lew@ihuxr.UUCP (10/07/83)
The increase in mass often referred to in relativity discussions is really just an artifice to preserve Newton's Second Law (F=ma). In "serious" relativity, the term "mass" is usually taken to be synonymous with "rest mass", so that it is a constant parameter rather than a dynamic variable. The total energy (rest plus kinetic) of a moving object is then given by: E = gamma * m * c^2 where gamma = 1/sqrt( 1 - beta^2 ) ; beta = v/c gamma * m is the "dilated mass". This mass dilation really represents nothing more than the kinetic energy of motion. The idea of using the dilated mass to further power the motion is the same as trying to use the kinetic energy of a rocket to make it go faster. Taking away dilated mass is the same as taking away speed. By the way, note that for beta << 1, gamma ~= 1 + 1/2 * beta^2 so E ~= m*c^2 + 1/2 * m*v^2 This is the classical limit, of course. In the ultra-relativistic limit gamma >> 1, and the rest energy is small compared to the kinetic energy. The kinetic energy, however large, is not available in the object's rest frame. Energy is not a relativistic invariant, just as it is not a classical invariant. Energy transforms as the time-like component of a four-vector, the space-like components being the momentum. The momentum is given by: gamma * m * v ... so you can see the inspiration for calling gamma*m the dilated mass and preserving the Newtonian formulation. Lew Mammel, Jr. ihuxr!lew