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The History of E=mc² 2008

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The History of


Image courtesy of:




Most people know that E=mc² is Einstein's most famous equation. But most of them don't know where it came from, or what it means.



So What Does It Mean?


In essence, E=mc² means that energy and mass are interchangable. Mass can be converted to energy, and energy to mass, under the right conditions. The factor of conversion is c², where c is the speed of light (300,000 km/s or 186,000 mi/s). This means that a tiny amount of mass could theoretically be converted to a huge amount of energy.


How Did Einstein Come Up With It?


In an earlier paper on relativity, Einstein concluded that energy has mass; he would later conclude that mass has energy. Although he was the first person to put these concepts together in such a simple way, several other people invented some of the ideas he needed to make his discovery.


One of these people was the Dutch scientist Christian Huygens, who lived during the 17th century. While trying to figure out why two swinging balls don't seem to lose energy while colliding (see image), he figured out that the energy of the balls, and every other object, does not follow the rules then believed by physicists. They thought that E=mv; that energy equaled the object's mass times its velocity. However, Huygens found that the energy depends on the square of the speed: E=mv².



When the raised ball hits the others, the ball on the other end

will fly away at the same speed, and reach the same height.

Huygens demonstrated why this happens by showing that the ball's

energy is proportional to the ball's mass times its velocity squared.

Image courtesy of:



Einstein was also influenced by Huygen's related idea that energy cannot be created or destroyed; this is conservation of energy. We can see why this would be important to Einstein, since E=mc² implies that the neither mass nor energy can be destroyed. Rather, it can only be changed to another form.



Others Who Influenced Einstein


In 1921, Michael Faraday realized that electricity and magnetism were connected; he'd discovered electromagnetism. Faraday's understanding that two seemingly different things had, in reality, a fundamental connection paved the way for Einstein to do what was essentially the same thing, except with light and matter.


Emilie du Châtelet (1706-1749), after studying the work of the German physicist Gottfried Leibniz and Dutch physicist Willem 'sGravesande, also showed that energy depended on the square of velocity. 'sGravesande's experiments were particularly important. They showed that a ball falling into a clay floor would penetrate four times farther if its mass was doubled, nine times farther if its mass was tripled, etc. This is consistent with the idea that it is the square of velocity, not just velocity, that determines energy.


Antoine-Laurent Lavoisier (1743-1794) figured out the opposite of Huygen's conservation of energy: conservation of mass. Einstein's equation unites the two ideas by showing that the two can be converted back and forth, thus keeping either from actually being "destroyed."


How to get E=mc² from E=mv²


We've figured out the relationship between a mass's energy and velocity, but how do we figure out how much energy is stored in that mass? The answer is to assume that the greatest possible energy of the mass is produced when the mass is moving at its greatest velocity. Theoretically, that greatest velocity is the speed of light. Taking this into consideration, Einstein decided that he could find the energy stored in the mass by plugging c into E=mv², creating the equation we all recognize: E=mc².


Taylor H.


Sources and Links


Calle, Carlos I. Einstein for Dummies. Hoboken, NJ: Wileyn Publishing, Inc., 2005.


Einstein's Big Idea:  Ancestors of E=mc². Public Broadcasting Service (PBS). March 20, 2008.


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