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 , relativistic energy (rest + kinetic) , kinetic energy , and momentum of massive particles follow: where . So relativistic energy and momentum significantly increase with speed, thus the speed of light cannot be reached by massive particles. In some relativity textbooks, the so-called "relativistic mass" is used as well. However, this concept is considered disadvantageous by many authors, instead the expressions of relativistic energy and momentum should be used to express the velocity dependence in relativity, which provide the same experimental predictions. Kaufmann–Bucherer–Neumann experiments First experiments capable of detecting such relations were conducted by Walter Kaufmann, Alfred Bucherer and others between 1901 and 1915. These experiments were aimed at measuring the deflection of beta rays within a magnetic field so as to determine the mass-to-charge ratio of electrons. Since the charge was known to be velocity independent, any variation had to be attributed to alterations in the electron's momentum or mass (formerly known as transverse electromagnetic mass equivalent to the "relativistic mass" as indicated above).