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In December 1900, Max Planck, a senior professor of thermodynamics at the University of Berlin, proposed a formula for energy distribution of black-body radiation using quantization of energy and probability. With this formula, he laid the foundation of quantum physics and deviated from the well-established classical physics. This event marked the birth of Modern physics, as well, and the use of probability by him encouraged other physicists to develop other formulae based on probability, which led to strange results. Quantum physics using such formulae is known to be absurd due to the use of probability, as Mr. Feynmann, a celebrated professor of Quantum physics, had famously quoted, “If you think you understand quantum mechanics, then you don’t.”
The world over, physicists have tried to get rid of probability from physics but it has not been possible to do so. The use of probability is so deeply rooted in physics that it is impossible to imagine physics without it. My article, “Energy Distribution of Radiation Emitted by a Black-Body, Independent of Probability”, published in the Indian Journal of Science and Technology in its 45th issue in December 2016 may be a first step in the direction of making physics independent of probability. Therefore, in this book, we’ll discuss the importance of this article, and try to present it in a simple manner such that it becomes easy for the readers to understand it.


Chapter I
Black-body Radiation Formula
First of all, we should know what a black-body is, and what the importance is of energy distribution of radiation emitted from it. A black-body is any surface that absorbs maximum radiation falling on it. It is not necessarily black, but it is given this name because the color black absorbs maximum radiation among all visible colors. Black-body is not only a very good absorber of radiation, it is also a very good emitter. It is formed in the shape of a cubical box having a small hole in one of the sides. The box is insulated from any heat dissipation due to radiation or convection. The exit of radiation is allowed only through the hole as shown in Figure 1.Picture 1.

Figure 1- Black-body with an Orifice for Emission of Radiation
When a black-body is heated, radiations of different wavelengths are generated on the inner surfaces (outer surfaces are insulated). These radiations strike with one-another and get mixed up. A small amount of the mixture of all radiations finds its way out through the orifice. At a particular temperature, the wavelengths and the energy of the radiations are measured and a graphical curve is drawn. Then the temperature is raised, and the process is repeated, to get a set of graphical curves at different temperatures as shown in Figure 2. The horizontal axis of the graph represents the wavelength of the radiation, and vertical axis represent Energy emitted. Different curves are due to different temperatures
Figure 2 – Relation Between Energy radiated and Wavelength at Different Absolute Temperatures
Why do we require these curves? Let us take a look at the history of these curves.
When the electric incandescent bulb was invented in the nineteenth century, its filament was initially made of carbon, which evaporated slowly on heating, and deposited black soot on the inner surface of the bulb, rendering the bulb useless. The life of the bulb was only about ten to twelve hours at that time compared to thousands of hours of present day bulbs.
To increase the life of the bulb, it was necessary to find another material which could replace the carbon; one that would allow the bulb to exhibit maximum brightness with minimum electrical energy input.
In that era, Germany was the leader in this technology; so naturally, this responsibility came upon German physicists to investigate. Physicists, by that time, had already learnt that visible light is a part of electro-magnetic radiations. The electro-magnetic radiations having a larger wavelength than the color red are called infra-red radiations, while electro-magnetic radiations having a smaller wavelength than violet color of visible range are called ultra-violet radiation. They reasoned that if they study the behavior of electro-magnetic radiation emitted by various elements when heated to different temperatures, they shall be able to evaluate the behavior of light as well.
To study the behavior of electro-magnetic radiations at different temperatures, they designed the black-body such that they could get a sample of all the radiations emitted by the material of the body at a particular temperature. Then, experiments were carried out with black-bodies of different materials, shapes, and at different temperatures. Data was recorded and graphical curves drawn as shown in figure 2.
The result of the experiments was surprising. They found that the energy given by the radiation neither depended on the shape of the black-body, nor the material. It depended only on the temperature of the black-body. Raising the temperature of the black-body gave out more energy of the radiation, and hence, it could be easily concluded that a higher temperature of the filament of the bulb was required in order to get brighter light. Material of the filament or the shape of the bulb was inconsequential. Therefore, a material with a high melting point, Tungsten, was chosen for the incandescent bulbs. Use of this material and evacuation of air from the bulb increased the life of the bulb.
Another important aspect of the experiments was the graphical curves themselves. Every graphical curve has a mathematical equation. Therefore, the physicists tried to give a mathematical equation to these curves also, but it was found to be a near impossible task as no mathematical equation was fitting these curves.
From figure 2, it can be observed that as we go from a starting point on the left toward the right side along the horizontal axis representing the wavelength, the energy emitted by the radiation increases sharply, becomes maximum, and then continuously decreases for a major part of the curve. Since the wavelength of the electro-magnetic radiation is inversely proportional to its frequency as per the formula λ=c/ν (where c is the speed of light), we can say that energy emitted by the radiation decreases as the frequency decreases for a major part of the curve, or, in other words, energy emitted by the radiation is proportional to the frequency of the radiation. In 1893, Wilhelm Wien used this relation to devise an empirical formula1 for the Energy emitted by radiation as:
B= 2hν3e-hν/kT/c3 (1)
where B is the amount of energy emitted at a frequency ν , T is the absolute temperature of the black-body, h is Planck constant, c is speed of light, and k is Boltzmann’s constant.
This formula provided accurate values of energy for short wavelengths, but it did not provide correct values at larger wavelengths of the radiation emitted, as can be seen by green curve in Figure 3. On the left hand side, it matched the black curve entirely, but on right hand side, it deviated from the black curve obtained from the experimental data.
In 1900, Lord Rayleigh derived a formula for the energy of radiation emitted from a black-body using classical electro-magnetic theory, and presented his formula2 as:
B=8πν2kT/c3 (2)
But this formula failed at short wavelengths of radiation, causing a condition known as ‘ultraviolet catastrophe’, where the energy contained in the radiation was divergent and reached infinity value for the radiation in the ultraviolet region, as shown in Figure-2 by a red line. The values obtained from the Rayleigh-Jean formula did not match with the black curve on the left side, whereas they matched exactly with the black curve on the right side which represented experimental data values.

