The Special Theory of Relativity 135
formula, m = mo/ 1 −v^2 /c^2. As the velocity of a particle approaches c
its mass becomes infinite to a stationary observer.
It is the increase of mass with velocity, which explains why the
ultimate or highest velocity of a particle is c. The mass of a particle is a
measure of its resistance to acceleration by a force. As one accelerates a
particle to velocities approaching c, its mass increases significantly
making it more difficult to accelerate. Because the mass becomes
infinite, exactly in the limit that the velocity becomes c, it is impossible
to generate an infinite force. This explains why the ultimate velocity of
matter is c. No massive particle actually obtains the velocity c since this
would require an infinite amount of energy. Particles whose rest mass is
zero, however, such as the photon, travel at the velocity c. In fact,
photons can never have a velocity less than c.
The expression for the energy in the Theory of Relativity differs quite
markedly from its expression in Newtonian physics. Einstein found,
however, that there is a simple relationship between the energy and the
mass of a particle, namely, the energy of a particle is equal to its mass
times the velocity of light squared, E = mc^2. If we express the relativistic
mass in terms of the particle’s rest mass, mo, and velocity, v, then the
familiar expression for energy, E = mc^2 becomes E = moc^2 / 1 −v^2 /c^2.
Einstein’s expression for the energy for velocities much less than
the speed of light, reduces to E = E = moc^2 + 1/2mov^2 , which differs from
the non-relativistic expression for the kinetic energy, 1/2mov^2 , by the
addition of the extra term, moc^2. This extra term is the rest mass energy
of the particle and is equal to the energy of the particle at rest. According
to the interpretation of this term given by Einstein, the particle has
energy simply by virtue of its rest mass.
This means that mass and energy are equivalent. If this is true, then
one should be able to convert mass into energy and energy into mass just
as one converts energy into heat and heat into energy. This was one of
the major predictions to grow out of Einstein’s Theory of Relativity. It
was on the basis of this prediction that work on the construction of the
atom bomb began in the U.S.A. during World War II. It is sad that the
prediction of a man who struggled for world peace, as Einstein did,
should be verified in a device of war and destruction such as the atom
bomb. The atom bomb was indeed the first device to convert mass into
energy on a large scale. Nuclear fission had only been observed in
laboratory situations before this in which only tiny amounts of energy
were generated.