The Amazing Journey of E=mc2 : The Most Famous Equation of the World

More than a hundred years back 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 of 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 most famous equation of the World

                                                                          A young Albert Einstein

The half inch equation may seem to be so simple at the first look, 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 sides of the equation. This is a story of those people who fought for the truth in spite of 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 change the direction of science forever.

Michael Faraday was the son of a blacksmith who was lucky to work for a book binder 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 makes its pursuers amiable and liberal. He was determined to break free from his daily toil. 

Michael Faraday

19^th century scientists were 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 got impressed with him and gave him a ticket to a lecture of the great chemist Sir Humphry Davy. Faraday never knew that this was going to change his life forever. 

                                                     Sir Humphry Davy

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 assistant. 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 totally separate subjects at that time!!! Everybody was surprised and nobody could give any explanation to the observed phenomenon. Faraday speculated that perhaps some sort of electrical force is emanating outwards from the wire which was responsible for moving the magnet. This came as a shock to the scientific society nearly 300 years back because the prevailing concept at that time was that electricity flows through a wire and not sideways or out of it.

Electricity creating magnetism

Lines of Forces

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 in 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 over-arching principle. The chemicals in the battery had been transformed into electricity in the wire which would combine with a magnet to produce motion of the wire. Behind all these various forces there was a common ENERGY.

The set up of Electric Motor

The achievements of the son of a blacksmith was 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 basis of his contributions to science. Davy died 5 years later, a victim of his many gaseous (specially 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 it was thought to be at that time) but are forces that can be clubbed together into what is known as Electro-magnetism. He had started what Einstein would call the great revolution of unification.

Electromagnetic fields

M is for Mass

Paris, France, late eighteenth century:

King Louis XV was at 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 men. The French Revolution was lurking in the corner. It was the era of enlightenment which 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 enforcements in Paris. Lavoisier had an idea of building a great wall around the city and to tax every commodity that came in or went out through the wall. These political and economic activities enabled him to fund his scientific research. 

Antoine Lavoisier

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: 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 transformation. 

Lavoisier's Experiment

To confirm this he conducted numerable other experiments which demanded accuracy. For this he had to commission very sensitive 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, solids may become liquid, but matter, the tiny atoms that make up all substances are never lost. This eventually laid the foundations of the law of conservation of mass.

On the other hand his methods of tax exactions was 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 adulteration of tobacco. Finally Lavoisier was denounced by a failed scientist turned radical journalist Jean-Paul Marat (whose scientific findings was once rejected by Lavoisier due to lack of proper scientific evidence) and was executed in front of the public at the guillotine on 8^th May, 1794.

French Revolution

Guillotine

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 is central to the discovery of E= mc2.

C is for the speed of light

C stands for ‘Celeretas’ (latin word for swiftness). Since light travels with an incredible speed of 670 million miles per hour it was always considered as something which will be beyond the realm of human understanding. It was almost 100 years after Lavoisier that the world witnessed a young and energetic Einstein attending classes in the Zurich polytechnic, 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 other things made absolutely no sense to him.

By that time everything that physically existed have been classified into two groups. One is matter, the building blocks of the universe and the other one 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 will bring about a revolution in science. With light he would re-invent the universe and find a hidden pathway that will unite energy and matter.

By the time Einstein arrived to the scene the speed of light have already been computed, but nobody actually knew what it was. One man whom we have already met was ready to make an educative 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 experimentations. His concepts of invisible lines of forces that gave rise to electro-magnetism was still difficult for the people to digest. Now he was ready with another outrageous proposal. He proposed that light is actually one form of these vibrating lines of electro-magnetism. But as it happens everytime with science, nobody believed in him.

For 15 years Faraday struggled to convince the people that light was actually an electromagnetic wave but what he lacked was the knowledge of advanced mathematics that will 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.

James Clerk Maxwell

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 electro-magnetism 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 electro-magnetic 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

Chateau Cirey, France, Early eighteenth century

For this we have go back more than a hundred years back, even before Lavoisier. At that time there was no idea how to quantify motion. All that existed was Galileo’s works and Isaac Newton’s Principia. Nobody ever thought that a crucial contribution to this subject will come from a very unusual source.

At that time King Louis XIV was at the throne of France. One of his courtyards had a daughter by the name of Emily Du Chatelet. She was a very intelligent young woman having 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 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 upto hundred years later.

                                                      Emily Du Chatelet

She was married to a general in the French army at the age 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 de Maupertuis, who was 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 Emily hid him in her country home in Chateau. Far from Paris Emily 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 at the army). 

 Voltaire

Newton stated that the the energy (force with which masses collide) is very simply mass of the object times its velocity. On the other hand a German scientist, Gottfried Wilhelm Leibniz had a different view to this. He believed that a moving object has a kind of inner spirit (which he called ‘vis viva’, 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. 

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. 

Gottfried Wilhelm Leibniz 

Finally she came across the experiments of a Dutch scientist, Willem’s Gravesande which showed that the observations indeed favour Leibniz. Gravesande’s experiment comprised 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 more deep into the clay rather 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 for the academy at that time.

All her life Emily tried to rise above the limitations placed on her gender. In the end it was an affair with a young soldier that brought about her demise. She conceived at an advanced age of forty-three which was considered to be dangerous in the 18^th century. Finally she died six days after giving birth to her fourth child. 

Emily Du Chatelet’s conviction in the idea that the energy of an object is the function of the square of its velocity sent shockwaves through the academic society. It took 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 in the scene it was all set for him to provide the final thrust towards framing the equation. All the quantities of 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 to 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 was boring. All he was interested in was light. As a result of this his professors in Zurich polytechnic did not like him at all and neither did they give him any recommendations for an academic position. He married his classmate Mileva Maric 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 now been thinking for ten years. Light became his obsession. His wife started complaining because his low wage 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 on him. He wanted to know how God created the universe.

In a stunning insight he turned everything upside down. He changed the way how people thought about the universe. In Einstein’s universe one true constant was the speed of light and the other quantities can be bent so as 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. 

Some time earlier that same year he had already published his paper on Photoelectric effect which later won him the Nobel prize. He had also published a work on the structure of 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 are huge reservoirs of nothing but energy. These masses are formed by the condensation of huge amounts of energy. So when these are annihilated, they give rise to huge 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 totally 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.

By Prabir Rudra