Figure 3- Deviation of Wein’s and Rayleigh-Jean’s Curves from Experimentally Observed Values.
Though Lord Rayleigh’s formula was not accurate, due to derivation of his formula from classical electro-magnetic theory, unlike Wein’s empirical formula, he provided a way forward for other physicists to improve on.
Lord Rayleigh used the Equi-partition theorem, which is the study of the average values of physical properties for very large groups of individual particles involved in random motion. The theorem3 states that the total energy contained in the assembly of a large number of individual particles exchanging energy among themselves through mutual collisions is shared equally (on the average) by all the particles. If the total energy available in a sample of a gas contained in a container is E, and number of molecules of the gas sharing that energy through mutual collision is N, then the average energy per molecule is E/N. Though the molecules may be differing in energy, some could be moving faster than others, yet the average energy will be E/N.
Secondly, Lord Rayleigh and Jeans observed that there is a similarity in the behavior of molecules of a gas and wavelengths of the electro-magnetic radiations which are emitted by heating any material. Therefore, they applied equi-partition theorem to the radiations generated in a black-body and derived the formula given in equation 2.
But this formula led to ‘Ultra-violet catastrophe’, as mentioned previously. The cause of this catastrophe was that, even if there were some similarities between molecules of a gas and waves of electromagnetic radiations, there was one major difference between the two. The number of gas molecules in a given container is always finite, whereas the number of possible waves generated by the black-body are infinite.
Max Planck solved this problem by assuming that the number of possible electromagnetic vibrations is not infinite, but there are a certain number of resonators which produce electromagnetic vibrations, and that these resonators have energy in certain multiples of a minimum amount of energy known as quantum of energy or quanta. This assumption was derived from Boltzmann’s concept that all matter is formed of indivisible atoms. Until then, Max Plank was a strong supporter of the theory of continuous matter where the matter could be divided into an infinite number of parts. He had accepted the idea of Boltzmann’s divisibility of matter and applied to energy as an ‘Act of desperation” to provide theoretical reasoning for his formula. He had used this concept as a temporary measure and expected to review this later and devise a different explanation, but could not do it. Later, this concept led to the development of Quantum Physics.
Before the assumption of the above reasoning by Max Planck, he had already derived and publicized a new formula4 conjoining the formulae of Wein and Lord Rayleigh as:
B=8πhν3/{c3(ehν/kT-1)} (3)
This formula gave correct values, but it lacked a theoretical explanation. Then, Max Planck started his research to find a theoretical explanation because he thought he was obliged to give the explanation too, after giving the correct formula, and then he came up with the above mentioned reasoning. We shall now learn in detail in the next chapter how he derived the formula from this concept of quantization of energy and probability.

Read Prologue of ‘Lines of Space’

Front Cover
Front Cover

“Why is he not answering the phone?” asked Shalini to no one in particular while dialling up for the third time to call her son Sahil. He had gone to attend his coaching classes as usual and returned predominantly by 10.00 pm. The bus for the Coaching institute left him near the end of their street, and from there he would stroll down to the house every day. But today it was already 45 minute past 10 o’clock and his parents were getting worried. It was a chilly night in the month of December in north India. At this time of the night, the fog also starts building up, adding up to the worry. “Sahil is not responding on mobile phone, what’s happening?” Shalini was wondering. Her husband was watching news channel but she knew that he was also getting restive because every few seconds, his gaze was shifting from the television to the clock on the wall and then to the main door of the house.
Sahil was studying in the XIIth class for engineering. He departed for school regularly at 7 am by bus that he boarded from the stop at the end of the street. This bus took him to a junction point where he changed to another local bus customarily packed with people. Sometimes he would barely get a place to stand on to the footboard. It was invariably a tough ride for nearly six kilometres before reaching the bus stop near the school. Then he mostly had to dash to make it to the school gate to beat the 8 o’clock time limit, otherwise the gate would close and then he would be fined for reaching school late.
After school, he rushed to board the bus again to home. He usually reached home at about 1.00 pm had a quick lunch and then got ready for the coaching institute. The bus for the coaching institute came regularly at about 2 o’clock. The coaching institute prepared him for the IIT and AIEEE entrance examinations. These are the examinations conducted throughout India to acquire admission to premier engineering institutes like the Indian Institutes of Technology and the National Institutes of Technology respectively. Every year more than one million students sit for these written examinations and only about top 10000 get admitted to IIT’s and up to a rank of about 25000 get admission to NIT’s. It is the dream of every student studying physics, chemistry and mathematics to gain entry into these institutes. Every student takes a crack at these examinations just as Sahil was doing.
He usually reached the institute at 3:30 pm and studied until 8:30 pm. Then he boarded the bus from institute to start his return journey at 9:00 pm daily. After his tiring day, he usually reached home at about 10:00 pm. After having dinner, he sat down for completing his school work and around midnight, he involuntarily slept with his books lying in front of him. His grandmother always kept checking whether he was still studying or had fallen asleep. As soon as she found Sahil asleep, she would quietly put the books away, cover him with a blanket and put the lights off.
But today he was late, and his grandmother was sitting near the window trying to hear any sound of footsteps or the opening of gate or the conversation with his mother on mobile, but nothing was happening. Suddenly the phone rang; everybody in the house came to attention except Sahil’s sister who had already fallen asleep. Sahil’s mother picked up the phone from its receiver and asked quickly, “What happened?”
“Bus broke down near petrol pump,” Sahil replied.
“Are you okay?”
“Where are you?”
“Inside the bus,” replied Sahil adding that driver had called for help.
“Okay, tell me the exact location, I’ll send your daddy to pick you up,” she told him. By that time she noted that her husband had already picked up the keys for the car, grabbed his jacket and was going to put on shoes.
“Where?” her husband asked.
“Near the HP petrol pump,” she replied.
“Okay, tell him to stay there, I’ll be there in five minutes,” and he was gone.
After about fifteen minutes, Sahil and his father came back to house and the normality reigned once again. Sahil’s grand-mother made fresh chapattis (indian bread made from wheat flour) for him while he washed his hands and face.
“It has become very tough these days,” said Sahil’s father who himself had sat for the entrance examinations for engineering college and had managed to get in one of the good institutes.
“Those days, the pressure was not so much, there were no coaching classes. You had to prepare on your own, but now it has become more professional. Coaching has become a business in itself and many engineers have become instructors at coaching centres instead of joining the industrial jobs.” Sahil’s father was expressing his feelings while standing at the door of the kitchen and watching his mother making chapattis. She had done same for him when he was a student. She always took care of his needs, whether he wanted tea in the middle of the night or when- ever he would just say, “Okay mom, I am going to sleep, wake me up at five in the morning.” His mother knew that the ringing of the alarm clock would not be sufficient to wake up her son after studying late in the night. He never knew whether his mom slept in the night or not, but she woke him up whenever he wanted. His mother was very dedicated when it came to supporting her son in whatever way she could, so that her son could become whatever he wanted. Now, she was trying to perform the same duties for her grandson because of her affection for him.
“How was the day today?” father asked Sahil when he came from bathroom.
“You had any tests today?”
“Which one?”
“How did you do?”
“Got 68 in maths.”
“Out of 80?”
“Good. What about physics and chemistry?”
“4 and 7”
“That too out of 80 each?”
“Why? Why don’t you attempt physics and chemistry?”
“I don’t know,” Sahil replied.
“Let him have food and take rest… talk to him tomorrow,” called Shalini from her bedroom.
Sahil felt gratitude to his mother for telling his father to leave him alone.
Sahil is a good student, works hard, gets very good marks in mathematics; generally ranks in the top five in his class in mathematics, but in physics and chemistry, he is last. His father and teachers have been trying to figure out why he is not interested in physics and chemistry.
‘This way, he cannot pass his entrance exam,” Sahil’s father was worried. Whenever he asked Sahil about his doubts of science, he always got the reply that he didn’t know. Sahil’s father tried to teach him on Sundays or whenever he was free, but nothing was working out.
When Sahil’s father spoke to his teachers, he found that they also had no clue why this boy was not interested in studying physics and chemistry. They had found him sleeping in the physics and chemistry classes many times. As the examination dates were coming closer, Sahil’s father was getting worried. He even agreed to his wife’s request of asking a pundit as to why their son was not able to study science. Though he had no belief in the advice given by pundit, Sahil’s father performed the puja(prayer) himself for one week for his son, and also shelled out fifteen thousand rupees ( approx. 300/- USD) to pundit in cash for performing puja on behalf of Sahil. The pundit gave few mantras for his son to recite in the morning and evening. Though it was against any logic, Sahil recited those mantras regularly in the hope that they would generate his interest in physics and chemistry. Whenever Sahil’s father warned him that he would fail if he did not start studying physics and chemistry, he replied that he knew it, but just couldn’t help it. It was strange, because Sahil had got good score in science in Xth class and there was no reason for him to lose interest in science now.
Day by day the examination date was coming closer; Sahil’s preparation classes were coming to an end. He had not benefited from the coaching classes in physics and chemistry even though his father had paid a good amount on his coaching for last two years. What had gone wrong?


