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Relativistic - E=m*c^2

c and Einstein  |  c Top Speed  |  Speed & Speed  |  Faster than c?
Mass Gain  |  E=m*c^2  |  Age Slower  |  Time Dilation  |  Twin Paradox
Dopper Shift  |  Ticketed  |  Simultaneity  |  Competition  |  Fast Strudel
Paradox? No!  |  Confusions  | 
 
On this page, we will discuss Einstein's famous energy formula and we explain where the extra mass for moving objects comes from, as we claimed in the previous "Slow down on the Highways!" page.

The theory of relativity predicts that mass is energy and energy is mass up to a multiplicative constant, the square of the speed of light in a vacuum. This means that every single gram of material hides a certain amount of energy inside it, which ultimately can be released in various forms. The best known process is annihilation, when a particle meets its antiparticle and the result is pure gamma radiation.

The opposite process is also possible. Here at Fermilab, we very often create particle-antiparticle pairs from electromagnetic fields.

This equivalency between energy and mass allows us to explain the effective mass gain of moving objects.According to Einstein's formula, before the object started to move, it had energy

where is the rest mass. When the object moves, it also has kinetic energy, so the above formula must be modified: . But is energy also, so we can find its mass equivalent by dividing it by c squared. The final form of the total energy of the object, then, is

Therefore, any moving object increases its mass due to its kinetic energy. This explains why we urged you to Slow down on the highway!

To illustrate how much energy is hidden in matter, let's plug in some typical numbers into the shown formulae. If you take 1 kilogram of matter and release all its available energy, you get Joules, which is roughly the amount of energy that an average U.S. state needs for one year!!! Pretty impressive, isn't it?

On the following pages, we discuss relativistic effects. On the next page we give a recipe how to grow younger than your twin brother or sister!!
 

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last modified 1/5/2001   email Fermilab