These definitions will prove useful: and B=v/c. v is the magnitude of the velocity of an object with respect to the observers refrence frame and c is the speed of light. Energy in relativity is defined as . m is called the rest mass. It is the mass measured in a refrence frame where the object is at rest. Depending on one’s refrence frame, different values of v will be observed. Thus, total energy is dependent on your refrence frame. However, there are quantities that are independent of the observor’s refrence frame. These are called concerved quantities. For example, in euclidean geometry, length is a concerved quantity (think about it for a second). In relativity, we have this famous equation WHICH ALWAYS HOLDS: . P is momentum, and equal to m*v. Now, suppose we are at rest, then p = 0 and we are left with the famous equation E=mc^2. m is a concerved quantity, like electric charge. It does not change from refrence frame to refrence frame. Now, lets see what happens whe v -> c. In this case, B ->1 and gamma -> infinity. This meens that the total energy also goes to infinity. Sometimes people define a relative mass as M=gamma*m. So, M also goes to infinity. The result is that nothing with mass can ever reach the speed of light because otherwise it would have infinite energy. But, what about light? For light, gamma = infinity but we know that photons have finite energy. Well, look at the equation for E again and note that while gamma = infinity, we also have m = 0 … the two cancel each other out to give finite energies. Now, here are some mathematical details. The laurence transformation: Those vectors are called four vectors and the matrix is called the laurence transformation matrix, or also the Minkowski Metric for flat space time. This tells you how to go from one refrence frame to another. It should be clear from observation that under such a transformation length is always contracted and time is dialated. These equations can be derived easily. Simply remember that the speed of light is constant and think about the geometry of a laser beem on a space ship, as observed from both the ship and earth. The momentum four-vector, which also transforms as above, is given by . From here it is easy to see that the total momentum squared is invariant. This then implies that . Ok, that’s as much as I feel like wrighting, for more info see

http://en.wikipedia.org/wiki/Special_relativity or get a book on special rel.