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6. The Standard Model page 25
Special relativity
One of the most famous equations in physics comes out of Einstein's Special Theory of Relativity. It is:
E equals m c squared E is energy
m is mass
c is the speed of light

But what does it mean and what are its implications?

The ultimate speed
Albert Einstein developed the theory of Special Relativity to explain the way in which light behaves. He stated that nothing can travel faster than the speed of light. And only massless objects (such as photons of electromagnetic radiation) actually travel at the speed of light. Anything that has mass can never reach the speed of light.

As a particle with mass approaches the speed of light, it becomes more and more difficult to make it accelerate. We call its resistance to acceleration its inertia. A particle with a bigger inertia has a bigger mass. Einstein showed that, in order to prevent the particle reaching the speed of light, it gains mass equal to its total energy divided by the speed of light squared. So:

formula m is the total mass

Using equations developed by Lorentz, Einstein showed that the way in which the mass of a particle changes with speed is given by:

formula for mass gain m is the total mass
m0 is the rest mass - i.e. the mass of the particle when it is stationary
v is the velocity of the particle

Notice that as v tends towards c, the denominator tends towards zero and so the mass tends towards infinity. This makes it impossible to accelerate the particle enough to reach the speed of light.

Matter into energy
When a particle of matter meets its anti-particle, they annihilate one another and release energy. The amount of energy they release can be found from Einstein's equation by putting in the total mass of the two particles.

For example, if an electron and positron meet, the energy released will be:

E = mc2
    = 2 x 9.11 x 10–31 x (3 x 108)2
    = 1.6 x 10–13 joules

This is 100, 000 times more than the energy released when two molecules of hydrogen combine with a molecule of oxygen to form water. The energy will be carried off as high-frequency gamma radiation.

. . . or back again
Sometimes, the reverse can happen. A system that has an extremely high internal energy can spontaneously create a particle and antiparticle. The masses of the particles can be found from the total energy using Einstein's equation. This is used by physicists who are trying to make new particles in accelerators (see page 21).
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