[net.physics] using mass dilation as an energy source

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