On September 28, 1905 Einstein completed work on a manuscript he entitled "Does the Inertia of a Body Depend on Its Energy Content?" This small 3 page paper contains an afterthought to Einstein's work on special relativity. It is in this paper that he stated a version of his most famous equation,
What this equation implies, is that energy and mass are two sides of the same coin. That is, energy can be converted into matter, and matter can be converted into energy. The meanings of the symbols are:
Unfortunately, it is very difficult to make this conversion. If we are not interested a controlled release of the energy, then there is one way to make the conversion...
On July 16, 1945 near Alamagordo, New Mexico at the "Trinity Site," the United States detonated an 18.6 kiloton bomb. The amount of energy released was equivalent to the conversion of 0.9 gram of matter into energy. One gram is roughly the mass of a standard paperclip.
The atomic bomb dropped on Hiroshima released an amount of energy equivalent to the conversion of 0.7 grams of matter into energy.
To get some grasp on the meaning of these numbers, let's consider the energy consumption of a typical Johnson City household. The Gardner household (consisting of 6 individuals) uses on average 2000 kilowatt hours per month. The amount of energy provided by the above mentioned atomic bombs would power this household for over 1000 years. The nuclear Tsar Bomba would power the Gardner household for over 2 million years.
Trinity | Hiroshima | Nagasaki | Tsar Bomba |
1250 years | 1000 years | 1300 years | 2.1 million years |
A mathematical derivation of E=mc^{2} by Bob Gardner is available from a math seminar presentation entitled "E=mc^{2} Turns 100" in both PDF and PostScript formats.
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