Origin of E=mc^2

[BruceZ]

Here's one of the few equations which has become well-known to the average man on the street, and most of you know that it relates the amount of energy contained in matter to its mass. However, I'll bet many of you assume that since this equation led to the release of some of this energy in atomic bombs and nuclear reactors, that the derivation of this equation must involve knowledge of nuclear or atomic physics. Then you would be surprised to learn that it does not, and moreover, all it depends on are the kinematical and dynamical concepts of velocity, momentum, and energy, which are within the grasp of the average student of high school physics. Probably most people on this forum have enough knowledge to sit down with a blank piece of paper and derive this equation if only they were "smart" enough. If you already know the conclusions of special relativity, the derivation is really straightforward.

If you never heard of special relativity, you would first have to recognize the fallacy of classical physics as it pertains to the relationship between velocities on frames of reference that are moving with respect to each other, and then derive the equations of special relativity which relate these correctly. Then using this relationship, rework the conservation of momentum equation for the classical elastic billiard ball collision. This leads to an equation for the mass of a particle which depends on its velocity. Now consider a particle, initially at rest, acted on by a force which moves the particle some distance, and plug the equation for mass into the standard definition of the work done on this particle, which equals the final kinetic energy of the particle. Evaluating this equation for a velocity of zero leads to the conclusion that a particle has energy even when at rest, and this energy is mc^2.

So amazingly, we have learned that matter is composed of bundles of energy, and we deduced this not from any consideration of the internal structure of matter, but just from the laws of motion.