More than a hundred years ago a deceptively simple formula revealed a hidden unity buried deep in the fabric of the Universe. It connects energy with matter and the speed of light, and was discovered by none other than the genius Albert Einstein in 1905. When we think about E=mc2, we have this vision of an old, white-haired Einstein. But E = mc2 is not about an old Einstein. It is about a young, energetic, and dynamic Einstein whose curiosity knew no bounds.
The half-inch equation may seem to be so simple at first glance, but it is just a deception. Einstein, in a stunning insight, united the works of many who have come before him, scientists who fought and even died to form each side of the equation. This is the story of those people who fought for the truth despite resistance and finally unveiled the secrets of nature. The story started long before Einstein, with the discovery of 'E'.
E is for Energy
London, England, early nineteenth century
At that time, scientists thought in terms of ‘force’, ‘pressure’, etc. They never had any idea about ‘Energy’, which could bring all these quantities under a single umbrella. Nobody knew that a lonely man’s quest for knowledge was going to change the direction of science forever. Michael Faraday was the son of a blacksmith who was lucky to work for a bookbinder as an apprentice. He never had the opportunity to acquire any elementary education. But he had an unending thirst for knowledge. He read all the books that reached him in the book binder’s shop. He wanted to escape from trade, which he found vicious and selfish, and wanted to become a servant of science, which he thought made its pursuers amiable and liberal. He was determined to break free from his daily toil.
19th century scientists were the real celebrities of their time, and getting a ticket to their lectures was very tough. Moreover, at that time, science was supposed to be a commodity of the so-called gentleman, which Faraday was not. He got lucky when one of his customers was impressed with him and gave him a ticket to a lecture by the great chemist, Sir Humphry Davy. Faraday never knew that this was going to change his life forever. He was highly impressed with Davy’s lecture and became his ardent follower. His real opportunity came when Davy met with an accident while working in his laboratory, which severely damaged one of his eyes. In such a crisis, Davy appointed Faraday as one of his laboratory assistants. This opened the doors of knowledge to Faraday, and he eagerly absorbed all that Davy deigned to impart. But who would have ever thought that, in time, the pupil would surpass the master!
Battery was newly invented at that time, and as a result, electricity was the order of the day. It was recorded by various scientists, including Davy, that a magnetic compass placed in the vicinity of a current-carrying wire showed deflections. How could electricity have any connection with magnetism, which were thought to be separate subjects at that time! Everybody was surprised, and nobody could give any explanation for the observed phenomenon. Faraday speculated that perhaps some sort of electrical force was emanating outwards from the wire, which was responsible for moving the magnet. This came as a shock to the scientific society nearly 300 years ago because the prevailing concept at that time was that electricity flows through a wire and not sideways or out of it.
But Faraday was determined to reach the heart of the problem and unveil the truth. In a great leap of imagination, he turned the problem on its head. Instead of an electrified wire moving a magnetic compass, he wanted to know whether a static magnet could move a wire. This became the experiment of the century: The invention of the Electric motor. Although he did not understand at that time, he invented a new kind of physics. He had actually invented an overarching principle. The chemicals in the battery had been transformed into electricity in the wire, which would combine with a magnet to produce the motion of the wire. Behind all these various forces, there was a common ENERGY.
The achievements of the son of a blacksmith were opposed by many, including his own master, Davy. Davy was the elected president of the Royal Society of London at that time. He accused Faraday of plagiarism (which was proved wrong) and asked Faraday to put down his application seeking to be a member of the society. Faraday refused to do so and was soon elected a member of the Royal Society on the basis of his contributions to science. Davy died five years later, a victim of his many gaseous (especially laughing gas N2O) inhalations. He was truly a great scientist of his time and had a few inventions to his name, but history will record his greatest invention as Michael Faraday.
With the passage of time, Faraday’s world of invisible forces would lead to a whole new understanding of energy. He had actually shown that electricity and magnetism were not different entities (as they were thought to be at that time) but were forces that could be clubbed together into what is known as Electro-magnetism. He had started what Einstein would later call the great revolution of unification.
M is for Mass
Paris, France, late eighteenth century
King Louis XV was on the throne of France. But this was the era when the ancient absolute power of the monarchy was starting to be challenged by the common man. The French Revolution was lurking around the corner. It was the era of enlightenment that reflected that the development of humanity lies in science. Antoine Lavoisier was an aristocratic, wealthy young man who had a passion for science. He was not a scientist by profession. He was actually the head of tax enforcement in Paris. Lavoisier had the idea of building a great wall around the city and taxing every commodity that came in or went out through the wall. These political and economic activities enabled him to fund his scientific research.
