Astrophysics for a Ten-Year-Old Mind

There is no math in Einstein's equation that goes beyond this, so why isn't it taught to ten-year olds?

Perhaps surprisingly to people outside the field, many educators object to "teaching relativity in grade school" on the grounds that students as young as ten lack the intellectual sophistication necessary to form a meaningful notion of the equivalence between mass and energy. The argument is that children learn science more readily if it pertains to the visible world.

Adherents to this view are too numerous, too respectable, and too well funded to discount. But if you spend much time around ten-year olds, you' ll find many of them already know about atoms, black holes, and antimatter. Their ideas may be a bit vague in detail, just as their ideas of life in London or of the relative sizes of Spain and Brazil are still forming, but children are exposed to media other than textbooks, and through their extracurricular sources, they have acquired some sophisticated interests.

Of course, you don't have to rely on either argument. If you have access to a ten-year old, you can do the experiment yourself.

E=mc2 on a big scale. Inside the Sun, an enormous amount of matter is converted to energy every second. Indeed, the Sun's energy output is equivalent to about four trillion trillion 100 watt light bulbs shining at the same time. Image courtesy of SoHO/EIT consortium. SoHO is a project of international cooperation between ESA and NASA.

Begin by telling her that one of the remarkable results of the century is that matter and energy are two forms of the same thing. Neither can be destroyed but, under special circumstances, either can be turned into the other. This is important. All the matter in the universe condensed out of pure energy over a period of about 700,000 years shortly after the Big Bang, and today, stars shine because matter at their centers is being slowly converted back into energy. Both annihilation of matter into energy and condensation of matter out of energy have been demonstrated in the laboratory.

Explain that one of the most amazing things about all this is that a simple equation will tell you exactly how much energy a given amount of mass contains. Invite your partner to write e=mc2 at the top of a piece of paper. Then take a moment or two for her to tell what she knows about the equation.

Then ask her to write the following just below the first equation.

Energy (in joules) = Mass (in kilograms) X The Speed of Light Squared (in meters squared per second squared)

Be sure she knows what a meter is and then explain that you want to figure out how much energy is contained in a one-liter bottle of water if the entire mass is converted to energy. Begin with the speed of light.

Light travels three hundred million meters in a second so now she can write:

energy = mass X (300,000,000)², or e = m (3 x 10⁸)²

You can leave the units for now, but we cannot forget them at the end. The next step, of course, is to square the speed of light. That produces an even bigger number and makes the need for scientific notation clear. Once that is done, however, the result is a constant that simplifies the equation to:

e = m (90,000,000,000,000,000), or e = m (9 X 10¹⁶)

Mass is next. It is given in kilograms, and, since a liter of water is defined to have a mass of one kilogram, most kids have no trouble with this unit. Because you want to know how much energy is in one liter of water, the mass term is equal to 1 and the equation becomes:

e = 1 (9 X 10¹⁶), or e = 9 X 10¹⁶ joules

That's it. That's the answer. And that is all there is to it. Square the speed of light in meters per second, and you get the energy provided by a kilogram of mass. Swapping values for mass will let kids calculate the energy equivalence for everything from the Sun to a hot dog.

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