Date: 12/18/97 at 18:50:50 From: Janice Trujillo Subject: Einstein Dear Dr. Math, I am a fourth grade student. I was wondering if you could explain what E = MC2 means in simple language. I am studying about Albert Einstein. Thank you.
Date: 12/19/97 at 14:47:10 From: Doctor Ceeks Subject: Re: Einstein Hi, You've asked a very challenging question! Strictly speaking, your question belongs to the field of physics, not mathematics. However, we'll try to answer anyway. "E = MC^2" is an equation relating various physical numbers (^2 means squared). "E" stands for "Energy." Energy is a number which you can give to different objects. In physical interactions (such as when you throw a baseball or when a rocket takes off), the amounts of energy the various objects have change. However, even though the amounts of particular objects change, the total amount of energy doesn't. When you throw a ball, the energy of the ball plus the energy of the thrower remains the same, but the ball's energy increases, while the thrower's energy decreases. We say that energy is transfered from the thrower to the baseball. If you want to lift up a book, you have to expend some energy and give it to the book. The book gains energy when you lift it, and the higher you lift it, the more energy it gains. Just by being high above the ground, the book has energy, and the higher the book is, the more energy it has. If you drop the book, the book falls. Because it falls lower and lower, the book loses the energy associated with its height. But remember, energy is always conserved, so the lost energy must be transferred to something. In this case, the energy lost by falling is turned into speed and the book moves faster and faster as it falls. When the book hits the ground, it loses its speed too. Since it is also lower than it used to be, the energy gained by going faster and faster cannot be transferred to the book being higher; instead the energy is transferred into sound, and you hear a big thud when the book hits the ground. "M" stands for "Mass." Mass is another number which you can assign to different objects. This number tells you how hard it is to push the object. The bigger the mass, the harder it is to push the object and make it move. Little pebbles are not very massive in comparison to big boulders; you can throw pebbles, but it's very hard to make a big boulder move at all and it takes more energy to make a big boulder move. "C2" stands for the speed of light multiplied by itself. (When writing this on a computer, it is accepted to write "C^2" and not "C2", as you've done.) The speed of light tells us how fast light travels. It is another number. Einstein's famous equation E = MC^2 says that an object with mass automatically has in its mass, some energy, and more massive objects have more energy. Einstein's equation gives us an idea of how high we can lift a book if we could somehow transfer the energy inherent in an object to the lifting of a book. Nuclear power reactors are big machines which extract the energy inherent in objects and transfer it to our homes so we can use the energy to do things, such as light up a room or bake a turkey. It isn't easy to transfer the energy in an objects mass into something else, and people aren't very good at doing it yet. People don't know how to convert a stone into energy yet, for instance. There are only a few substances for which people know how to extract the energy inherent in the mass and transfer it to some other object. These substances are "radioactive" and should be handled only by experts who know how to handle them safely. Plutonium is an example of such a substance. (Sixty years ago, people didn't know that these substance could be harmful if improperly handled, and some of the first people who worked with them got sick.) Even today, people can't transfer the energy from these substances efficiently. It's like trying to transfer orange juice from a container into a glass and spilling most of the orange juice on the floor. (The orange juice spilt on the floor is still there, but it can't be drunk very easily anymore. When people try to take the energy inherent in the mass of radioactive substances and put it into something else, a lot of the energy goes into uncontrollable things such as noise.) One really amazing thing about Einstein's formula is that before Einstein, nobody even thought that there was energy in an object's mass. In fact, there is so much energy stored in the mass of an object that Einstein's discovery has completely changed the world. Before Einstein, boats couldn't go very far because they would run out of fossil fuels, which is something you can get energy out of by burning. After Einstein, boats were built which could stay at sea for months and months without ever refueling. This is because these "Nuclear powered boats" use things like plutonium to push them through the water now. There are other very profound changes that have taken place because of Einstein's discovery which you can ask your parents about. -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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