In modern
particle accelerators at high energies, the predictions of special relativity are routinely confirmed, and are necessary for the design and theoretical evaluation of collision experiments, especially in the
ultrarelativistic limit. For instance,
time dilation must be taken into account to understand the dynamics of particle decay, and the
relativistic velocity addition theorem explains the distribution of
synchrotron radiation. Regarding the relativistic energy-momentum relations, a series of high precision velocity and energy-momentum experiments have been conducted, in which the energies employed were necessarily much higher than the experiments mentioned above.
Velocity Time of flight measurements have been conducted to measure differences in the velocities of electrons and light at the
SLAC National Accelerator Laboratory. For instance, Brown
et al. (1973) found no difference in the time of flight of electrons and visible
light, setting an upper limit of velocity differences of \Delta v/c=(-1.3\pm2.7)\times10^{-6}. Another SLAC experiment conducted by Guiragossián
et al. (1974) accelerated electrons up to energies of . They used a radio frequency separator (RFS) to measure time-of-flight differences and thus velocity differences between those electrons and
gamma rays on a path length of . They found no difference, increasing the upper limit to \Delta v/c=2\times10^{-7}. Already before, Alväger
et al. (1964) at the CERN
Proton Synchrotron executed a time of flight measurement to test the Newtonian momentum relations for light, being valid in the so-called
emission theory. In this experiment, gamma rays were produced in the decay of pions traveling at 0.99975. If Newtonian momentum p=mv were valid, those gamma rays should have traveled at superluminal speeds. However, they found no difference and gave an upper limit of \Delta v/c=10^{-5}.
Energy and Calorimetry The intrusion of particles into
particle detectors is connected with
electron–positron annihilation, Compton scattering,
Cherenkov radiation etc., so that a cascade of effects is leading to the production of new particles (photons, electrons,
neutrinos, etc.). The energy of such
particle showers corresponds to the relativistic kinetic energy and rest energy of the initial particles. This energy can be measured by
calorimeters in an electrical, optical, thermal, or acoustical way. Thermal measurements in order to estimate the relativistic kinetic energy were already carried out by Bertozzi as mentioned above. Additional measurements at SLAC followed, in which the heat produced by electrons was measured in 1982. A
beam dump of water-cooled
aluminium was employed as calorimeter. The results were in agreement with special relativity, even though the accuracy was only 30%. However, the experimentalists alluded to the fact, that calorimetric tests with electrons were executed already in 1969. There,
copper was used as beam dump, and an accuracy of 1% was achieved. In modern calorimeters called electromagnetic or
hadronic depending on the interaction, the energy of the particle showers is often measured by the
ionization caused by them. Also excitations can arise in
scintillators (see
scintillation), whereby light is emitted and then measured by a
scintillation counter. Cherenkov radiation is measured as well. In all of those methods, the measured energy is proportional to the initial particle energy. For instance, the rest energy of electrons and
positrons is respectively. When a photon interacts with an
atomic nucleus, electron-positron pairs can be generated in case the energy of the photon matches the required
threshold energy, which is the combined electron-positron rest energy of . However, if the photon energy is even higher, then the exceeding energy is converted into kinetic energy of the particles. The reverse process occurs in
electron-positron annihilation at low energies, in which process photons are created having the same energy as the electron-positron pair. These are direct examples of E_0=mc^2 (
mass–energy equivalence). There are also many examples of conversion of relativistic kinetic energy into rest energy. In 1974,
SLAC National Accelerator Laboratory accelerated electrons and positrons up to relativistic velocities, so that their relativistic energy \gamma mc^{2} (i.e. the sum of their rest energy and kinetic energy) is significantly increased to about each. When those particles collide, other particles such as the
J/ψ meson of rest energy of about were produced. Much higher energies were employed at the
Large Electron–Positron Collider in 1989, where electrons and positrons were accelerated up to each, in order to produce
W and Z bosons of rest energies between . Later, the energies were considerably increased to to generate pairs of W bosons. Such bosons were also measured using
proton-
antiproton annihilation. The combined rest energy of those particles amounts to approximately each. The
Super Proton Synchrotron accelerated those particle up to relativistic velocities and energies of approximately each, so that the
center of mass energy at the collision reaches . Thereby,
quarks and
antiquarks gained the necessary energy and momentum to annihilate into
W and Z bosons. Many other experiments involving the creation of a considerable amount of different particles at relativistic velocities have been (and still are) conducted in
hadron colliders such as
Tevatron (up to ), the
Relativistic Heavy Ion Collider (up to ), and most recently the
Large Hadron Collider (up to ) in the course of searching for the
Higgs boson. ==Nuclear reactions==