Randall Munroe and the Size of the Observable Universe

Randall Munroe of the fabulous webcomic xkcd has a great logarithmic height poster showing the size of everything from folks all the way up through the edge of the Solar System, on to the radius of the observable Universe. As a logarithmic plot, each gap of the same size vertically on the plot represents a doubling of the distance from the surface of the Earth; this is why he can show things of such vastly different scales as people and the whole Universe in the same plot.

But, wait, I thought you cosmologists kept saying that the Universe was infinite! How can this picture show the whole Universe then?

It doesn’t… it shows the observable Universe. Because the Universe is only 14 billion years old, and the speed of light is finite, we can only see things that are as far away as light has had time to reach us from. There is more Universe beyond that, but the light hasn’t reached us from it yet; the part of the Universe beyond our horizon is not the observable Universe.

But wait… if the Universe is only 14 billion years old, then, we should only be able to see things that are 14 billion light-years away… yet the xkcd pictures says the top of the Universe is 46 billion years away. What’s up with that?

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