Olberís Paradox


The fallacy that Barrow and Tipler fall into with respect to ETIs is because they believe in the certainty of the scientific method.And it is a reliable and sound way to discover truths about reality provided it is applied within the correct set of assumptions.For an example of how this method can go wrong, we turn to 19th century astronomy. The explanation below is based on an analysis presented by physicist Hermann Bondi in his 1959 book The Universe at Large.I follow his description in general and add my own mathematical addition to what he presented based on Olbers.I add it, to show how Olberís paradoxical argument can be corrected.

19th century German astronomer, Heinrich Wilhelm Oblers first proposed an argument concerning starlight coming to Earth from distant galaxies in 1826. It later became known as Oblerís Paradox.Oblers made a few assumptions about our galaxy and the stars in it, and then proposed what to him seemed to be a paradoxical result.He wondered why the night sky wasnít full of starlight. It was well-known in this century that there were millions of distant stars. Moreover, he wondered with many millions of stars and numerous distant galaxies, why the flood of starlight reaching us didnít vaporize the Earth.First, lets look at his assumptions and then show how he calculated the intensity of incoming starlight to the Earth.


Oblers made the following assumptions.I have taken the most basic assumptions in the interest of brevity:


  1. All regions of space are like or similar to our own. That is to say, there are stars that radiate light to space.there is an average distance between stars and planets (if there were in fact other planets) and it would be similar to our region.


  1. The law of physics apply everywhere in the universe.


  1. The universe is static.


Hermann Bondi described Oblers argument based on the above assumptions.


Oblers built a model of the surrounding galaxies, and stars within them from the reference point of Earth.He envisions 2 spheres or shells as he called them.They are concentric circles with Earth at their center.The first circle is at a distance R. The volume of this sphere is equal to 4пR2.The second shell has a thickness H and has a volume of 4пR2(H).Let N represent the number of stars in shell 4пR2(H).Then the total number of stars would be 4пR2(H)(N).Let L represent the light sent out by any star in the second shell.So the total light sent out by all stars in the second shell is 4пR2(H)(N)(L).But, as stated earlier, Oblers wanted to know the intensity of the light coming to Earth, not just how much.He reasoned that the intensity I of any given star is defined by the equation I=L/4пR2.Thus to obtain the intensity total I, we must divide out the distance 4пR2.Now, we have a definite calculation of the intensity of starlight reaching Earth.It is clear that I=HNL should flood our planet with light.He tried to explain this paradox by considering nebula dust as an obstructing agent. He realized however, that these stellar bodies would be eventually irradiated themselves by all the incoming starlight and would only increase the flood of light to Earth.So, why didnít all the starlight streaming in vaporize Earth?


The answer is simple to us today.We know that the universe is expanding.The galaxies are receding from one another and every ray of starlight is actually getting farther and farther away from as it travels to Earth from all the receding galaxies.Actually, while a more rigorous treatment of light propagation would involve a differential geometric model of our universe, a simple modification to Oblerís treatment incorporating the present knowledge that the universe is expanding can be made. It would immediately correct the paradox, even using his model.


Lets assume that the outer shell volume is expandable. Thus, we modify the term 4пR2 to N4пR2

Where N represents a factor of expansion of the outer shell 4пR2


As stated previously, I=L/4пR2 describes the intensity of light of any average star


Replacing the spherical volume in this equation with the new term we get the following. Since all the other variables in this equation are known the only real variable is N.


I=L/ N4пR2.†† If we take the Limit of this equation we get


Lim I=L/N4пR2= 0

Lim N->∞


That is, as the outer shell expands toward infinity, the intensity of starlight reaching Earth tends to zero.And this is exactly what the Big Bang theory predicts.


A well-formed model can be wrong, as the above analysis shows. Lacking factual information, this flawed model would appear to be correct.Oblerís paradox is reminiscent of the logical fallacy that Drs. Barrow and Tipler are making, in that it used the Scientific Method to arrive at the wrong conclusion.

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