Olber’s Paradox Why is the night sky dark?

Night Sky

If you are in a big forest and keep walking you will bump into a tree If you are in a big (infinite) universe and keep going in a straight line you will bump into a star.

Newton thought the Universe was infinitely old and static Gravity makes the stars collapse towards their centre of mass There must be more stars pulling out to stop this happening And more outside these to stop them collapsing So the universe must be infinitely big or it would have collapsed Centre of mass

Remember Inverse Square Law As light travels it spreads out At a distance of 2d the light will have spread out over 4 times the area So the object will have quarter the brightness Apparent brightness is proportional to 1/d 2 d 2d

Imagine spherical shells surrounding Earth d 2d 3d Shell at 2d has 4 times the area, hence 4 times the volume. It contains 4 times as many starts so emits 4 times as much light 9 times as many stars Look in any direction

Each shell has same brightness Shell at 2d has 4 time as many stars Remember inverse square law They have ¼ brightness So apparent brightness of each shell is the same If the universe is infinite Then there are an infinite number of shells. Each shell has the same brightness If you add the light from each you get an infinitely bright sky

Here’s the Paradox So if the universe is infinitely big then the sky should be bright But the sky is dark So the universe is not infinitely big So it should have collapsed

What assumptions did Newton make? 1. The universe is infinitely old. 2.The universe is static 1. Hubble constant estimates age of universe about 15 billion years. Light from stars beyond 15 billion light years hasn’t reached us yet 2.The universe is expanding. Gravity slows the expansion and may eventually reverse it. (This depends on how much matter is in the universe.) Note that clouds of dust blocking light does not solve the problem because the clouds would heat up and re-radiate the energy