Big Bang Theory Real or Imagination
(View Related Article: Birth of the Universe – The Mathematics of It)
Recently some of my young relatives asked me with some concern, what they should believe about the birth of the universe. Should they believe in Big bang theory. To them the big bang theory is mere imagination devoid of any mathematical or scientific observations.
They looked confused but curious. They stated that in the absence of concrete scientific observation, why not simply believe that Almighty created the universe with an order and it happened.
I am a firm believer in Quran and I believe my religion does not encourage dogma; instead insists upon us to contemplate the universe to better understand the creator. However this must be noted that the universe is so huge that the more we learn about it, the more we admit that how limited our knowledge it.
I would like to quote Albert Einstein here. “ As our circle of knowledge expands, so does the circumference of darkness surrounding it.” The more we advance with our research and observations, the more complex the universe looks. Today the observable universe is 92 billion light years wide and it is still expanding. We are still in total darkness as to what is the limit of the universe.
The famous 17th century scientist and astronomer Galileo Galilei, whose contribution towards the study of universe is commendable, especially in spite of such strong resistance from the church, once stated quote “I believe bible is the words of God. But it is not a book of science and astronomy. You cannot understand the universe, without the knowledge of mathematics” unquote.
I endorse the same view. To understand the universe with the help of mathematics, you don’t have to compromise on your faith in Quran, Bible or any holy book.
Now I will try to explain the birth of the universe with the observable scientific information and mathematical interpretation. We all know that the scientists believe that the universe came into being with a big bang or a command by almighty out of nothing. With one bang the matters and energy which remained squeezed to a singularity (a dimensionless entity) were released 13.7 billion years ago and gradually formed into this universe what we observe today. To understand this phenomenon I will explain in steps so that a common man can understand the scientific principle behind these theories.
To accept this theory we have to first accept that such a huge mass can be squeezed to zero dimension and all mass has been converted into energy.
Mass Energy Equivalence
The students of science or otherwise are aware of Albert Einstein’s famous formula E=mc2. In fact Albert Einstein did not write this formula in this format. In one of his scientific publication of his miracle year 1905 he wrote a sentence.
If an unstable matter releases energy “L” in the form of radiation, then its mass must be reduced by a value L/V2. Where V is the speed of light.
Using the present day abbreviation for Mass, Energy and Speed of Light. The formula will be written as m = E/C2. Or more commonly accepted E = m * C2. This means that mass can be converted into energy and energy can be converted into mass. Before I go for the more complex explanation of this phenomenon, I will explain one of the simplest example of this mass energy equivalence.
We know that smallest and simplest of all atoms is Hydrogen (The first element on the periodic table). It has one proton and one electron.
Mass of one proton is 1.6727 x 10-27 Kg
Mass of one electron is 9.11 x 10-31 Kg
According to the laws of classical physics (Newtonian physics) mass of one hydrogen atom should be equal to mass of one proton and mass of one electron. However the mass of one hydrogen atom is 1.6 x 10-27Kg which is even less than the mass of one proton. Where did the excess mass disappear? That mass has in fact been converted into energy because the protons and electrons are in continuous vibration. Vibration requires energy and energy is neither manufactured nor destroyed. Hence the required energy has been extracted from the mass itself.
Let me clarify why I am using the unit of mass in Kg and not in gram of milligram. For figures which are to be used in mathematical calculations, we have to first select a unit system. In electrical engineering and physics we use MKS system of measurement. Where
Unit of length is meters m
Unit of mass is Kilograms Kg
Unit of time is seconds s
Now coming back to the main subject of how the universe was borne from singularity it is imperative that we first understand how a star thousands or million times more massive than the sun ultimately gets squeezed into a black hole and then into a singularity. This is easy to understand because this theory is bases upon credible scientific observations.
Life and Death of a Star
We know that stars are made of extremely hot gases. Gravity of the sun is some 27 times that of the earth (using the formula g=GM/r2) . Let us consider the same gravity for a massive star (it is not possible to compute the gravity of the star in the absence of figures pertaining to mass and diameter).Gravity of the sun by putting the parameters of the sun (in MKS system) will be;
Gsun =6.67*10-11 x 2*1030 /(0.7*109)2 = 6.67*2/(0.7)2 x 10-11-18+30
Hence Gsun = 27.224 x 10 = 272.24 m/sec/sec
Earth gravity has no significant effect on the size of the earth because earth is made of rocks and metals. Gravity of 8.91 m/sec/sec cannot squeeze the earth. On the contrary the stars are made of hot gases. Hence a gravity 27 times or larger than that of the earth tends to squeeze and collapse the star. This collapse increases the temperature of the inner core of the star (25 -30 % of the external diameter). When the temperature of the inner core reaches in excess of 14 million Kelvin, this imparts enough energy in hydrogen atoms and start the fusion of hydrogen atoms. They fuse together to create a larger atom which is helium. 4 hydrogen atoms fuse together to form one atom of helium plus some energy.
