Tests of relativistic energy and momentum

Tests of relativistic energy and momentum are aimed at measuring the relativistic expressions for energy, momentum, and mass. According to special relativity, the properties of particles moving approximately at the speed of light significantly deviate from the predictions of Newtonian mechanics. For instance, the speed of light cannot be reached by massive particles.

Today, those relativistic expressions for particles close to the speed of light are routinely confirmed in undergraduate laboratories, and necessary in the design and theoretical evaluation of collision experiments in particle accelerators. See also Tests of special relativity for a general overview.

In classical mechanics, kinetic energy and momentum are expressed as

On the other hand, special relativity predicts that the speed of light is constant in all inertial frames of references. The relativistic energy–momentum relation reads:

from which the relations for rest energy ${\displaystyle E_{0}}$, relativistic energy (rest + kinetic) ${\displaystyle E}$, kinetic energy ${\displaystyle E_{k}}$, and momentum ${\displaystyle p}$ of massive particles follow:

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