Read first chapter of ‘Lines of Space’
Chapter 1
Development of Science

“I don’t understand what I shall obtain by studying protons and neutrons,” wondered Sahil one day when I was conversing with him about the significance of studying physics.
“It is all scientists’ imagination,… there’s no logic behind it,” Sahil expressed his feelings.
I was taken aback, “How he could think of the science like this!” Then it occurred to me, that this might be Sahil’s justification for his misplaced perception of physics and chemistry as both of them involve the structure of atom and he believes that the structure of the atom is only the imagination of scientists and not true. I could not believe that he could be so mistaken in his comprehension of the structure of the atom, but there it was and now his belief had become so cogent that he was not ready to listen to any other reasoning. Then I realized why his teachers at coaching institute were unable to understand him, because he believes that the structure of the atom is not true. The reason for his conviction was that he had missed studying basic level science in the rush to study the higher level of science that the coaching institutes try to dump onto the students. Putting him in the coaching institute had burdened him physically and mentally and he was not able to cope. Although he was trying hard, his efforts were going in vain. I cursed myself for putting him under this stress. But this is what every student aspiring for IIT has to do these days, he himself also wanted it this way. I was helpless. Now it was too late to tell him to not to attend the coaching institute.
There was not enough time for me to explain this to him from basics as his examinations were approaching fast. Still, I guessed- it would be better to clear his misunderstanding on the subject as much as possible, and may be that would help him. Now I knew that no psychologist, no pundit could help him. And if his well-qualified teachers could not understand and help him, then it was going to be a challenging task for me. I had no other option but to go for it and try to talk to him.
I needed once again to perpetrate the role of a teacher which I had done long ago when I was teaching at a coaching institute. I was inured to tutoring science and mathematics to classes X, XI and XII.
So I started to brace myself again. I took a few notes from his text-books and from the internet. After few days when I reckoned I was ready, I went to Sahil’s room for talking to him on the subject. He was working on a problem in mathematics. I directed him to take an interlude from his mathematics and come with me to drawing room. He was hesitant yet followed me.
“I cannot answer your questions about not studying physics and chemistry,” he spoke up, as he anticipated my line of questioning.
I told him assuredly, “I am not going to ask you anything about your interest in physics and chemistry. I just want you to listen to what I have to say. If you deem it necessary, you can ask me any question, but from my side, no questioning.”
“Okay,” he said, as the deal seemed fair to him.
I told him that when we see around us, we find many substances such as water, earth, iron, aluminium, various gases and liquids. For centuries, the human race has been wondering, what these substances are made of? Whether these are made of the five basic elements air, earth, fire, water, and sky, or are there some other core constituents too?
“They are made of elements,” interrupted Sahil as the answer to this question seemed very undemanding to him, though I had not directly asked him to give answer to this question. While furnishing the answer, his face still showed that he was not interested in this talk at all… he wanted it to be over soon.
“Oh yes, you know that!” I appreciated him. “But do you know how difficult it was to ascertain that they are made of elements?” I tried to engage him in simple conversation.
“No, it’s easy. Everybody knows, they are made of elements,” he replied.
“Imagine about four hundred years ago when there was no knowledge of elements,” I continued. “People were only familiar with the objects they observed such as air, sand, iron, gold, copper, water, fire, and the sky. So they envisioned that only five elements constituted the whole universe namely air, water, fire, earth, and sky. And every other substance could be created from these five basic constituents.”
“Then how did the other elements came to be known?” Sahil asked, as he now seemed a little interested.
“In 1661, Robert Boyle proposed that matter was composed of various combinations of different “corpuscles”, and not the classical elements of air, earth, fire and water.”
“What is a corpuscle?” Sahil asked.
“A corpuscle is an indivisible part of a substance just like atom.”
“But did they know about atoms back then?”
“No, atom is a Greek word meaning an indivisible part. The word “atom” was in use at that time but not in the sense that we identify it today.”
“Yes, I am aware that atom is a Greek word. So, corpuscle and atom were one and same thing,” Sahil suggested.
“Quite similar but not exactly alike. Corpuscle was also used for light, whereas atom was used for matter only,” I informed him. “During the 1670s Issac Newton used corpuscularianism in his development of the corpuscular theory of light.”
“What is this theory?” asked Sahil.
“Newton visualized that light was made of some indivisible particles called “corpuscles”. He considered these corpuscles to behave like particles and travel at very high speed.”
“Then how did the atom come into existence?” Sahil asked.
“The atom came into existence when the science of chemistry began to develop,” I replied.
“Why chemistry, I thought we were doing physics now.”
“I am neither educating you on physics nor chemistry, just telling you the story of development of science. Do you want me to continue?” I asked, just to gauge whether he was becoming interested.
“Yes, we can go on, but I hate chemistry.”
“In 1789, French researcher Antoine Lavoisier discovered the law of conservation of mass and defined an element as a basic substance that could not be further broken down by the methods of chemistry.”
“Yes, I know what an element is; it is the purest form of a substance.”
“But until Lavoisier discovered this, nobody knew about element,” I told him. “All substances are either compounds or mixtures of these elements. Two or more elements when combined in a particular ratio, form compounds. But it was still not known how these elements combined?”
