# Chapter 4.3 Mass is energy: energy is mass

Einstein had a mind that leapt nimbly from one new idea to the next. His powerful sense of intuition steered him to a safe landing and a new discovery. These leaps make his scientific essays miniature works of art. They are simple and graceful, but reveal a mind dancing among the deepest ideas. One example of such a leap is his claim that energy and mass are the same thing. Strictly speaking, relativistic mass increase says only that a given hunk of mass will gain or lose weight as its speed changes: more or less speed is more or less mass.

Strictly speaking, this does not imply that all mass is made up of energy. For example, just because blowing air into a balloon or releasing it from the balloon changes the size of the balloon, we do not say that the balloon is entirely made up of air. The red plastic must be there first.

But Einstein leapt. If some mass is produced by increased energy then, he claimed, all mass is just energy. Thus his famous formula does not say that adding energy produces a change in mass – as adding air swells a balloon. It just says that energy is mass, and mass is energy. It took some time before other physicists were convinced that Einstein was right. Now they routinely transform mass into energy and vice versa in their experiments. It is even common to transform solid matter into nothing but pure energy.

Thus the first important idea contained in Einstein’s short formula is that energy can be converted into mass and vice versa: the interconvertibility of mass and energy. This interconversion has an important consequence; it shows that the law of conservation of energy and the law of conservation of mass are false. In classical physics before Einstein, these were regarded as fundamental. But when mass is converted into energy, the total amount of mass in the universe decreases just as the total amount of energy increases.

Thus neither total is conserved. To save the general idea of conservation, physicists combined the two laws. After Einstein, they said that the total amount of mass and energy together is conserved when all measurements are made by the same set of rulers and clocks. This new idea is called the law of conservation of mass–energy. (Physicists discovered later that this law holds only on average: for short times the total amount of mass–energy can fluctuate up or down.) Einstein’s formula also contains a second idea lodged in the little letter c. It is this which makes the formula so dangerous, and so profoundly shaped the twentieth century. How much energy comes from a given hunk of matter? Suppose we have one ounce or one gram of matter and convert it into energy. How much oomph do we get?

The formula makes the calculation easy. For the letter m substitute the amount of mass to be converted. Then multiply by c squared to get the energy. This looks very innocent, but in fact c squared is a very big number: 9,000,000,000,000. In words, this is nine trillion (using units of metres per second squared).

Thus one gram of matter, about the weight of a feather, will produce an explosion about the same size as 20,000 tons of exploding dynamite! This was the size of the atomic bomb dropped on Hiroshima. If the energy trapped in your body were suddenly all released, Earth would be shattered.