²³ years to fill the sky. The universe is too young by a factor of 10 trillion!
Space itself is expanding. Light from distant galaxies gets redshifted—stretched to longer wavelengths. Visible light becomes infrared, then microwaves, invisible to our eyes.
Before 380,000 years after the Big Bang, the universe was opaque plasma. There are no stars older than ~13.6 billion years. The light simply doesn't exist!
The Cosmic Microwave Background (CMB) fills all of space with radiation at 2.7 Kelvin. It's the "afterglow" of the Big Bang, redshifted from 3000K orange light to invisible microwaves. In microwave vision, the entire sky glows uniformly—Olbers was right after all!
Olbers' paradox, posed in 1823, was one of the first hints that the universe couldn't be static and eternal. It foreshadowed the Big Bang theory by over a century. The darkness of night is evidence that we live in a young, dynamic, expanding cosmos.