## Thursday, 9 July 2009

### Mass-Energy Equivalence

Mass-Energy Equivalence:
Since special relativity demonstrates that space and time are variable concepts from different
frames of reference, then velocity (which is space divided by time) becomes a variable as well. If
velocity changes from reference frame to reference frame, then concepts that involve velocity must
also be relative. One such concept is momentum, motion energy.
Momentum, as defined by Newtonian, can not be conserved from frame to frame under special
relativity. A new parameter had to be defined, called relativistic momentum, which is conserved,
but only if the mass of the object is added to the momentum equation.
This has a big impact on classical physics because it means there is an equivalence between mass
and energy, summarized by the famous Einstein equation:
The implications of this was not realized for many years. For example, the production of energy in
nuclear reactions (i.e. fission and fusion) was shown to be the conversion of a small amount of
atomic mass into energy. This led to the development of nuclear power and weapons.
As an object is accelerated close to the speed of light, relativistic effects begin to dominate. In
particular, adding more energy to an object will not make it go faster since the speed of light is the
limit. The energy has to go somewhere, so it is added to the mass of the object, as observed from
the rest frame. Thus, we say that the observed mass of the object goes up with increased velocity.
So a spaceship would appear to gain the mass of a city, then a planet, than a star, as its velocity
increased. Likewise, the equivalence of mass and energy allowed Einstein to predict that the photon has
momentum, even though its mass is zero. This allows the development of light sails and
photoelectric detectors.