# E=mc2: Einstein and the World's Most Famous Equation (2005)

## Channel 4

### Documentary Description

**E=mc ^{2}: Einstein and the World's Most Famous Equation**

**Aired on PBS under the name "EINSTEIN's BIG IDEA**". First shown on Channel 4 in August 2005

From the producer of Touching the Void, this drama documentary tells the story of history's most celebrated equation, E=mc

^{2}, and the five great scientists who brought it to life.

Shot on location and boasting an all-star cast, including Aidan McArdle, Shirley Henderson, Emily Woof and Julian Rhind-Tutt, the film spans 250 years, telling the human story behind the science – replete with heartbreak, execution and betrayal, romance, dedication and joy.

**Emile in the drama**

Based on David Bodanis' bestseller, the film intertwines the youthful romance of Einstein and his future wife Mileva with some of the great scientific discoveries of the 19th century, which Einstein ultimately combined in his astonishing theory of relativity.

E=mc

^{2}is the story not just of the brilliant Einstein, but of those who preceded him: of Michael Faraday's ground-breaking theories and complex relationship with his employer, Sir Humphry Davy; of the execution of brilliant chemist Antoine Lavoisier by French revolutionaries; and of physicist Emilie du Chatelet's fight for recognition in spite of her sex. And of course, it is the story of Einstein's own stunning scientific vision that changed the world. It is also the story of his legacy, inspiring Lise Meitner to split the atom – an event that, to Einstein's eternal regret, made the atomic bomb possible.

**The Equation**

E=mc

^{2}is the world's most famous equation. It has changed the way we view the very substance of our being. The take-home message, that matter is equivalent to energy, explains at once why the stars shine, why time travel is possible and how a single bomb can kill 130,000 people.

The year of 1905 was Einstein's most creative period: he made three huge leaps of understanding, which he published in three separate papers, any one of which would have guaranteed him scientific immortality. The first described the nature of light, the second was about the energetics of atoms, and the third laid out the theory of special relativity. It was in a supplement to this last paper that he finally raised the curtain on E=mc

^{2}.

E=mc

^{2}was an astoundingly bold assertion. It means that energy is equal to the mass of an object multiplied by the speed of light squared, which is a huge number. From this we can understand that a very small amount of matter holds an enormous amount of energy. Stars shine by converting mass into energy, atom bombs mirror the same reaction and so do the nuclear reactors that fire electricity grids daily.

Here, you can find out all you could wish to know about the world's most famous equation. Read about the minds and the science behind Einstein's great discovery and about the technology it helped to create.

**E=mc**

^{2}Dr Duncan L Copp

August 2005

E=mc

^{2}, the world's most famous equation, was formulated by Albert Einstein 100 years ago this year. The equation has totally revolutionised our understanding of the world around us; its implications rippling out to the furthest reaches of the Universe. Through this equation, Einstein was able to describe the incredible and profound connection between energy, matter and light. Yet, as with so many scientists, Einstein came to his conclusion only by 'standing on the shoulders of giants'. The understanding of each letter of this beautifully simple equation came from a long history of blood, sweat and toil.

**E=mc**

^{2}:**E is for energy**

How would you describe energy? Heat from a coal fire? A bolt of lightning? Sunlight? In fact, all of these are the expression of energy. But remarkably, less than 200 years ago, scientists considered these phenomena as very separate and totally unrelated – no notion of an overarching theory of energy existed.

Michael Faraday changed this perception in the early 1800s. Although he had scant training, Faraday, born in Surrey, had a passion for science. In particular, he was gripped by a newly discovered observation associated with electricity: the mysterious way a compass needle was deflected when placed close to a wire through which an electric current flowed.

Faraday mused on this observation. He noticed that the position of the needle changed with the position of the compass relative to the wire. He concluded that an invisible force was acting on the needle; a force that rotated around the wire. He discovered that when an electric current flows through a wire, a magnetic field is formed at right angles to the direction of flow. But Faraday went a step further.

Next, he turned the experiment on its head. If an electric current in a wire could generate a magnetic force that moved a compass needle, could a magnet deflect a wire with a current flowing through it? Faraday imagined that a magnet also had an invisible force flowing around it. He was right.

