Relativistic Mechanics - Implications
Whenever a physical theory is replaced, the new theory must give the same answers as
the old theory in all those situations where the old theory was found to be consistent with experiment.
In physics, we never throw anything away.
Different inertial frames see time in different ways and there is no one absolute inertial frame.
However, when a moving object is being described, there is one inertial frame which is uniquely "priviledged": the inertial frame in which the object is momentarily at rest. Definitions given in that frame work
The total energy E of a particle of rest-mass m with velocity v is
The kinetic energy K.E. is just the difference between the energy at velocity v and the energy at rest.
As v approaches c, the kinetic energy increases without limit.
Rewrite the total energy E in the form
Einstein found that, for a system of particles, the sum of the total energies is always conserved.
That result only makes sense if the mc terms include all non-kinetic
forms of energy. The total energy of a particle of mass m when it is at rest is given by