Einstein

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/