Olbers’ Paradox: the appearance of the universe

Olbers’ Paradox: the appearance of the universe

In this page, I will think about the universe from the Olbers' paradox. The simple question that Olbers contemplated was a question that caught  the appearance of the universe. I will think about the appearance of the universe from the paradox of Olbers and Hubble 's law.

・What is Olbers’ Paradox?
・Cause of paradox
・Age of universe
・Is universe finite?

What is Olbers’ Paradox?

The Olbers’ Paradox is a question about the universe raised by scholar Heinrich Wilhelm Matthäus Olbers of the 19th century.

“There are many shining stars in this universe. If the universe is infinite in size, the number of stars will also be infinite. Then the sky seen from the earth should be filled with light from countless stars. 

In other words, the earth should always be illuminated by countless stars and there should be no night. However, day and night actually exist, and when the sunlight does not plug in at night, the sky of the earth becomes a night sky and some starlight shines only. Why is the night dark?”

 Olbers’ Paradox

Cause of paradox

Why does this contradiction arise? There is an error in the Olbers’ assumption. The mistake is to think of the history of the universe as infinite. Today, the age of the universe is considered to be limited. Then, what does it mean to consider the history of the universe as infinite? 

Usually we are not conscious, but the speed of light is not infinite speed. It takes time for the light of the stars that are far from the earth to reach. As shown in the figure, the starlight from infinity distance will reach the earth taking an infinite period of time. If the age of the universe was infinite and the beginning does not exist, the light of all the stars could fall on the earth. 

In other words, the assumption “The light of all the stars present can reach the earth” is wrong. The answer to Olbers' paradox is "because the age of the universe is finite". Hubble's Law (1929) gives proof about this.

 Olbers’ Paradox2

Age of universe

American astronomer Edwin Hubble announced the following observations. ”All of the galaxies have moved away from the earth. And the more distant galaxies, they are getting away from earth faster. That speed is proportional to the distance from earth.”(Look at the figure below. When t0, all things exist in the point, for example earth, sun, and etc. Starting from the point, the celestial body which move fast should be far from the point at a certain time t. We assume that each celestial object moves at a constant speed.)

This is called Hubble's law, and it is represented by the formula V = Hr(V is the recessional velocity, H is Hubble's constant, r is the proper distance) When the equation is transformed t = r / V = 1 / H, the age of the universe can be approximated as about 13.9 billion years. In other words, there is origin in the universe. Even if there are stars at 13.9 billion light years away or more, the light cannot reach the earth yet. So, the light of an infinite number of stars never falls down.
Hubble's law
 Olbers’ Paradox3
The dotted line is more than 13.9 billion light-years away.
Only the light within the dotted line (finite range) can reach the earth.

Is universe finite?

About Olbers’ Paradox, some people say “because the universe is infinite”. I think that this explanation is not accurate. Even if the size of the universe is limited, there are cases where stars can be seen indefinitely. Interestingly, Hubble’s law applies to any part of the universe. That is, the earth is not the center of the universe. On the contrary it is suggested that there is no center in this universe. 

There are various theories of the universe' appearance, full proof is still not done. However, the appearance of the universe presumed from the Hubble's law is close to the surface of the rubber balloon. It is not the rubber balloon itself but the surface of the balloon. The point marked with a pen on the surface of the balloon represents our galaxy or star. Even though the size of the balloon surface (universe) is limited, if the universe has a circulating structure for light, the star will be visually present indefinitely. Therefore I think that explanation with the size of the universe is complicated and inappropriate.

This time I imagined the appearance of the universe from Olbers’ Paradox and Hubble's law. If there are opportunities next time, I will describe the universe more.