“It must have been very difficult time without awareness on the method of combination of elements; we now know all the rules of their combination, valance electron rule, covalent bonds etc.” Sahil was amused.
“Yes, you know all these rules, but you don’t know how these rules were unearthed?”
“In 1805, John Dalton explained why elements always react in ratios of small whole numbers and devised the law of multiple proportions. He proposed that each element consists of atoms of a single, unique type, and that these atoms join together to form chemical compounds.”
“So, the atom was proposed by scientists while working on chemical compounds and that was nearly 150 years after the corpuscles, but how did the atom became so complicated with all the protons, neutrons, electrons etc., and we have to remember so many rules about them?” asked Sahil.
“John Dalton proposed the existence of atom but at that time, nobody knew the size of the atom. In 1865 Johann Josef Loschmidt measured the size of the molecules that make up air, and this was considered a great discovery,” I informed Sahil.
“But how did this scientist measure the size of one molecule of air?” asked Sahil.
“You can check that yourself on the internet. For the time being we shall move ahead,” I told him as I did not know the answer to his question. “After establishing the existence of such a small particle, which was basic for all elements and hence for all substances, it was very difficult to study it further as it was not visible in microscopes,” I said moving on further.
“If you can’t see something then how can you study it further or even say that that thing exists. So protons and electrons are just imagination of scientists,” Sahil declared his doubts.
“There are many things in this universe that you can’t see but they exist. You cannot rule out their existence just because you can’t see them,” I told him.
“I don’t believe that,” objected Sahil.
“I’ll tell you one incident. Once a physics teacher was explaining to his students that there exist only those things that we can register by using our sense organs: eyes, ears, skin, nose; just as you are saying that things don’t exist if you can’t see, hear, feel or smell them,” I told Sahil.
“Then what happened?” he asked.
“Then one of the students got up and asked his class-mates whether anyone had seen, heard, touched or smelt the teacher’s brain?”
“No” everybody replied.
“Then it implies that our teacher does not have a brain,” the student reasoned and all his classmates laughed.
“That is interesting, but isn’t it different than a physical quantity?” Sahil was still not ready to accept the logic.
“I agree, this is not a physical quantity but many physical entities are not registered by our senses such as X-rays but they exist. Do you want to know who that student was?” I asked Sahil.
“You mean to say that this incident was true?” he asked in surprise.
“Yes, I think so. The student in this incident was Albert Einstein,” I told him.
“If Einstein believed that way then surely it must be,” said Sahil, accepting that there can be things that our senses cannot register. “But does that mean that protons and electrons really exist?” he asked.
“Yes, they exist and it took lot of hard work and imagination by great scientists to prove this fact,” I told him and continued how these particles could be found that were not visible under any microscope. In the early 19th century, British scientist Michael Faraday explored the phenomenon of electrolysis. Electrolysis involves passing an electric current through a substance, such as an ionic compound dissolved in a solution of water. The current separates the constituent elements of the compound—the positively charged ions collect at the (negative) cathode and the negatively charged ions collect at the (positive) anode. Faraday discovered that the amount of an element formed increased in proportion to the amount of electricity passed through the substance. This suggested that atoms, although themselves electrically neutral, are made up of smaller particles that carry electric charge.
Toward the end of the 19th century, physicists realized that if they applied a high voltage between two electrodes (a cathode and an anode) in a vacuum tube, the cathode would release a discharge. This discharge was called a cathode ray. In 1897 the British physicist Sir Joseph J. Thomson revealed that these rays were made up of tiny particles almost 2,000 times lighter than an atom of hydrogen. He also showed that electric and magnetic fields could move them around, thus proving they were electrically charged. These tiny, light, electrically charged particles were named electrons.
From his experiment J.J.Thompson concluded that electrons were a component of every atom. Thus he overturned the belief that atoms are the indivisible, ultimate particles of matter.
At that time, the structure of atom was not established because atom could not be seen even with powerful microscopes but since it had been found that electrons were a part of every atom and the atom as a whole was neutral, it was contemplated that there must also be a positive charge on an atom. Until that time protons were not known, so Thomson postulated that the low mass, negatively charged electrons were distributed throughout the atom, possibly rotating in rings, with their charge balanced by the presence of a uniform sea of positive charge. This was known as the Plum Pudding model. In this model, the presence of a uniform sea of positive charge was an assumption yet to be verified.

Figure 1
Plum Pudding model of AtomPlum pudding model

”Yes, I know about the Plum Pudding model, but I never knew why they needed this model when they already knew about the behaviour of electrons?” said Sahil. “Now, I see that this was the basic model when scientists did not know about protons and neutrons. But did they not wonder why the negative charged particles did not cancel out the positive charge in the Plum Pudding model?”
“Yes, there were shortcomings in that model, but at that time, that gave the best explanation,” I replied.
“How did the things change after that?”
In 1909, physicist Ernest Rutherford bombarded a sheet of gold foil with alpha rays, which were known as positively charged helium atoms at that time. He discovered that a small percentage of these particles were deflected through much larger angles than was predicted using Thomson’s proposal. Rutherford interpreted the gold foil experiment as suggesting that the positive charge of a heavy gold atom and most of its mass was concentrated in a nucleus at the centre of the atom. This was known as Rutherford’s model.
Figure 2
Rutherford Experiment
Rutherford's experiment