Faraday's observations led to the monumental discovery that electricity and magnetism are one and the same thing; they are two expressions of the same energy. He called it 'electromagnetism'.

The discovery of electromagnetism began a revolution in the concept of energy. It was now understood that one form of energy could be transformed into another form of energy; energy was in fact 'conserved'. Energy, not a series of discrete forces, was actually the same force manifested in different ways.

Einstein knew this had big implications for his great equation, since he delved into the nature of energy that is contained deep within the heart of matter.

**E=mc**

^{2}:**m is for mass**

Understanding matter or mass would fall to a Frenchman Antoine-Laurent Lavoisier, a meticulous taxman and astute scientist. During the last decades of the 1700s, when Lavoisier lived in Paris, the science community thought that as substances reacted, eg when wood burned or metal rusted, the mass of these objects was simply lost.

That loss of matter, it was thought, came from the release of a substance called phlogiston. For example, wood, which contained a certain amount of phlogiston, when burnt, was reduced to ashes weighing less than the original wood. It was thought that during burning the wood lost its phlogiston, which simply vanished into thin air.

Lavoisier changed chemistry from a qualitative to a quantitative science. He didn't believe that an unknown amount of a mystery substance was lost in a chemical transformation like the burning of wood or rusting of metal. He was convinced that if he could trap and weigh the substances given off during a reaction, and weigh the remaining substance after the reaction, the two added together would equal the weight of the original material. In other words, Lavoisier thought that in any transformation of matter, no mass was lost or gained.

After years of experiments, in which he chopped, melted, burned and boiled every conceivable substance, he demonstrated his belief. Metal may rust and wood burn, but the tiny atoms that make up these substances are never lost. Matter is conserved, in much the same way energy is conserved.

Lavoisier's astonishing insight into matter is crucial in E=mc

^{2}, since it shows that matter can be broken apart and recombined, but never lost – with 'm', nothing disappears.

**E=mc**

^{2}: c is for lightLatin for 'swiftness', c actually stands for celeritas. Light is indeed swift; it travels at a staggering 670 million miles an hour! An astute 21-year-old Dane called Ole Roemer discovered this way back in the 17th century. But light itself remained very much a mystery until the 1900s.

It was the very same man who had discovered that the forces of electricity and magnetism were the same as suspected the true nature of light. Michael Faraday had rocked the physics fraternity in 1821 with his bold conclusion and many had a hard time accepting his electromagnetism. But Faraday struck out again.

Perhaps, he thought, electromagnetism was the building block of light. Faraday struggled for many years to prove this theory because he lacked sufficient skills in mathematics to do so. But help was at hand. In the late 1850s, a young Scot, James Clerk Maxwell, and the aging Faraday began corresponding. When it came to mathematics, Maxwell excelled. More importantly, he was able to transform Faraday's often sketchy electromagnetic ideas into hard formulae. The result was crucial.

Maxwell proved mathematically that electricity can produce magnetism and magnetism produce electricity only at a particular velocity. The velocity was, he calculated, 670 million miles an hour – the velocity of light! Maxwell's mathematics vindicated Faraday's theory. Light was an expression of electricity and magnetism, interwoven and travelling at an incredible, and most importantly, fixed, speed.

The weird thing is that whatever speed you or I could travel at, we would never catch up with the speed of light. Light will always get away from us at 670 million miles an hour. Einstein's most daring insight was to suggest that if the speed of light is always fixed, then something else must give – mass must change. An object must get heavier as it approaches the speed of light. This brainwave was what led him to conclude that energy and mass must be interrelated.

**E=mc**

^{2}: 2 is for squaredThere is only one 'number' represented in Einstein's great equation and it designates that the speed of light, c, must be squared. A number which is squared is simply one that is multiplied by itself. Squaring 4 equals 16, for example.

In E=mc

^{2}, the speed of light is multiplied by itself, 670 million (miles an hour) by 670 million, giving the preposterously large number of 448,900,000,000,000,000. But why square the speed of light at all? The answer lies with the discovery made by a brilliant French aristocrat, Emilie du Chatelet.

At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton.

