Einstein's Special Relativity and Mass Energy Equivalency, E=mc²

Jan 4, 2011
Paul A. Heckert

Einstein's Mass Energy Equivalency Equation - Paul A Heckert

Einstein's famous equation, E=mc², revolutionized physics by equating mass and energy and by providing an equivalency between mass and energy.

Albert Einstein's equation, E=mc², or E equals mc squared, is perhaps the best known equation in physics. This equation is so well known and often so poorly understood that movie star, Cameron Diaz, in a March 1997 interview for Movieline magazine responded that explaining E=mc² would be the hardest question she could ever be asked.

Origin of E=mc²

E=mc² is associated with Einstein's special theory of relativity. This equation does not, however, appear in Einstein's original paper on special relativity. Einstein wrote a short follow-up paper developing the equivalency of mass and energy.

Applying the principles of special relativity to the problem of an object emitting light energy in two opposing directions, Einstein concluded that the object's mass decreased as it emitted energy. Continuing with his logic, Einstein concluded that an object's mass measures the amount of energy it contains. Hence there is an equivalency between mass and energy.

Mass Energy Equivalency

Einstein's equation, E=mc², expresses an equivalency between mass and energy. Mass and energy are two different manifestations of the same thing. Mass is just another form of energy, or energy is just another form of mass. Hence mass can convert into energy, and energy can convert into mass.

The equation, E=mc², acts as a conversion factor telling how much mass converts into how much energy. The quantity, E, represents the amount of energy; m represents the amount of mass; and c represents the speed of light. If mass converts into energy, multiplying the amount of mass by the speed of light squared gives the amount of energy produced.

In the units physicists usually use, mass is measured in kilograms, energy in joules, and speed in meters/second. The speed of light is 3E8 meters/second. Applying Einstein's equation, 1 kilogram of mass converts into 9E16 joules of energy. A joule is very little energy, approximately the amount needed to lift an apple from the floor to a table. However a kilogram of mass converted into energy produces lots of joules and a very large amount of energy.

Implications to Conservation of Energy and Mass Laws

Conservation laws are fundamental laws in physics. They state that the total amount of the conserved quantity in the universe must remain constant. In physics jargon, the quantity is conserved.

Before Einstein, physicists considered mass and energy as two completely different things, both of which were conserved. Mass and energy had separate conservation laws.

When Einstein showed that mass and energy were two different versions of the same thing, the law of conservation of energy and the law of conservation of mass merged into the unified law of conservation of mass-energy. The total amount of mass-energy in the universe must remain constant, but mass and energy can each change into the other according to the conversion equation: E=mc².

To conserve the total mass-energy in the universe, nuclear and chemical reactions that release energy must decrease the total mass of the reactants according to E=mc². The lost mass is the energy source in reactions.

Einstein's Explanation of E=mc²

There is nothing like hearing something directly from the original source. The historical division of the American Institute of Physics (aip.org/history/einstein/voice1.htm) has a recording of Einstein himself explaining the meaning of his famous equation. Hearing Einstein's voice explaining E=mc² is fun.

Despite its simple appearance, Einstein's equation had profound implications for the development of twentieth century physics.