This is a remarkable discussion of energy sources. No politics, just math and physics.

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Energy Tribune- Understanding E = mc2

When I was in college, I took a course in the great political philosophers. We studied them in order – Hobbes, Locke, Rousseau, Kant, John Stuart Mill and Karl Marx.

In my mind, I had placed them with the historical eras they had influenced – Hobbes and the 18th century monarchs, Locke and the American Revolution, Rousseau and 19th century Romanticism, Kant and the 19th century nation-states, Marx and 20th century Communism.

Then one day I saw a time-line illustrating when they had all lived and died. To my astonishment, each had lived a hundred years before I had placed them in history. The implicated seemed clear. “It takes about a hundred years for a new idea to enter history.”

Almost exactly 100 years ago, Albert Einstein posited the equation E = mc2 in his “Special Theory of Relativity.” The equation suggested a new way of describing the origins of chemical energy and suggested another source of energy that at that point was unknown in history – nuclear energy. Nuclear power made its unfortunate debut in history 40 years later in the form of an atomic bomb. But 100 years later, Americans have not quite yet absorbed the larger implications of Einstein’s equation – a new form of energy that can provide almost unlimited amounts of power with a vanishingly small impact on the environment.

E = mc2. Who has not heard of it? Even Mariah Carey named her last album after it. “E” stands for energy, “m” for mass, and “c” is the speed of light – that’s easy enough. But what does it really mean? (The answer is not “relativity.”)

What E = mc2 says is that matter and energy are interchangeable. There is a continuum between the two. Energy can transform into matter and matter can transform into energy. They are different aspects of the same thing.

This principal of the equivalence of energy and matter was a completely unexpected departure from anything that had gone before. In the 18th century, Antoine Lavoisier, the great French chemist, established the Conservation of Matter. Performing very careful experiments, such as burning a piece of wood, he found that the weight of the resulting gases and ashes were always exactly equal to the weight of the original material. Matter is never created nor destroyed, it only changes form.

Then in the 19th century a series of brilliant scientists – Count Rumford, Sadi Carnot, Rudolf Clausius, Ludwig Boltzman – established the same principal for energy. Energy can take many forms – heat, light, motion, potential energy - but the quantity always remains the same. Energy is never created nor destroyed either.

Now at the dawn of the 20th century, Albert Einstein posited a third principal that united the other two in a totally unexpected way. Einstein stated a Law of Conservation between matter and energy. Nothing like this had ever been imagined before. Yet the important thing is that co-efficient – the speed of light squared. That is a very, very large number, on the order of one quadrillion.

We really don’t have a reference point for a factor of one quadrillion. We know what a trillion is – that’s the federal budget deficit. But a quadrillion is still a bit beyond our ken. What it means, though, is that a very, very large amount of energy transforms into a very, very small amount of matter and a very, very small amount of matter can transform into a very, very large amount of energy.

Perhaps the way to understand the significance of Einstein’s equation is to compare it to another equation, the formula for kinetic energy:


Kinetic energy is the energy of moving objects, “E” once again standing for energy, “m” indicating mass and “v” representing the velocity of the moving object. If you throw a baseball across a room, for example, its energy is calculated by multiplying the mass of the ball times the square of its velocity – perhaps 50 miles per hour.

The two formulas are essentially identical. When brought into juxtaposition, two things emerge:

1. For any given amount of energy, mass and velocity are inversely related. For an identical amount of energy, the higher velocity goes, the less mass is required and vice versa.
   
2. When compared to the velocities of moving objects in nature – wind and water, for instance – the co-efficient in Einstein’s equation is fifteen orders of magnitude larger – the same factor of one quadrillion.

How is this manifested in everyday life? Most of what we are calling “renewable energy” is actually the kinetic flows of matter in nature. Wind and water are matter in motion that we harness to produce energy. Therefore they are measured by the formula for kinetic energy.

Let’s start with hydroelectricity. Water falling off a high dam reaches a speed of about 60 miles per hour or 80 feet per second. Raising the height of the dam by 80 or more feet cannot increase the velocity by more than 20 miles per hour. The only way to increase the energy output is to increase the mass, meaning we must use more water.

The largest dams – Hoover and Glen Canyon on the Colorado River –stand 800 feet tall and back up a reservoir of 250 square miles. This produces 1000 megawatts, the standard candle for an electrical generating station. (Lake Powell, behind Glen Canyon, has silted up somewhat and now produces only 800 MW.)

Environmentalists began objecting to hydroelectric dams in the 1960s precisely because they occupied such vast amounts of land, drowning whole scenic valleys and historic canyons. They have not stopped objecting. The Sierra Club, which opposed construction of the Hetch-Hetchy Dam in Yosemite in 1921, is still trying to tear it down, even though it provides drinking water and 400 megawatts of electricity to San Francisco. Each year more dams are now torn down than are constructed as a result of this campaign.

Wind is less dense than water so the land requirements are even greater. Contemporary 50-story windmills generate 1-½ MW apiece, so it takes 660 windmills to get 1000 MW. They must be spaced about half a mile apart so a 1000-MW wind farm occupies 125 square miles. Unfortunately the best windmills generate electricity only 30 percent of the time, so 1000 MW really means covering 375 square miles at widely dispersed locations.

Tidal power, often suggested as another renewable resource, suffers the same problems. Water is denser than wind but the tides only move at about 5 mph. At the best locations in the world you would need 20 miles of coastline to generate 1000 MW.

What about solar energy? Solar radiation is the result of an E = mc2 transformation as the sun transforms hydrogen to helium. Unfortunately, the reaction takes place 90 million miles away. Radiation dissipates with the square of the distance, so by the time solar energy reaches the earth it is diluted by almost the same factor, 10-15. Thus, the amount of solar radiation falling on a one square meter is 400 watts, enough to power four 100-watt light bulbs. “Thermal solar” – large arrays of mirrors heating a fluid – can convert 30 percent of this to electricity. Photovoltaic cells are slightly less efficient, converting only about 25 percent. As a result, the amount of electricity we can draw from the sun is enough to power one 100-watt light bulb per card table.