Yes it is relevant. One possible solution to Olbers' paradox in a steady state universe is a fractal structure.
It's not enough though to just have galaxies. Because if you have galaxies approximately equally spaced out to infinity (randomly spaced but uniform density), then still, any line of sight from your eye in any direction would eventually meet a star in one of the galaxies. It would pass through many galaxies without meeting any star - but eventually it would hit a star, 100% probability of that in an infinite universe with randomly arranged equally spaced galaxies. So as with the paradox for a random distribution of stars, you still find that the entire sky has to have the same temperature as the surface of a star.
But the galaxies are also arranged in clusters of galaxies, and those clusters are arranged in superclusters. And the superclusters in even larger structures (which is about as far as it goes to our knowledge). If that kept going on to larger and larger heirarchies - that's one other possible solution to Olbers' paradox. In such an infinite fractal universe, though it has many stars, and locally the density can be high, the average density of stars can be zero, in the limit, as you go to larger and larger regions.
Technically, in an infinite universe, with zero averaged out density in the limit, Olbers' paradox no longer applies. If the averaged out density is non zero and the distribution is random you still get the paradox.
(If the distribution is non random, you could figure out a distribution of stars that makes sure that when seen from some special point, all the other stars in the galaxy are hidden behind nearby stars - so then in such a universe, some points in the universe may have lower temperatures than the surface of a star.)
Of course are other effects. In an expanding universe, then the further away a star is, the more it is red shifted. So even an infinite uniform density steady state expanding universe - if such was possible (e.g. matter continually forming everywhere in small quantities to keep the density the same) - could get around Olbers' paradox in that way. The 3 degree background radiation instead of coming from the big bang, would come from all those red shifted distant stars.
The problem with all this though is the shape of the 3 degree background radiation curve. It's this strange shape - the black body curve:
Measured dots shown in red, and the theoretical curve in green. The error bars are too small to see on the curve at this resolution.
By comparision, black body curves for other temperatures, and compared with the classical theory which fails spectacularly to predict it.
The black body curve was one of the early success stories of quantum mechanics.
It has this property that if you add together black body curves from many sources at different temperatures, the result is no longer the same shape.
So the fact that the three degree background radiation curve so exactly fits a black body curve shows that all the light, or almost all, comes from a source that is at the same temperature throughout.
That's what really put an end to the steady state theory. It held out for a few years but, as the black body curve was measured more and more precisely, it was really hard to think of any other explanation except a single event in the distant past when all the universe was at the same temperature, i.e. a "Big Bang".
It simply won't work to try adding together lots of sources from individual stars at different temperatures. If you do that you might (depending on the temperature distribution of the stars) get something more like this:
Or something in between more likely, or it could be other shapes, depending on the temperature distributions of the stars. But apparently, it's not possible to get a black body shaped curve, with such an exact fit as we observe - from mixing together black body curves with different temperatures from each other.
(There's an early paper on this, where the author goes into this in mathematical techy detail which I remember reading, but can't find it just now, if anyone knows what it is, do say in the comments.)
If you wanted to develop a modern Static universe, this is one of the most challenging observations you'd need to somehow explain with your model.
It's not enough though to just have galaxies. Because if you have galaxies approximately equally spaced out to infinity (randomly spaced but uniform density), then still, any line of sight from your eye in any direction would eventually meet a star in one of the galaxies. It would pass through many galaxies without meeting any star - but eventually it would hit a star, 100% probability of that in an infinite universe with randomly arranged equally spaced galaxies. So as with the paradox for a random distribution of stars, you still find that the entire sky has to have the same temperature as the surface of a star.
But the galaxies are also arranged in clusters of galaxies, and those clusters are arranged in superclusters. And the superclusters in even larger structures (which is about as far as it goes to our knowledge). If that kept going on to larger and larger heirarchies - that's one other possible solution to Olbers' paradox. In such an infinite fractal universe, though it has many stars, and locally the density can be high, the average density of stars can be zero, in the limit, as you go to larger and larger regions.
Technically, in an infinite universe, with zero averaged out density in the limit, Olbers' paradox no longer applies. If the averaged out density is non zero and the distribution is random you still get the paradox.
(If the distribution is non random, you could figure out a distribution of stars that makes sure that when seen from some special point, all the other stars in the galaxy are hidden behind nearby stars - so then in such a universe, some points in the universe may have lower temperatures than the surface of a star.)
Of course are other effects. In an expanding universe, then the further away a star is, the more it is red shifted. So even an infinite uniform density steady state expanding universe - if such was possible (e.g. matter continually forming everywhere in small quantities to keep the density the same) - could get around Olbers' paradox in that way. The 3 degree background radiation instead of coming from the big bang, would come from all those red shifted distant stars.
The problem with all this though is the shape of the 3 degree background radiation curve. It's this strange shape - the black body curve:
Measured dots shown in red, and the theoretical curve in green. The error bars are too small to see on the curve at this resolution.
It has this property that if you add together black body curves from many sources at different temperatures, the result is no longer the same shape.
So the fact that the three degree background radiation curve so exactly fits a black body curve shows that all the light, or almost all, comes from a source that is at the same temperature throughout.
That's what really put an end to the steady state theory. It held out for a few years but, as the black body curve was measured more and more precisely, it was really hard to think of any other explanation except a single event in the distant past when all the universe was at the same temperature, i.e. a "Big Bang".
It simply won't work to try adding together lots of sources from individual stars at different temperatures. If you do that you might (depending on the temperature distribution of the stars) get something more like this:
(There's an early paper on this, where the author goes into this in mathematical techy detail which I remember reading, but can't find it just now, if anyone knows what it is, do say in the comments.)
If you wanted to develop a modern Static universe, this is one of the most challenging observations you'd need to somehow explain with your model.
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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