- #1
HowardTheDuck
- 33
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I'm having a bit of a problem getting my head around Olber's paradox. The explanations haven't convinced me (I'm sure the fault is with me). According to Wikipedia:
"To show this, we divide the universe into a series of concentric shells, 1 light year thick (say). Thus, a certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away, say. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2,000,000,000 to 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear four times dimmer than the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell."
Yes, I can agree that the second shell has more stars, but those stars are spread over the greater surface area of the second shell, and they don't seem to take that into account. When you're looking up from the earth, surely the only factor that matters is the density of stars in the shell, not the total number (it is the surface density which decides how bright a region of sky is). It seems to me that the density (stars per surface area) is going to be the same for all shells (more stars, but spread over more area). Therefore, the deciding factor is the distance - and that means that the further shells will be less bright.
So, yes, as Wikipedia suggests, the total light received from the second shell will be the same, but the total light received is surely irrelevant. The surface density is the same in all shells, and the distance is further, so the shell will appear less bright the further away it is.
At the very least, surely the Wikipedia explanation is wrong.
Am I wrong? Thanks.
"To show this, we divide the universe into a series of concentric shells, 1 light year thick (say). Thus, a certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away, say. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2,000,000,000 to 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear four times dimmer than the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell."
Yes, I can agree that the second shell has more stars, but those stars are spread over the greater surface area of the second shell, and they don't seem to take that into account. When you're looking up from the earth, surely the only factor that matters is the density of stars in the shell, not the total number (it is the surface density which decides how bright a region of sky is). It seems to me that the density (stars per surface area) is going to be the same for all shells (more stars, but spread over more area). Therefore, the deciding factor is the distance - and that means that the further shells will be less bright.
So, yes, as Wikipedia suggests, the total light received from the second shell will be the same, but the total light received is surely irrelevant. The surface density is the same in all shells, and the distance is further, so the shell will appear less bright the further away it is.
At the very least, surely the Wikipedia explanation is wrong.
Am I wrong? Thanks.
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