Olbers’ Paradox: Problem

Hello everyone, today we are going to talk about Olber’s paradox. This is a very simple question, but it’s very interesting. Let’s get started. In 1823, German astronomer Heinrich Wilhelm Olbers

asked a simple but profound question: Why is the night sky is dark? We all know the night sky is dark, right?

But his argument is like this: If the universe is static, static means the universe is not expanding or not shrinking. That’s what people believed at that time, and if the universe has infinite number of stars, then any line of sight would end up with a star. Well in fact, the Milky Way galaxy, our Milky Way galaxy has one hundred billion stars inside. And in the uni- in the whole universe there are galaxies like Milky Way they are one, uh, one hundred billion galaxies like the Milky Way galaxy. So there would be, there is one hundred billion times one hundred billion stars in the universe, it’s almost infinite.

Then, when you look at the sky, any night outside would end up with a star. Then, the night sky should be as bright as daytime. However, we don’t, we know the night sky is dark, so, why? This schematic view graph shows what I just said, in any line of sight, if you look up the side, end up with a star. Then, if there’s an infinite number of stars in the universe, the night sky should be as bright as a star like this. The argument, his argument, is like this.

So, we’re here on earth observing the night sky, and sometimes we see a star nearby, and then these four starts are more distant, it’s actually twice as distant as the first star, and then we see because in the more distant universe the same angle subtends more area, so we see four stars in this case. Well, the distance is twice as far so these stars are actually one-quarter of the brightness of the first one so these stars are fainter. But, in this second layer there are four stars because volume is larger. So, each one of these stars are one-quarter of the brightness, but there are four. So, in total the second layer has the same brightness as the first layer.

The same argument for two, for the third layer too, these stars because distance is three times more distant, these stars are one-ninth of the brightness of the first star. However, there are nine stars in this third layer, so the total brightness of the third layer is the same as the first one. And then, this argument goes continues, it goes on and goes on and goes on. If there’s an infinite number of stars any line of sight will end up with a star, so the night sky should be as bright as the daytime. However, we all know the night sky is dark, it’s like this, dark sky, not like daytime.

So, what was wrong in this argument, what did I do wrong, in the argument so far? So this is an interesting question to ask, so please try to discuss, and then leave your opinion in the next step.