“Yes, now I’ve got it. Earlier I had read about Rutherford model, but had some difficulties in understanding it. Now things are falling in line,” said Sahil.
“Rutherford model led to the discovery of nucleus,” I told him.
“Before this, we never knew that the nucleus existed!” Sahil had a surprised look on his face.
“Yes, we did not know about the nucleus before Rutherford’s experiment,” I agreed. “Rutherford suggested that electrons revolved around the nucleus and that the attraction toward the nucleus due to the electrostatic force between the nucleus and electrons is balanced out by the centrifugal force on the electrons due to their circulatory motion.
So, it was Rutherford’s imagination that gave us nucleus, said Sahil and I realized that he was now trying to prove his point that protons and electrons are the imagination of scientists.
“Yes, but imagination supported with logic,” I corrected him.
“Daddy, I thought that protons and electrons etc. are in the imagination of scientists, but now I understand that they had some basis for imagining these particles,” Sahil said and this surprised me.
“Good,” I appreciated him, as I felt some relief on hearing that he had begun to see some logic in the existence of protons and electrons. “So, it became evident that the electrostatic force between the nucleus and electrons is balanced by the centrifugal force of electrons revolving around nucleus,” I added further.
“Yes I know that. But Daddy, where do the electrons get their negative charge?” asked Sahil.
I did not know what to say. I thought for some time and the best answer I could give was that they have the smallest negative charge. But why? I had no clue. I made it a point to think about this question and to do some research on it.
Next day, when I had some free time while sitting in my factory office, I thought of searching on the internet about Sahil’s question. I found that Benjamin Franklin had given the convention of negative charge on electrons when he gave his conjecture regarding the direction of charge flow (from the smooth wax to the rough wool) when wool and wax were rubbed together. He then set a precedent for electrical notation, which is prevalent today. It meant that the positive and negative charges are just a convention to differentiate between the two. But why does this difference exist? Until we know the reason for this difference, we cannot find the source of negative charge on electrons. What is negative charge? I was thinking, but I could only understand that where-ever there is negative charge, there is abundance of electrons. This meant that negative charge is due to presence of electrons but I was unable to find the source of negative charge on electron. It is true that negative charge is the basic property of electron but how the electron attained this basic property, I was not able to understand.
When I reached home after finishing work , Sahil came and told me that he had read about the structure of atom in his physics book and he could now understand it a little better, but he still had some doubts. Settling down into sofa in the drawing room, I asked him, ‘‘What are your doubts”?
“Rutherford model had some limitations… I don’t understand them.”
“Yesterday I told you that Rutherford suggested that electrons revolved around a nucleus in fixed orbits,” I reminded him.
“Yes,” he agreed.
“Then a discovery was made that when a charged particle has motion, it loses energy and hence the electrons revolving around nucleus will lose their energy continuously and eventually fall into the nucleus,” I supplied further information.
“Oh yes, I have read about this too but could not understand how this discovery was made?”
“Here’s your tea,” said Shalini, handing me a cup of tea.
“Do you want your milk now or later?” she asked Sahil.
“I’ll take later. Now I am busy. Daddy, tell me about this discovery,” said Sahil indicating me to go on.
“I don’t know how this discovery was made but it led to a number of changes to the atomic model. We won’t concern ourselves how this discovery was made, but will make use of it,” I suggested to Sahil.
He agreed.
“Due to this discovery, it was evident that the electron will slow down due to loss of energy. As it slows down, its centrifugal force will reduce and it will be attracted towards the nucleus and slowly it will fall into the nucleus.”
“It means that Rutherford’s model was not correct,” Sahil guessed.
“You cannot say that it was entirely wrong but things needed further explanation if we were to accept this model,” I advised him.
“In 1913, Niel Bohr suggested that the electrons were confined into clearly defined, quantized orbits, and could jump between these, but could not freely spiral inward or outward in intermediate states. An electron must absorb or emit specific amounts of energy to transition between these fixed orbits.
Figure -3
Bohr’s model of the hydrogen atom, showing an electron jumping between fixed orbits and emitting a photon of energy with a specific frequency
Release of photon

“Why do electrons behave like that and how did Bohr knew that electrons can only jump from one orbit to another and not have intermediate position?” queried Sahil.
“Bohr only suggested that electrons should behave like that, and then only they can stay surrounding the nucleus; otherwise, they will fall in nucleus as per the new discovery of losing energy when a charged particle has motion,” I responded.
“So it was Bohr’s imagination to give the electrons a reason to keep revolving around the nucleus and prevent them from falling in nucleus,” wondered Sahil, and indicated one more cause for his belief that subatomic particles are in the imagination of scientists.
“You are right; this was Niel Bohr’s imagination but he came up with a better model than Rutherford’s. Though this model was based on imagination, there was one more reason to accept his model,” I tried to defend.
“What was that?” countered Sahil.
When the light from a heated material was passed through a prism, it produced a multi-colored spectrum with some fixed lines. The appearance of these fixed lines in the spectrum was successfully explained by these orbital transitions.”
“This was the best model of atom then,” suggested Sahil.
“Yes, but Bohr’s model also had its limitations.”
“I have read about the limitations, but never understood them. Can you repeat them for me?” Sahil requested.
“I don’t remember all the limitations but the main one was that Bohr’s model violated the uncertainty principle because it considered electrons to have known orbits and angular momentum: two things that cannot be directly known at once,” I expressed.
“Daddy, the ‘uncertainty principle’ name itself is confusing. How can there be a principle of uncertainty?” questioned Sahil.
“You know that electron is very small.”
“You know that for seeing anything, light has to hit that object and then reflect from it back to our eyes.”
“Yes, we cannot see anything if light does not hit something and come back to our eyes.”
“You also know that light has a ‘photon’ as its smallest unit.”
“Yes, it is a packet of energy and can be considered to have dual nature of particle as well as wave. I have read about it.”
“When this photon hits the electron, it imparts some energy to the electron.”
“Due to that energy, the electron will start moving if it was at rest or it will change its direction of motion, if it was moving.”
“Then by the time photon reflects back to your eye, the electron must have already moved to some other position.”
“This is the uncertainty principle, that you cannot measure the position and velocity of particles like electrons at the same time. If you want to know the position, you cannot be certain about its velocity, and if you want to know the velocity of an electron, you cannot be certain about its position. In Bohr’s model, he suggested that electrons are moving in fixed orbits. When we assume fixed orbits, then we are fixing their position and since the angular momentum in a fixed orbit is fixed for electrons, it means their speed is fixed. This becomes contradictory to the uncertainty principle.”
“I understand it now. I just used to cram this, never knowing what it meant. Now, I think I’ll not forget it. I will read further in my book and ask you if I have any doubts,” Sahil seemed satisfied with my explanation.
I was happy that he had started showing some interest in physics. But I had his question still roaming around in my mind: where do the electrons get their negative charge? During my internet search, I had found that it is just a convention given by Benjamin Franklin: electrons are negative and protons are positive. Something must make them different; assuming them to be different and following a convention was not satisfying for me. Then a thought came to me: besides not knowing the reason of negative charge on electron, I also didn’t know how the electron was created. If I don’t know how the first electron was born then how could I know how the protons, neutrons, and other particles were born? It means we don’t know how the universe was born. I had read that the universe came into being due to the Big Bang. The Big Bang happened about 15 billion years ago and created the universe, but what kind of matter was present before the Big Bang? Did that material also contain the elementary particles like protons and electrons or was something different from our world? Sahil’s one simple question had started my chain of thoughts, which now moved on to the creation of the universe.


