Everyone knows the equation E = mc2 . But how many know what it means? And how many understand why it is the key difference that puts nuclear power is in a class by itself when it comes to generating clean energy.

E stands for energy, m is mass and c2 is the speed of light squared. Now the speed of light is a very large number – 186,000 miles per second. That’s 7 ½ times around the world in one second. When you square that number, you get a number that is almost incomprehensively large.

What E = mc2 says is that matter and energy are interchangeable. They are different forms of the same thing. This was a totally new idea when Einstein proposed it in 1905. The 18th century had formulated the idea of the conservation of matter. Matter is never created nor destroyed in chemical reactions but only changes form. If we burn a log and capture the gases, for example, we will find that the residual matter weighs exactly the same as the original log, even though it has now changed form.

The 19th century extended this idea to the conservation of energy. Energy is never created nor destroyed but once again simply changes form. When we burn gasoline in a car engine, it becomes the kinetic energy of the moving car with much energy “wasted” as low-grade heat. But it is not lost. It is just very difficult to recover. If we capture solar energy and use it to generate electricity that runs out over transmission wires to operate an electric motor, much energy will be dissipated along the way. But when added together they will all equal the original amount of solar energy.

Now in 1905 along comes Einstein and posits another form of equality. Matter can become energy and energy can become matter. There is a new co-efficient to this transformation, however – the speed of light squared. This is a number in the quadrillions. We have gotten used to the idea of a trillion – it’s the federal deficit. But a quadrillion is still pretty much beyond our comprehension.

A humongous amount of energy can be transformed into a very, very small amount of matter and very, very small amount of matter can be transformed into a humongous amount of energy.

We can see the first in the creation of the known universe. At one point very early in cosmological history the universe was filled with nothing but energy in the form of radiation. Then at some point most of this radiation condensed into matter. The result was the stars and the planets. But these specks of matter are few and far between with vast, almost incomprehensible distances between them. This is because a huge amount of energy condenses only into a very, very, very small amount of matter, which can be expressed as m = E/c2.

What concerns us far more in our daily life, however, is the conversion of matter into energy. This takes place in a gasoline engine. It also takes place in a nuclear reactor. In a gasoline engine, an undetectable amount of matter is transformed into the kinetic energy of the automobile. In a nuclear reactor, a tiny portion of the uranium in the fuel rods is transformed into a huge amount of electrical energy.

To get an idea of the comparative dimensions with other forms of energy generation, let’s take a look at the formula for kinetic energy, which is what governs anything in motion, particularly hydroelectric water spills, windmills, tidal flows and other forms of what we are calling “renewable” energy. These are energy flows found in nature.

The equation for this kinetic energy is almost exactly the same as Einstein’s formula: E = ½ mv2. The “m” is the mass of the moving object, the “v” is the velocity at which it is moving and “E” is the energy that results.

For windmills, the mass of the air – not very large – must be multiplied by the square of the velocity, usually around 40-50 miles an hour. For hydroelectricity, the energy is the mass of the water – much heavier than air – times the speed it reaches falling off a dam, sometimes as high as 60 miles an hour.

Now a car travelling at 60 miles an hour can cover the length of a football field in three seconds. To us, that’s pretty fast. But compare this to the speed of light - 7 ½ times around the world in one second. The differences are almost incomprehensible.

This is why a nuclear reactor sitting on one square mile can generate 1000 megawatts of electricity, enough to supply a large city. To generate that same output from a wind farm you would need 40 square miles of windmills – and that would only work the 1/3 of the time when the wind is blowing. The same numbers govern hydroelectricity. The two biggest dams in the country – the Hoover Dam and the Glen Canyon Dam – each back up a reservoir of 250 square miles to generate 2000 MW and 1296 MW respectively. No one has yet figured out a way to harness tidal energy but if they do it is easy to calculate to calculate the territory that would be involved. To generate the same 1000 MW will require some kind of energy-capturing device deployed over a stretch 25 miles of coastline.

This “energy density” is what differentiates nuclear from the so-called “renewable” sources. Solar has about the same density as wind and would require the same 40 square miles or more to generate the output of one nuclear reactor.

Fossil fuels occupy an intermediate range but closer to the renewables than to nuclear. Think of it this way. Any chemical reaction involves the same E = mc2 transformation. But the conversion takes place in the electrons, which only constitute about 0.1 percent of the mass of an atom. (The loss of matter is so small that no one has ever been able to measure it.) Yet the amount of energy we get from this undetectable transition is still remarkably large. Think of the effort it would take to push your car for 25 miles. Then recognize you can get the same effort from a gallon of gasoline that can sit on your tabletop.

When we move beyond the amount of energy that we can get from electrons, however, we move into the nucleus, which is where 99.9 percent of the mass of the atom is located. That means we can quickly get almost 1000 times as much energy as we can get from fossil fuels. If a kilogram of gasoline can drive a car 20 miles, a kilogram of nuclear fuel can drive it 20,000 miles.

This is the reason why nuclear is so easy on the environment. Its great energy density makes it possible to run whole cities from one relatively small facility. One 1000-MW reactor can power a city the size of Cincinnati or San Francisco from a one-square-mile installation. With smaller reactors it will be possible to run a town of 20,000 with a modular reactor the size of a gazebo buried beneath the basement of city hall.

The so-called problem of “nuclear waste” does not change this. “Nuclear waste” is simply nuclear fuel that we have not learned to use. Almost everything that comes out of a standard nuclear reactor can be recycled as fuel in other reactors. The French are doing this and when they’re done they are able to bury all their unusable nuclear waste from 40 years of producing 70 percent of their electricity with nuclear beneath the floor of one room at Le Hague. As the French like to say, “All the nuclear waste produced by one person over the course of a lifetime can be contained in one cigarette lighter.”

The comparisons, once again, are so enormous that we fail to comprehend them. Coal produces whole reservoirs of coal ash plus all the carbon dioxide and other polluting gases that are thrown into the atmosphere. Oil and natural gas have similar residues.

When a set of nuclear fuel rods is taken out of a reactor after four years of operation, a mere six ounces of matter have been totally transformed into energy. Yet those six ounces are enough to power a city the size of San Francisco for four years.

How is this possible? Because E = mc2.