He was obsessed with matter and wanted to study and classify all its types. He had a great ambition to demonstrate that nature is a closed system and that in any transformation, no amount of matter (mass) is ever gained or lost. He conducted an experiment where he heated water and produced its constituent hydrogen and oxygen gases. Then he combined the gases and got back water again. In the whole process, he demonstrated that the total initial mass of the reactants was equal to the total final mass of all the products and successfully showed that no amount of matter was gained or lost during the transformations.
To confirm this, he conducted numerous other experiments that demanded accuracy. For this, he had to commission some very sensitive and expensive apparatus, which became possible only because of his position as a tax collector. He became obsessed with accuracy. His experiments showed that forms of matter may change with transformations like solid, liquid, or gas. Wood may become ash and smoke, metals may rust, and solids may become liquid, but matter- the tiny atoms that make up all substances- is never lost. This eventually laid the foundations of the law of conservation of mass.
On the other hand, his methods of tax exactions were making the poor common people very angry. With the explosion of the French Revolution, aristocrats like Lavoisier started losing their heads at the guillotine. After all, he was the despised tax collector who was always seen as an enemy of the common people. He was accused of tax fraud and the adulteration of tobacco. Finally, Lavoisier was denounced by the failed scientist turned radical journalist Jean-Paul Marat (whose scientific findings were once rejected by Lavoisier due to lack of proper scientific evidence) and was executed in front of the public at the guillotine on 8th May 1794. Lavoisier was a great chemist of his time and is aptly known as the father of modern chemistry. His greatest accomplishment lies in changing science from a qualitative to a quantitative one. His findings with mass are central to the discovery of E=mc2.
C is for the speed of light
C stands for ‘Celeretas’ (the Latin word for swiftness). Since light travels at an incredible speed of 670 million miles per hour, it has always been considered something beyond the realm of human understanding. It was almost 100 years after Lavoisier that the world witnessed a young and energetic Einstein attending classes at the Zurich Polytechnic in Switzerland. He was never an ideal student for his teachers. All he cared for in this world were Physics, Mathematics, Philosophy, and his violin. All the other things made absolutely no sense to him.
By that time, everything that physically existed had been classified into two groups. One is matter, the building blocks of the universe, and the other is Energy, which excites matter. But nobody ever thought of any connection between the two entities. It was Einstein’s relentless pursuit of light that would bring about a revolution in science. With light, he would re-invent the universe and find a hidden pathway that would unite energy and matter. By the time Einstein arrived at the scene, the speed of light had already been computed, but nobody actually knew what light was. One man whom we have already met was ready to make an educated guess on this. Michael Faraday became Professor Faraday after the death of Sir Humphry Davy. He became popular as a scientist and was known for his great experiments. His concepts of invisible lines of force that gave rise to electromagnetism were still difficult for people to digest. Now he was ready with another outrageous proposal. He proposed that light is actually one form of these vibrating lines of electromagnetism. But as it happens every time with science, nobody believed in him.
For 15 years, Faraday struggled to convince people that light was actually an electromagnetic wave, but what he lacked was the knowledge of advanced mathematics that would back up his idea. Eventually, a man by the name of James Clerk Maxwell came to his rescue. Maxwell not only believed in Faraday’s visions but also had the mathematical skills to prove Faraday right. Maxwell, in his calculations, showed that the interlinking between electricity and magnetism can only happen at a particular speed, 670 million miles per hour. It was the speed of light. He had proved Faraday right. Electricity and magnetism woven together as electromagnetism in its visible form, was nothing but light itself.
Einstein, with his never-ending pursuit of light, was slowly and unknowingly moving towards the link that would connect Energy with matter. He was studying rigorously the electromagnetic theory of light that Maxwell had already proven. But one last mathematical ingredient that Einstein would need was the ‘everyday process of squaring’.
2 is for squared
Château de Cirey, France, Early eighteenth century
For this, we have to go back more than a hundred years, even before Lavoisier. At that time, there was no idea how to quantify motion. All that existed were Galileo’s works and Isaac Newton’s Principia. Nobody ever thought that a crucial contribution to this subject would come from a very unusual source (considering the social status of women during that time). At that time, King Louis XIV was on the throne of France. One of his courtyards had a daughter by the name of Émilie du Châtelet. She was a very intelligent young woman with an inclination towards science. In her tragic and short life, she had a great impact on physics. She published many works of scientific research, including a translation of Newton’s Principia in French, which is still the standard text in France. She did all these things at a time when science was considered to be a male commodity. She was ahead of any other woman of her time or even anyone up to a hundred years later.
