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*E = mc*^{2}

You can calculate the **equivalence between mass and energy** using the special theory of relativity.

##### Explanation

The law of conservation of relativistic momentum applies. Energy can change it's form in a short period of time. An increase in energy is sometimes the product of force and distance traveled. In doing so, the force then causes a change in momentum per time. Therefore you can write

Substitution of the relativistic mass then gives

We use the chain rule and first determine the derivative to *v* and get

To this we apply the product rule

which you can convert to

This can be written as

and that apparently is (but I can't explain that)

This shows that change in energy is equal to change in mass multiplied by the square of the speed of light.

## HistoryGerman physicist Albert Einstein (1879 - 1955) and French mathematician Henri Poincaré (1854 - 1912) developed this formula. |