E=mc^{2}

This is one of the most elegant equations in physics (Maxwell’s might outrank this one, at least among physicists), and certainly the most famous. It is Einstein’s formulation of the equivalence of matter and energy. This formula expresses that equivalence not in theoretical terms, but in solid numbers.

The “e” stands for energy, “m” is for mass, and “c” is the speed of light. As always with plugging numbers into physics equations, we must specify the units we will use. For this we will use kilograms for mass and meters per second for the speed of light. How much energy is equivalent to a specified amount of mass?

Let’s use a kilogram of water. A kilogram of anything else works just as well, but we say water to illustrate how much energy we are talking about in everyday stuff. The solution is one kilogram times the speed of light squared. The speed of light is right at 300,000,000 meters per second. Square that and we have 90,000,000,000,000,000. That is a really big number. We will call this 9 times 10^{16}. But 9 times 10^{16 }what? The units of kilogram-meter-second give us an answer in joules. The joule can be defined in several ways, including the work required to produce one watt of power for one second. It is approximately the amount of heat given off by a person at rest in one hundredth of a second. In other words, a joule does not amount to much. But we have 9 times 10^{16} of them. How much energy is this, really? About the same as that involved in burning 10 million gallons of gasoline. All of that is bound up in one kilogram of water (or anything else).

Is all of that energy available? It is not, at least not with our current technology. Chemical processes, such as burning and conventional explosives, release very little of that energy. The first atomic bomb, set off in New Mexico, released about 80 times 10^{12} joules. That is a miniscule portion of the 10^{16} joules in a single kilogram of matter. Of course, we have improved in weapons since then (if a bigger blast and release of more energy is an improvement). Our biggest nuclear weapons can release almost 1% of the energy in a single kilogram of matter.

We are certainly smart enough to get an even bigger bang. Are we smart enough to decide not to use them?