Energy - Momentum Relation

Not only the energy changes accompany the mass changes. The momentum also changes. We will write the formulae of energy and momentum and make simple algebraic transformations with these two equalities:

and

Subtracting the second equality from the first one we get:

Or

.

Since the rest mass and the speed of light are invariants in any inertial frame of reference, is constant in all inertial frames, we say it is invariant relative to Lorenz’s transformations. Thus we come to a conclusion that energy and momentum are two components of one quantity, energy-momentum. In other words, energy and momentum are relative quantities, but their relation is absolute.

Moreover, energy-momentum relation may be written as

.

Formula for energy-momentum relation is similar to space-time relation. Thus the energy-momentum invariant can also be construed as a four-dimensional vector with three momentum projections as three components of this vector and as its fourth component.

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