Read first four chapters of ‘The Big Bang and Lines of Space’

Front Cover
Front Cover

Chapter 1
At the Airport

After passing through the security check at the Chandigarh Airport, I proceeded to the waiting lounge. I paused at the Information screen and learned that my flight would be delayed an hour. I frowned. Although it had taken me quite some time to check in and get through the security check because of the unusually large holiday crowd, I had still managed to reach the waiting lounge an hour earlier than my scheduled departure time. Now my wait would be considerably longer.
I surveyed the crowded lounge for an empty chair. Having finally spotted one, I excused my way past an elderly lady and a middle aged man to get to it. As soon as I sat down, the man beside me struck up a conversation by commenting on the unusual rush on a Sunday morning.
I agreed, and the conversation progressed. He told me that he was an engineer who worked in Mohali, a nearby town, and was going back home to Mumbai for a two week holiday.
“Do you work in Mumbai?” he asked as he guessed that I was a local and must be going to Mumbai for work.
“No. Just going to attend training for one week,” I told him.
“Working in IT or insurance?” he asked as he tried to make a second guess.
“No. Shipping,” I corrected him.
“Okay,” he acknowledged, then grew silent. I took the opportunity to ask him whether he would be interested in reading my book. I had recently published my first book and was declaring the fact to almost everyone who came my way. As he was an engineer, and my book dealt with science, I reckoned him to be a good candidate for giving me feedback.
He asked, “What is the subject?”
“It is about a new concept for the creation of the universe.”
“I know about the creation of the universe…the Big Bang theory.”
I became hopeful that the man would be interested in my book, but contrary to my hope, he said, “There is nothing more to know about that.”
Not ready to give in just yet, I quickly added, “My book is about a different concept on the creation of the universe.”
He replied with certainty, “I’ve known of the Big Bang theory since my early days; there can’t be any other reason for the creation of the universe.”
He was obviously a strong believer of the Big Bang theory, and I needed to tread very carefully if I wanted to avoid infuriating him and losing any chance of getting him interested in reading my book. To continue the conversation with him, I asked him politely if he would be kind enough to explain the Big Bang theory, as he understood it.
He replied, “It is very easy; millions of years back, two planets collided and they caused a big bang, thus creating more planets and stars. This way, the entire universe was created.”
I was dumbstruck at his answer and did not know whether to attempt correcting him or just stay indifferent. From his point of view, he was right as he gave the explanation, for which he did not require any further persuasion.
He continued, expanding on his statement,“You know…it’s how everything gets created; two living beings meet and they reproduce a new being. Similarly, there must be two planets meeting and forming a younger third planet and hence their population also could keep growing. This is the Big Bang theory.”
I opted to stay quiet for awhile and wondered at the difficult task that lay ahead of me if I were to convince him about the incorrectness of his long-held belief in his own kind of Big Bang theory.
“How did those first two planets come into being?” I finally asked.
“They were there from the beginning of the universe itself,” was his instantaneous reply, but my question left him wondering about it, as could be observed from his face. I felt certain nobody had ever posed such a question to him. I waited for him to speak instead of resuming the conversation, giving him plenty of time to reconsider the notion he’d probably learned as a child.
“Yes, you are right,” he finally said. “Where did those two planets come from in the beginning? They couldn’t have been there from the beginning of the universe.”
“Right. If there were not even two planets in the beginning of the universe, they couldn’t have collided, and then there couldn’t have been a Big Bang,” I carefully added and looked at him for a response.
“Then what was the Big Bang?” he asked me.
I was surprised at the ease with which I could make him understand that his notion of the Big Bang was incorrect, but it was his capacity to think as a logical person that helped to dispel his wrong notion more quickly than anything to do with my own knack of teaching.
I clarified the current popular theory to him, “The Big Bang theory is not really about a big, loud, bang of two massive objects as you probably assumed it to be, from the words ‘Big Bang’. The name is a misnomer: the theory does not imply a collision of two big objects. It is an explosion of a very small point-like particle that caused the creation of the universe.”
“That is more improbable. How can one small point explode to form the universe?” he disagreed with me.
“You are right. It is not possible that the universe could have been created either from the colliding of planets, as you believed formerly, or by the explosion of one small point-like object into billions of stars and galaxies, as the Big Bang theory advocates,” I agreed with him.
“Then how did the universe get created?” he asked.
Before I could respond, there was an announcement that the flight had been cancelled. There was suddenly a chaotic scene. People were asking one another, “What happened?” Nobody had a clue for a few moments until a second announcement was made that the plane had developed a snag and it would have to go for repairs. The announcer expressed deep regrets and assured all the passengers that an alternative arrangement would be made soon.
“What is this?” the man sitting beside me asked disgustedly, whereas the elderly lady sitting on the other side seemed worried. She grumbled, “My son has already left after seeing me off. What do I do now?”
“Don’t worry, Madam; the airline will make some arrangement. We should wait.” I assured her, while I noticed some passengers becoming restless and blaming the airline for canceling the flight at the last minute.
Seeing the commotion, the airline staff came to pacify them. An official of the airline tried to explain the situation, but things were getting out of control. A security guard came to her rescue and asked the people to listen to her. She explained that the airline would provide a road transport to the Delhi airport, and from there they could board the next flight to Mumbai.
“Why not a flight from here?” asked someone.
“We operate only one flight from here daily,” she replied and then added, “But we can connect from Delhi.”
“Why not make the adjustment with other airlines?”
“They are all full.”
“If we don’t want to go by road transport?” asked another passenger.
“Then you can either take a refund, or you can travel tomorrow,” she clarified.
“Where will we sleep tonight, here?” asked a South Indian man, who probably didn’t have a place to stay in Chandigarh.
“We’ll provide you a hotel stay.” The airline official seemed to be in full control of the situation and had the authority to make all decisions necessary to handle the situation.
“When will the transport leave for Delhi?” someone asked her.
“In two hours from now. It will reach Delhi by 6:00 p.m. We have a flight for Mumbai departing at 9:00 p.m. from Delhi,” she said.
I made a mental calculation that if I took the flight the next morning, then I’d reach Mumbai in the afternoon and would miss the first day of my training. This was not a good idea considering my company was going to pay a hefty sum of 4000 USD for my one week of training, in addition to the expenses incurred on my travel, food, and lodging. No, I couldn’t postpone my travel by one day. Lost money for the company, and a day of learning lost for me was unacceptable. But a flight at 9:00 p.m. from Delhi also would not be convenient as I would reach Mumbai at midnight. I was in a fix, but I had to make a quick decision.
It was Sunday, so I hesitated disturbing my company manager in Mumbai, but I had to inform him about this sudden change. I called him up. After listening to me, he told me to wait for his call while he tried to make some arrangement online.
In the meantime, other passengers had started informing the airline staff about their preferences. After five minutes, I got the instructions from my company manager to hire a taxi and reach Delhi airport within six hours as he was going to book the flight departing at 4:15 p.m. from Delhi.
I hurried through the security gate after informing the airline staff that I was going on my own, and the refund would be handled by my company. I collected my baggage and rushed towards the taxi counter.