She was married to a general in the French army at the age of nineteen and had three children. She ran a busy household and simultaneously pursued her passion for science. Emily took lessons from one of the greatest mathematicians of that time, Pierre Louis Moreau de Maupertuis, who was an expert on Newton. She also had an affair with Voltaire, who was France’s greatest poet and a fierce critic of the king and the church. Voltaire was in prison twice and was exiled to England, where he learned a lot about Newton. When he came back to France, he again got into problems with the king. At that time, Émilie hid him in her country home in Château. Far from Paris, Émilie and Voltaire turned her house into a centre of learning and culture, along with the support of her husband, who mostly remained away, busy with his duties in the army.
Newton stated that energy (the force with which masses collide) is very simply the mass of the object times its velocity (mass * velocity). On the other hand, a German scientist, Gottfried Wilhelm Leibniz, had a different view on this. He believed that a moving object has a kind of inner spirit (which he called ‘vis viva’, the Latin word for living force). In his theory, Leibniz was convinced that the energy of a moving body must be its mass times its velocity squared (mass * velocity2). But defying Newton and convincing the people against Newton’s theory in those days was almost an impossible task. This was where Emily came into the picture. She was highly convinced that Leibniz’s theory was correct, but the support for Newton was overwhelming. What she needed was proof in favour of Leibniz.
Finally, she came across the experiments of a Dutch scientist, Willem ’s Gravesande, which showed that the observations indeed favoured Leibniz. Gravesande’s experiment consisted of simply dropping lead balls into a pan of clay from a certain calculated height. His experiments showed that when we double the speed of the drop by increasing the height, then the ball goes four times deeper into the clay than twice, thus giving evidence in favour of squaring the speed. Emily published the result in her famous book ‘Institutions De Physique’. It is quite understandable that the work was not at all acceptable to the academy at that time.
All her life, Émilie tried to rise above the limitations placed on her gender. In the end, it was an affair with a young poet, Jean François de Saint-Lambert that brought about her demise. She conceived a child at the advanced age of forty-three, which was considered to be dangerous in the 18th century. Finally, she died six days after giving birth to her fourth child. Émilie Du Châtelet’s conviction in the idea that the energy of an object is the function of the square of its velocity sent shockwaves through academic society. It took a hundred years after her death for the idea to be completely accepted, probably just in time for Einstein.
Einstein and his BIG idea
By the time Einstein arrived on the scene, it was all set for him to provide the final thrust towards framing the equation. All the quantities in the equation were already developed by the people who came before him. The timing was so perfect for him that it seemed to be God’s wish. Now all he had to do was find a way to unify the physical quantities to produce the equation.
Einstein was not the so-called good-obedient student in the class, as it was stated earlier. He had the least interest in attending classes, which he said were boring. All he was interested in was light. As a result of this, his professors at Zurich Polytechnic did not like him at all, nor did they give him any recommendations for an academic position. He married his classmate, Mileva Marić, and had a child.
Bern, Switzerland, 1905
After passing out of the Zurich Polytechnic in 1900, Einstein had to take a low-paying job as a clerk in a patent office in Bern, Switzerland, in order to run his house. After completing his daily work, he had enough time at the office to think about science. He was relentlessly pursuing his question of light, which he had been thinking about for ten years. Light became his obsession. His wife started complaining because his low wages made it difficult to run the house. His friends advised him to find a better job so that he could provide more comfort to his family. But Einstein had no effect of these advises on him. He just wanted to know how God created the universe.
With stunning insight, he turned everything upside down. He changed the way people thought about the universe. In Einstein’s universe, one true constant was the speed of light, and the other quantities could be bent to match the constant speed. In his amazing world, neither space nor time were absolute quantities. This idea produced his paper on the Special Theory of Relativity.
Sometime earlier that same year, he had already published his paper on the ‘Photoelectric Effect’ which later won him the Nobel Prize. He had also published a work on the structure of an atom that same year (known as his miracle year). But he was not done yet. In one last great 1905 paper, he would propose an even deeper unity. As his ten-year journey with light was drawing to an end, he noticed another strange connection between energy, mass, and light. He finds out that energy and mass are not at all separate entities but different forms of the same thing. As a result, they can be converted into one another. Mass can be transformed into energy, and vice versa. In fact, all the matter that we see around us is a huge reservoir of nothing but energy. These masses are formed by the condensation of huge amounts of energy. So when these are annihilated, they again give rise to the same amount of energy. With this clear idea in his mind, Einstein calculated his way through to the most famous equation of the world E = mc2.
With four familiar notes in the scale of nature, this patent clerk had composed a fresh melody - the culmination of his ten-year journey into light. Irrespective of how far we reach in our scientific quest in the time to come, Einstein and his E = mc2 will keep whispering through the ages.
