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Relativistic Energy and Mass

As it turns out, while length decreases between two points at high speeds, the mass of an object will increase. This has one significant effect on what the object is capable of doing; however, as Einstein once said, "It is not good to introduce the concept of the mass of a moving body." Therefore relativistic mass is not often used, simply the rest mass is calculated. However, the equation to the right does show that as a body approaches the speed of light, the mass of the object approaches infinity, the consequences of which are discussed below.

Right along with time, distance and mass, the kinetic energy of an object needs to be reevaluated for high speeds. Traditionally, physicists thought of kinetic energy as being the product of the mass and the square of the velocity. However, through a few calculations, Einstein found that kinetic energy was the product of the mass, the speed of light squared and gamma minus product of the mass and the speed of light squared, or equivalently:

Note that when the velocity is small compared to the speed of light, this equation will reduce down to the traditional equation for kinetic energy. Also note what happens when the velocity approaches the speed of light. The amount of kinetic energy required to bring the velocity closer to the speed of light approaches infinity. This is because it to reach a speed of c, it would take an infinite amount of energy to accelerate an infinite amount of mass to c. Also, if the velocity were equal to c, the equation would fall apart because there would be a zero in the denominator. Therefore, we can conclude that it is not possible to travel up to or beyond the speed of light.

Einstein's Special Theory of Relativity not only predicted that strange things will happen in space and time when objects approach the speed of light, as has already been shown, but also that matter and energy have more in common than had ever been thought before.

Einstein determined that matter could be thought of as a form of energy and that there would be a quantity called "rest energy" which would be the amount of energy that composed a piece of matter. This rest energy can be determined by Einstein's famous equation E=mc^2 where m is the mass at rest. This equation not only says that mass and energy are equivalent to each other with the speed of light as a conversion factor, but that energy and mass are interchangeable between each other. In other words, mass is a form of energy. We can also add this form of energy to the kinetic energy described above to find the total energy of an object. The result of this is KE + mc^2 or equivalently, the product of gamma, mass and c squared.