E=mc² is probably the world’s most famous equation. It means “Energy equals mass times the speed of light squared.” The formula implies that a small amount of rest mass corresponds to an enormous amount of energy, which is the physics behind nuclear fission and fusion – the latter being how stars, including our Sun, work. In this amazing video, Albert Einstein explains his famous formula in his own voice.

## Einstein explains his famous formula E=mc²

Transcript of the video above. Albert Einstein explains:

It followed from the special theory of relativity that mass and energy are both but [for] different manifestations of the same thing. A somewhat unfamiliar conception for the average mind.

Furthermore, the equation “E” is equal to “m [times] c squared” in which energy is put equal to mass multiplied by the square of the velocity of light showing that a very small amount of mass may be converted into a very large amount of energy, and vice versa.

The mass and energy were in fact equivalent, according to the formula mentioned before.

This was demonstrated by Cockcroft and Walton* in 1932, experimentally.

* In 1932, the British physicist Sir John Douglas Cockcroft and the Irish physicist Ernest Walton demonstrated E=mc² experimentally by building the first particle accelerator and using it to bombard lithium atoms with protons. This process caused the lithium nuclei to split into two helium nuclei, a reaction known as nuclear transmutation. The experiment confirmed that the mass of the resulting helium nuclei was slightly less than the original mass of the lithium and proton. The missing mass had been converted into energy, as predicted by Einstein’s equation, providing experimental validation of mass-energy equivalence. They shared the Nobel Prize in Physics in 1951 for splitting the atomic nucleus.

## E=mc²: Understanding Mass-Energy Equivalence

On September 27, 1905, Albert Einstein published a paper titled “Does the Inertia of a Body Depend Upon its Energy-Content?” In the paper, Einstein described the interchangeable nature of mass and energy, known today as mass-energy equivalence, or E=mc².

In the 1905 paper, Einstein used L to denote energy. The sentence in the paper’s conclusion, “If a body gives off the energy L in the form of radiation, its mass diminishes by L/c²,” can be written as the equation **“m = L/c².”**

Using the more modern E instead of L to denote energy, this can be trivially rewritten as **“E = mc².”**

Energy (E) equals mass (m) multiplied by the speed of light (c) squared

E = mc²

At the most basic level, the equation states that energy and mass (matter) are interchangeable; they are different forms of the same thing. Under the right conditions, energy can become mass and vice versa.

Since the speed of light is a very large number 299,792,458 meters per second (approximately 300,000 kilometers per second, or 186,000 miles per second, or 671 million miles per hour), the formula implies that a small amount of rest mass (the mass that is measured when the system is at rest) corresponds to an enormous amount of energy. This principle explains how stars, including our Sun, function.

The Sun fuses about 620 million metric tons of hydrogen into 616 million metric tons of helium each second. The difference in mass (about 4 million metric tons) is released as energy. In other words, the Sun loses about 4 million metric tons of mass each second.

Another example: if we could convert all the atoms in a paper clip (which weighs about 1 gram) into pure energy (leaving no mass whatsoever), according to Einstein’s formula, the paper clip would yield about 90 trillion joules or about 21 kilotons of TNT. This is even greater than the energy released by the atomic bomb that destroyed Hiroshima in 1945, which exploded with an energy of approximately 15 kilotons of TNT.

However, there is no practical way on Earth to convert a paper clip or any other object entirely into energy. It would require temperatures and pressures greater than those at the core of our Sun.

## Sources

- Mass-energy equivalence on Wikipedia
- “E = mc
^{2}Explained” on the NOVA Science Programming on Air and Online website - “Einstein’s most famous equation: E=mc
^{2}” on the Earth Sky website - Cockroft-Walton Machines on the Manhattan Project History website

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