Newton stated that the energy (or force) of a moving object could simply be expressed as its mass multiplied by its velocity. But while corresponding with a German scientist called Gottfried Leibniz, du Chatelet learned that Leibniz considered the energy of a moving object is better described if its velocity is squared. But how to test this? Du Chatelet tried an experiment that would prove her point – dropping lead balls into clay.

Newton's formula says that doubling the velocity of a ball would double its energy and so one would expect it to travel twice as far into the clay. But if the velocity is squared, as Leibniz and du Chatelet believed, the force should be four times greater, and the ball should travel four times the distance into the clay.

Du Chatelet conducted her lead ball experiment and sure enough, doubling the velocity of the ball (by dropping it from twice the height) resulted in the ball travelling four times further into the clay. This simple but brilliant experiment proved that when calculating the energy of moving objects, the velocity at which they travel must be squared. The energy of an object is a function of its velocity squared – it is for this reason that the speed of light in Einstein's equation must be squared.

This was a factor that profoundly changed the meaning of Einstein's equation – since c is already a large number, once squared it is vast. Thus, a vast amount of energy (E) can be associated with a very small amount of mass (m) because mass is always multiplied by the speed of light (c) squared – a vast number. Under these laws, even a tiny amount of mass will equate to a huge amount of energy.

The equation

The equation

Many could not accept Maxwell's theory that the speed of light can never vary; that even if you are travelling at some incredible speed, a beam of light will still travel away from you at 670 million miles an hour. But Einstein did, and from this acceptance and greater understanding came E=mc

^{2}.

Einstein realised that if the speed of light cannot change, then as an object travels faster and faster, an incredible thing happens – its mass must change. No object can travel faster than the speed of light, so what happens to the energy given to an object if you try and do this?

Through the equation E=mc

^{2}, the energy is converted to mass and so the object actually becomes heavier. By understanding that the speed of light was a cosmological constant, Einstein had cracked the relation between energy and mass. No longer can mass and energy be thought of as distinct, they are in fact the same; energy is mass and mass is energy.

In fact, energy is equal to the mass of an object multiplied by the speed of light squared, which is an incredibly large number. Hence a small amount of mass holds a huge amount of energy.

This one fact is perhaps the most profound insight of Einstein's great equation. It unlocked the secret of how stars shine (by converting mass into pure energy) and revealed the promise and destruction of atomic energy. The atom bombs dropped on Hiroshima and Nagasaki, just 40 years after Einstein published his equation, emulated the process by which the Sun produces energy and the stars shine, as do the nuclear reactors that fire electricity grids daily.

**Albert Einstein**

(1879-1955)

Dr Duncan L Copp

December 2001

Updated August 2005

E=mc

^{2}, the one equation almost everyone knows by heart. It describes the simple yet profound link between energy and matter and has totally changed the way we view the Universe. It has overturned the understanding of the physical world which stood unchallenged for hundreds of years. It explains why stars shine, and indirectly, is responsible for the mushroom cloud that appeared over Hiroshima. In many ways this equation has changed many lives and it still challenges our common sense view of the world. The man who derived this equation was born in Ulm, Germany. He was called Albert Einstein.

**Einstein the scientist**

There is a commonly held myth that Einstein was an underachiever at school, but it really isn't true. While he may have had difficulties with languages, Einstein excelled in physics, mathematics and music. In 1900, he graduated from the Federal Institute of Technology (EHT) in Zurich with a teaching diploma in mathematics, but he failed to get a university appointment.

For nine years after graduation from EHT, Einstein remained without a university position. He first earnt a living as a mathematics teacher and then worked at the Swiss patent office in Bern. Einstein held many patents himself and was a keen inventor. While at the patent office he took it upon himself to write his own scientific papers in his spare time, mostly at weekends and in the evenings after work.

1905 was Einstein's Annus Mirablis – his miracle year. During this year he wrote three fundamental papers, any of which would have guaranteed him immortality in the world of physics.

His first was on a new understanding of the structure of light. Einstein argued that light is composed of small particles of energy, called photons, as well as oscillating waves.

The second paper built upon the theory of kinetics. Einstein explained how atoms were responsible for the buffeting of particles of material in suspension, like cigarette smoke suspended in air. This paper presented the first direct evidence for the existence of atoms vindicating an idea that had been around for over 2000 years.