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Chapter 2
Nandi Bull

The taxi was on the highway to Delhi within five minutes of departure from the airport thanks to light Sunday morning traffic. I was seated comfortably in the back seat of the taxi when my mobile rang.
“Hello,” I said into the mobile.
“Hi, where are you…In the plane?” came the voice of my wife on the other end.
“No. In a taxi.”
“What? I had dropped you at the airport, not a taxi stand.”
“Then…Oh! You mean the plane is taxiing?”
“No. I am in a taxi going to Delhi,” I replied.
“Why? What happened?” She sounded concerned. I told her the whole story and disconnected the phone after saying goodbye.
Then I realized that I didn’t even say goodbye to the man with whom I was talking to at the airport. I had left in a hurry. It was not that it mattered much now, but it would have been nice to say goodbye; after-all we had talked for quite some time. I had become speechless momentarily when he had told me about his idea of the Big Bang, but on taking a second look, I realized it was probably not his fault.
I remembered the day, nearly four decades back, when my grandfather was having his lunch and I was standing by, ready to serve him more vegetables or chapattis. He sat on a rug spread out on the ground. There was only one table and two chairs in our house, but they were specifically used only when guests arrived. Otherwise, everyone sat on the ground while eating their food.
I must have been only nine or ten years old at that time. I was keeping an eye on the plate in front of him so I could bring more chapattis as soon as he needed them. Suddenly, the plate started moving away from him as if a ghost was pulling at it. He tried to pull the plate back towards him, but it moved away again.
He abruptly stood up and shrieked, “Earthquake!, Run! Come out!”
I was spellbound and did not know what was happening. He caught hold of my arm and pulled me along with him, dashing out of the room while holding the folds of his dhoti (lower garment) with his left hand, and continuously shouting for others to come out of the house. Within a few seconds, I saw my family members and the neighbors rushing out of their homes into the street. A crowd had started gathering in the open area in front of our house.
Our house was in the center of the street, so the open space in front of our house was the usual meeting point for all our neighbors. Young ones were bewildered at what was happening whereas the elders did seem to understand and were guiding the others. There was a sense of urgency as they accounted for their loved ones, making sure no one had been left in the houses.
That had been my first encounter with an earthquake. We were lucky that none of the houses had fallen and nobody had been hurt. As the realization dawned on the people that the worst had passed and they were safe, they relaxed. Some of them started telling their stories, what they were doing when it started. Someone said, “My cot started shaking, and I asked my brother why are you doing that? Then I heard the shouts of earthquake.” A woman said, “My overhead fan started swinging.”
Within minutes the scary situation had turned into a cheerful one, as the people realized that they had not incurred any losses. They were blissfully narrating their incident as if the earthquake was a play thing.
An old lady said, “It has come after nearly thirty years.”
“Why did it come?” asked a young man who had gotten married recently.
“Nandi changed his horn,” the lady replied.
“Nandi?” he asked and looked at the man standing a few feet away. Nandi was the grocery store owner. How could he do something like this? It was beyond his comprehension. Not only he, but many others looked bewildered.
“No. She does not mean this Nandi; she means God Shiva’s Nandi. His bullock,” my grandpa clarified.
“Oh! Nandi Bull.” Some of the elder people understood and lowered their head in reverence.
“Yes, Nandi is the bullock, the vehicle of God Shiva, and he holds the Earth balanced on his one horn. When he gets tired, he changes it to the other horn, that causes an earthquake,” explained the old lady, and everyone listened intently. It was not only believed by her, it was quite a common anecdote there, which was apparent as the other elders agreed with her immediately.
I kept wondering for several days why Nandi could not carry the Earth on both of his horns so that he wouldn’t have to shift it from one to the other, and earthquakes could be avoided. Even better would be to carry the Earth on his back as normal bulls do when they carry a load. But I was not to question the ways of the Lord, as was instilled into me. I was simply told to believe it. It was only after two or three years, after I had read about seismology in a school text book, that I understood the real reason earthquakes occurred.
That incident taught me how mislaid the beliefs of the people could be. Thus, the mistaken belief of the man at the airport was no wonder. It is only education that can set things right. But our education also has such misconstructions. For example, in the case of the Big Bang, how can a point-like particle suddenly burst into stars and galaxies? It seems like a fallacy. Not only religious beliefs, but also scientific studies, sometimes appear to have no reason. I would have kept pondering it over, but a drop in the speed of the taxi pulled me out of my deliberations. I propped myself up from the reclining posture to find out the reason. A toll barrier lay ahead of us.
After paying the toll, I informed the driver that we had to reach the airport before 3:00 p.m.
“What time is your flight, sir?” he asked.
“4:15 p.m.”
“The highway is no problem, but I can’t say about passing through Delhi. That can delay us.” He expressed his apprehensions.
“You will get two hundred rupees extra if we reach the airport before 3:00 p.m.” I offered. I suspected that he was not the owner of the taxi and could only be getting about four hundred rupees (Approximately seven USD) per day. An addition of fifty percent to his daily wages would be attractive for him.
“You will reach there before that,” he said with a grin. The additional offer had the desired effect.
“But drive safely,” I warned him.
“Don’t worry, I will not over-speed. We’ll cut down the break time of about half an hour. I will take a rest only after I drop you at the airport,” he said making me aware of his plans.
“That will be good,” I approved.