This is interesting to note that the mass of one helium atom is less than that of 4 hydrogen atoms combined by a value 0.048 x 10-27 Kg. This is this mass which has been converted into energy (E = mc2). The energy is released in the form of gamma rays which race towards the outer edge of the star. These gamma rays counter the inner collapse of the star by gravity, and thus maintain the size of the star.
Gamma rays due to extremely high kinetic energy emanate from the core and rush towards the edge of the star. In the course of this travel, collides with hydrogen and helium atoms, get sucked into the atoms, then release themselves and ultimately reach the edge of the star in about a million years (it takes about 100,000 years for a single gamma ray photon to reach the edge of the sun after releasing from the core). In this process they lose most of the energy and the gamma rays turn into light waves of lesser energy i.e. ultraviolet, visible lights and infrared. These are the lights (UV, visible and infra-red) what we on earth receive from the sun. Also 14 million Kelvin of temperature is reduced to 5800 Kelvin at the surface of the sun and the star.
In due course, which may go for a billion years, all hydrogen atoms are consumed and turned into Helium. Sun consumes about 620 million tons of hydrogen each second. Massive stars will consume more. At the end of this process, almost all hydrogen atoms are consumed. Hydrogen will remain on the extreme edge of the star and remaining volume including the core will be full of helium. The temperature of the core may reach 70 million Kelvin. However this temperature is not adequate to trigger fusion of helium atoms. The core stops producing gamma rays and there is no longer any force to counter the gravitational collapse. The star gets squeezed, thus further increasing the temperature of the core until the temperature of the core exceeds 100 million Kelvin. At this temperature helium atoms get sufficient energy to start fusion and the process of gamma rays release restarts and the star regains its size due to balance between gravitational force and the gamma rays.
This process continues in the following sequence producing heavier atoms after each step.
Hydrogen (H) – Helium (He) 70 million K
Helium (He) – Carbon (C) 200 million K
Carbon (C) – Oxygen (O) 800 million K
Oxygen (O) – Neon (Ne) 1200 million K
Neon (Ne)– Silicon (Si) 1800 million K
Silicone (Si) – Iron (Fe) 2500 million K
The star will produce all the elements from atomic no. 1 (hydrogen) to atomic no. 26 (Iron)
The star will appear like this after the core is full of iron atoms.
When the core is full of iron (heavy element) in gaseous state, an interesting phenomenon takes place. Fusion of iron is not an exothermic event, rather it is endothermic. That means at extremely high temperature iron atoms may be subject to fusion but will not release any energy. Hence the release of gamma rays which was so far countering the gravitational collapse of the star, will cease forever. The star will start collapsing under its own gravity so as to hugely increase the temperature of the star and it will become a supernova or a red star. The supernova is so bright that in a week’s time the supernova will release so much energy as much it has released in its entire life span. Because of its extreme brightness supernovas are observed from the earth and recorded. If you hear a reference SN1964, this represents a supernova which was observed in the year 1964.
The supernova or the red star will become so hot that it cannot remain stable. Ultimately it will explode and throw all the heavy elements away from it with a speed of 30000 Km per second. This is how planets are formed. The extremely high temperature of the supernova creates the heavier elements from Cobalt to Uranium which are thrown out. In this process the elements from atomic no 1 (hydrogen) to atomic no. 92 (uranium) are produced. That’s why the stars are also called element factory.
However even after throwing the heavy elements, the process of the gravitational collapse will continue and cause the electrons which were present on the orbits surrounding the nucleus, to be pulled tightly with the nucleus. The electrons having one negative charge and protons having one positive charge, will neutralize each other’s charges and convert into a zero charge entity i.e. neutrons. The star will become a neutron star. The size will be drastically reduced.
An atom comprises of 99.999999999999% space because the electrons orbit far away from the nucleus. When this space is squeezed to zero, the size of the star will be reduced to a diameter of 70 – 80 KM but containing all the mass of the original star. Neutron star will be so dense and its gravity so immense (of the order of 4 x 1012 m/s/s) that one table spoon of neutron star dust will weigh about 5 billion tons.
You may ponder that the star has been losing mass through fusion which was converted into energy. Also it has thrown out the heavy element out of it, then how the mass remains the same. In fact the total mass, the star will lose through fusion process as well as the mass thrown out by the supernova, amounts to not more than 0.7% of its original mass. Hence it is considered negligible for the purpose of calculations and case study.
Here it is worth noting why I am not giving the example of our sun, and talking about an imaginary star more massive than the sun. In fact sun is a small star and due to its limited mass, it will not decay into a neutron star or to a black hole.