His third paper of 1905 was 'On the Electrodynamics of Moving Bodies'. Here Einstein derived the theory of 'special relativity'. In a supplementary paper four months later, he formulated the famous equation, E=mc

^{2}, where mass and energy are equivalent, showing that a very small amount of mass converts to a huge amount of energy. This is the driving force behind atomic bombs, and all the stars in the Universe.

Einstein's next great achievement came after 10 years of dedicated and at times frustrating work. In March 1916, he published his paper on 'general relativity' describing a profound way of interpreting the action of gravity. His mathematical equations showed how mass can warp space. In a similar way to how a heavy bowling ball placed on a trampoline would warp the fabric. Einstein predicted that the warping of space would effect the way objects moved. He predicted that such a huge body as the Sun would warp space around it and bend the light of distant stars that passed close to it.

In 1919, his theory was proved during a total solar eclipse, when indeed starlight was observed to bend 'around' the Sun. Einstein was delighted: 'I have just completed the most splendid work of my life', he wrote to his son, Hans. In the same year, at the tender age of 30, Einstein became the first superstar scientist, grabbing worldwide media attention. In many ways, science would never be the same again.

**Einstein at home**

While at the Institute of Technology in Zurich, Einstein fell in love with Mileva Maric, his first wife. Lieserl, his first child, was born out of wedlock in 1902 in Novi Sad, Hungary. In 1903, Einstein and Mileva married in Bern, but Lieserl remained in Hungary with Mileva's parents. The daughter was eventually adopted before falling ill. Little else is known about Lieserl; all records of her have disappeared. Albert and Mileva had two more children together: Hans (1904-1973), who became a hydraulic engineer and Eduard (1910-1965), who developed schizophrenia. Einstein's marriage to Mileva was not a particularly happy one; Einstein himself admitted it was much out of 'a sense of duty'. In 1914, they separated.

In 1917, Einstein fell ill. Stomach problems, ulcers and liver complaints dogged him for four long years. During this period he saw little of Mileva. It was his cousin Elsa that nursed him back to health. Having made a partial recovery by 1919, Einstein and Mileva were divorced and in the same year he married Elsa in Berlin. While Elsa and Albert had no children of their own, Elsa's daughters legally took the name Einstein.

Einstein the humanitarian

Einstein the humanitarian

Although his name is associated principally with science, Einstein's humanitarian efforts were also significant. The man did not formulate his theories in ivory towers; he lived through a tumultuous time witnessing two world wars and conflicts that had a direct significance on his life.

Einstein was a Jew and a strong believer in the social ethics of Judaism. A year before the Nazis came to power, in 1932, Einstein left Germany to work at Princeton in the US – he would never return. He abhorred the treatment of the Jews and was a signatory on a letter to President Roosevelt that urged the development of atomic weapons in the US, in the belief that the bomb would act as a deterrent to Germany, who was developing her own. Aside from this, Einstein was a passionate pacifist.

Einstein often made 'excursions into politics', as he put it, and his left-wing political views were well known. In 1952, the opportunity arose for him to enter politics formally when the Israeli government offered him the country's presidency. He politely declined.

It is fitting that a few days before his death, Einstein put his name to a manifesto prepared by Bertrand Russell that called for all nations to ban the use and development of nuclear weapons. The Russell-Einstein Manifesto, as it became known, formed the cornerstone of all major initiatives to abolish nuclear weapons, like the Pugwash Conferences and CND.

On 18 April 1955, Einstein's heart failed. He died in Princeton and his ashes were scattered in an undisclosed location.

The Theory of Everything

The Theory of Everything

We attempt to unravel one of the most ambitious and perplexing scientific theories ever proposed – string theory.

String theory promises to revolutionise our understanding of the Universe by uniting the natural laws that govern space (general relativity) with the natural laws that govern atoms (quantum mechanics). If successful, string theory will break the conceptual logjam that has frustrated the world's brightest scientists for nearly a century.

If you, like most of us mere mortals, are grappling with the theory of everything without a head for numbers, then you will have to sit back, take a deep breath and prepare to throw out everything you know about your world. Have faith, you are about to enter a realm of science fiction turned fact.

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