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Chapter 3
Meeting at the Airport

The taxi stopped at the domestic airport terminal of Delhi after a non-stop run of five hours since the driver had not taken his customary break mid-way. I paid the driver along with the extra money that I had promised to him. He gladly accepted it, quickly took out my luggage, loaded it onto a trolley, and bade me a happy journey. I almost ran towards the entrance of the airport, but slowed and felt a wave of relief when I noted the check-in counter open, and only a few passengers waiting to check-in.
“Good afternoon, sir,” I heard a somewhat familiar voice say while I was heading towards the check-in counter. I turned in the direction of the sound and found Gaurav.
“Hey, how are you?” I was surprised to see him there. He had worked as an assistant engineer under my supervision about seven years back. Then, he was a young boy fresh from the engineering college. Now, he was in his early thirties, looking more confident and handsome, but his voice had not changed much. I was quick to recognize him after so many years.
“Fine, sir. I have been waiting for you. You were delayed.”
“Yes. But how did you know that I was coming? What are you doing here?” I had lost touch with him six years ago after we both left the ship we had been working on together. We now sailed on separate ships.
“First, let me help you with check-in, then we shall talk,” he replied and guided me towards another counter that had become vacant.
He picked up my suitcase from the trolley and put it up for check in, while I told the female airline attendant to check for my online booking, as I had no time to print my e-ticket before reaching the airport. She asked for my identification, and checked her computer. She found my e-ticket and asked for any seat preference.
“Next to mine, if possible,” Gaurav replied before I could say anything, and gave his seat number to her.
“Done. Have a nice journey, sir,” the attendant said as she handed me my boarding pass.
“Sir, I was told by the Mumbai office that your flight from Chandigarh to Mumbai was canceled and you shall be traveling with me from here to Mumbai, so I was waiting for you.” Gaurav informed me. “Let’s go for the security check.”
“Why are you going to Mumbai?” I asked.
“I shall be attending the same training course as you,” he replied and headed towards the security gate.
“What are you sailing as?” I asked him after clearing the security check.
“I am presently second engineer, but the company has promised me a promotion soon, and I expect to go on the next ship as Chief Engineer.”
“Congrats!” I appreciated his fast rise from assistant engineer to the highest rank as engineer on a ship in such a short span.
“Thank you, sir. I have been sailing longer than I stayed at home, so I had good sailing experience in a short time, and got faster promotions than my colleagues,” he explained and kept talking until we reached the boarding gate area.
“We have about ten minutes before boarding. I shall have a coffee. Are you coming with me?” I asked after we had found two empty seats in the boarding area.
“No, sir. I am good. You go ahead.”
“Then please watch my bag.” I left my carry-on on a seat next to him and ambled towards a coffee shop, fully trusting a man whom I had met again after nearly six years.

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Chapter 4
On the Flight

Gaurav had gotten the window seat and I sat next to him. It was nice that he had waited for me at the check-in counter so we could get adjacent seats. Talking to him would help pass the flight time, I thought. It becomes boring during short flights due to non-availability of a video screen in front of your seat, unless you have a book to read or the company of someone. The aisle seat next to mine was vacant, although the rest of the seats were almost full.
I asked Gaurav about what he had been doing the past six years. He told me the names of the ships on which he had worked, and when he had cleared his examinations for promotion. He had a son who was now one year and seven months old. He kept on talking until the plane reached the runway and got ready to take off.
As the plane took off, Gaurav started peeking through the window and looked like he was observing the buildings of the city underneath, which appeared smaller as the plane kept gaining height. He became quiet as the panorama outside seemed to entrance him. I wanted to tell him about my book, but restrained myself from disturbing him. I had a hunch that he would resume the conversation as soon as the scenery outside faded out of his sight. But he kept observing the blue sky, seemingly fascinated by the white clouds above which the plane was flying.
There was nothing else to hold my attention there, so I pulled out the flight magazine tucked into the pocket of the seat in front of me. After a few minutes, while I was poring over the pages of the magazine, Gaurav decided to break away from his sky watching spell and spoke up. “Sir, whenever I fly, I become conscious of the vastness of the sky. In comparison to sky, the people living on Earth are tiny…even multi-storied buildings look like toys from here…It is always mesmerizing to watch.”
“Yes, it is,” I said without taking my eyes off the magazine.
“Sometimes I wonder how spacious the sky must be; it is intriguing to just think of the vastness!” he conveyed his thoughts to me.
“Yes, it is,” I agreed.
“I’ve heard there are billions of stars in the universe,” he expressed further.
“Yes, there are,” I concurred with him and closed the magazine to give more attention to the conversation.
“Would you like to buy some snacks?” the air hostess asked as she approached our seats.
“Yes, one veggie sandwich and tea please,” Gaurav requested, whereas I opted for one juice.
I opened the tray on the backside of the seat in front of me to set my juice on and made the payment for both of us, as per the Indian custom that the senior person should pay.
After the air hostess left, I asked Gaurav, “Do you know how it was created?”
“The universe.”
“By the Big Bang.” He gave the more or less standard reply.
“What do you know about the Big Bang?” I found myself asking someone about the Big Bang for the second time in one day. I had gotten a vague answer earlier, so I wanted to know what Gaurav had to say.
“The Big Bang means that the universe was created from a tiny particle due to a huge explosion,” he replied correctly.
“You are correct. But it does not appear rational to me,” I stated.
“Why? This is the scientific theory of the creation of the universe. Everyone believes that.”
“I doubt that.”
“But it is so popular,” Gaurav countered.
“Popularity of something is not a yardstick of its truthfulness,” I said philosophically.
“That is right, but you must have some reasoning to have doubts on such a popular theory.”
“Yes, I have. It is a long story.”
“Tell me. You are saying something contradictory to what I have read and believed. It will be interesting to hear.”
“To explain this, I shall have to start from the beginning.” I hesitated as I was not sure whether he was truly interested or merely asked in order to pass the time.
“We have enough time. I want to hear it,” he expressed his interest clearly. I felt like telling him about my book Lines of Space, but stopped myself. I thought it might be better to first talk about the concept of Lines of Space and create an interest, rather than telling him straightaway to read the book, and decided to answer his questions.