In the fractal universe the question of finiteness and endlessness are mathematically puzzling....
...The nearest star is the sun and the light takes about eight minutes to reach the earth from the sun. The sun is about 500 times more distant from us than the moon. The next nearest star is 4.3 light years away, which means that it is more than 240 000 times farther away from us than the sun. Sirius, which is the brightest star in the sky, is the fifth nearest star. It is 8.6 light years away. Rigel, which lies in the constellation Orion, is the seventh brightest star. Its distance is estimated to be about 90 times more than Sirius. Some stars are even farther away than Rigel. The light from those stars take many thousands of years to reach our eyes. Though they may appear as dots in the sky some of them are much more brighter and bigger than our sun. For example, Rigel is so bright that if it was placed at the distance of the sun it would have shone 40 000 times brighter than the sun. Sirius is not so bright. It is only about 23 times more shining than the sun. But it appears brighter than Rigel because it is much closer to us.
The sun is situated about 28 000 light years away from the centre of the
island universe to which all the stars in the sky belong. The size of the disk
that forms our galaxy is about 100000 light years across. There are millions of
such islands of stars in the universe. The galaxy closest to us is called
Andromeda galaxy. Its distance is estimated to be around 2.5 million light
years. These innumerable galaxies are not evenly distributed in the sky. They
form clusters of galaxies. A cluster may contain hundreds or thousands or more
of such galaxies. Our galaxy together with Andromeda belong to a small local
group of galaxies containing more than thirty galaxies. The local group is
believed to occupy an area spanning more than 10 million light years.
The clusters of galaxies also are not evenly distributed in the sky. The
clusters themselves clump together to form superclusters. The Local Group is a
part of a larger structure called the Local Supercluster, or Virgo supercluster,
which contains around hundred groups and clusters of galaxies. It is estimated
to be about 200 million light years in diameter. The biggest supercluster so far
observed is estimated to be nearly 500 million light years in size and it lies
several billions of light years away.
Do there exist even bigger structures than those already discovered? Where does the universe really ends?
...In this book I shall explain this new theory, where the universe is a fractal. It is not only a fractal but it could, in fact, be a multifractal. One may use a simple example of a cauliflower to describe the way the fractal universe may have been constructed. A cauliflower is made of similar smaller flowers, which in turn are made of similar flowers of even smaller size, which in turn again are made of even smaller flowers and so on. However by picking the smallest size and looking through a magnifying glass one will discover a structure which is similar to the structure of the original big cauliflower. The structures in the universe appears to be built in a similar way: The big universe images itself in the smaller and smaller cosmic objects, which it embodies. The example of the cauliflower is more simplistic than the hierarchical building of the universe. I shall describe it later.
Where do these hierarchical structures end? Will the superclusters form super superclusters and super superclusters will in turn form super super superclusters and so on? The fractals in nature, where one may see such hierarchical construction, often are delineated by boundaries in space. However, the descriptions of these boundaries could be mathematically intriguing. In the geometry we have learnt from school, we know that a line possesses a dimension 1, a surface has a dimension 2, and the volume is 3 dimensional. In contradiction to this geometric concept, a fractal line may possess a fractional dimension between 1 and 2 and a surface may not be two dimensional. It may have a fractional dimension between 2 and 3 depending on the crumpling, which may hide fractals.
In the fractal universe the questions of finiteness or endlessness are
mathematically intriguing and the answer depends on the way one makes the
measurements. It is more relevant to ask if the hierarchical building in larger
and even larger scales of cosmic structures may ever come to an end? The
observations only reveal that the hierarchy exists up to the scale of the
superclusters. Whether it may continue beyond that size can only be speculated
only with a model which may explain the formation of such a fractal universe.
Read more ....
Copyright ©2006 Anup Rej, All Rights Reserved.
