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.

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