According to Chandrasekhar limit (Dr. Chandrasekhar Subramanian was one of the greatest Astro-physics scientist of the 20th Century.), a star must be at least 1.4 times more massive than the sun to become a neutron star and must be at least 5 times more massive than the sun to become a black hole.
If the star is massive enough the process of collapse will not stop after decaying to a neutron star. Consider the formula of the force one Kg load on the star in its original condition and after becoming a neutron star.
The force applied on the star due to a weight of 1 kg
Force applied F = G x M x m/r2 where G is the gravitational constant (6.67 x 10-11), M is the mass of the star, r is radius of the star which is reduced to 50 Km (from the original value of millions of KM) when it is reduced to a neutron star and m is 1 Kg.
G and M remain constant ‘r’ has been drastically reduced for a neutron star, the force applied on the neutron star will be millions of time larger. There are cosmic pressures, there are meteors hitting the neutron star, hence the star continues to shrink so that at one stage the star is reduced to black hole.
Black hole is where the scape velocity is equal to or larger than the speed of light. For a star 10 times massive more massive than the sun, let us calculate the diameter of a black hole.
In order to compute the scape velocity of a planet or the star, the kinetic energy of the projectile due to speed should be equal to the potential energy due to gravity, both working in the opposite directions.
Hence ½ m V2 = G*M*m/ r.
G is the gravitational constant (6.67 x 10-11), M is mass of the star (2 x 1031 Kg for a star 10 times more massive than the sun), m is the mass of the projectile whose value is not important because ‘m’ on either sides of the equation will neutralize each other, V is the escape velocity which in case of a black hole is equal to the speed of light ‘C’ (3 x 108m/s). Applying these values in the formula
r = 2 G*M/ V2 = 2* 6.67 *10-11 * 2*1031/ (3 x 108)2 = 29.6 Km
This means that when the star(10 times more massive than the sun) is squeezed to a diameter of 60 Km it becomes a black hole meaning thereby that anything, matter or even light approaching the border of this diameter cannot escape and will be sucked in. The gravity of the black hole is infinity and due to gravity time dilation, time will freeze.
The boundary of the black hole is called event horizon and the radius is called Schwarzschild radius. Thus the star has been squeezed to a black hole. However the squeezing of the massive star does not stop there. It is further squeezed due to cosmic pressures and ultimately turns into a singularity which is a dimensionless entity. Entire mass of the star which was had a mass 2 x 1031 Kg and having a diameter in millions of KM, has been squeezed to zero dimension (singularity). Now the question is “where, this entire mass, disappear? In reality the mass did not disappear, rather the entire mass has been converted into energy.
According to Albert Einstein’s theory of general relativity, mass and energy have the same effect on gravity as well as on the curvature of space time.
So the mass and energy remain in that singularity, the 60 Km diameter will remain recognized as the black hole or the event horizon from where nothing including light can escape.
This is interesting to note that when black holes don’t allow light to escape, then it will look dark similar to an empty space between the stars. How do we know that the dark space we are looking at is really a dark space or a black hole. Let us consider a black hole which was once a massive star. When it was a star, there were planets or even small stars encircling it due to the gravitational force between the massive star and the planet or smaller star.
The force between them is F = G* M* m /r2
Where G is the gravitational constant, M is the mass of the massive star, m is the mass of the planet or the small star and r is the distance between them.
While the star is going through the process of its decay, to neutron star, then into a black hole and finally into a singularity, the factors in the above formula do not change. Mass of the massive star remains the same (massive star to singularity), mass of the planet or the small star remains the same, G, the gravitational constant remains the same and r, the distance between the massive star and small star/ planet also remains the same. Hence the planet or the small star will remain indifferent to the changes the massive star is being subjected to and they will keep on orbiting the black hole. Hence if scientists observe a dark space being orbited by planets or small stars they know that this is a black hole and not an empty space.
We know that our sun along with the entire planets (complete solar system) encircles the galactic centre with a speed of 800,000 Km/hr. The galactic centre is in fact a supermassive black hole and not only our solar system, but millions of other stars are orbiting the galactic centre due to gravitational forces between the supermassive black hole and the stars. This supermassive black hole was once a supermassive star, billions of times more massive than the sun.
Now it is clear to us that a supermassive star millions or even billions time more massive than the sun can be squeezed to a singularity.
Now let us consider the reverse of it. If a supermassive star, billions of time more massive than the sun can be squeezed into a singularity, meaning thereby that entire mass of the supermassive star has been converted into energy and remain active within that singularity, then why all the mass and energy squeezed into a singularity could not be released 13.7 billions of years ago to create the universe.
Exploring the universe further strengthens our faith on the holy books which encourage us to contemplate the universe in order to understand the creator better.
Mohammad Fakhar Mahmood
27 August 2017