Tests of relativistic energy and momentum
Tests of relativistic energy - momentum relation are used for experimental verification of statements of special relativity, which energy affect kinetic energy, momentum, and mass. According to this theory the properties of very fast moving matter is extremely different from the properties known from classical mechanics. For example, the speed of light can not be achieved by involving mass bodies.
The relativistic energy - momentum relation for example, must be taken into account in the design and in the evaluation of particle physics experiments, and is routinely detected in particles near the speed of light in simple experiments in the context of undergraduate studies in physics. See also Tests of special relativity.
The energy - momentum relation
Refers to the mass, the velocity of a body and the speed of light, then according to classical mechanics the momentum and kinetic energy. This would allow for the appropriate power supply, the light speed is exceeded.
In contrast, says the special theory of relativity, among other things, that the speed of light is an unattainable limiting velocity in inertial frames. This is expressed both by the Lorentz transformation as well as by the relativistic energy - momentum relation:
From this, the relationships for the rest energy of relativistic energy follow ( rest exercise ), kinetic energy and momentum of particles involving mass:
Where. Relativistic energy and momentum to rise as it approaches the speed of light beyond all limits. Therefore, mass -prone particles can not reach this speed.
In some representations, the so-called relativistic (also apparent, effective, or dynamic ) mass is used; with her to keep the equations for momentum and kinetic energy of the classical form. This concept is, however, considered by many authors as unfavorable. Instead, the above expressions for energy and pulse should be used which reproduce the same experimental results.
Initial experiments
First experiments to demonstrate the type of relationship were capable conducted by Walter Kaufmann, Alfred Heinrich Bucherer and others 1901-1915. They were designed to measure the deflection of beta radiation (electrons) in a magnetic field, thereby to determine the charge - to-mass ratio. Since the constancy of the charge was known changes could affect only the mass or the momentum of the electromagnetic field of the electron. The term of the transverse electromagnetic mass was formerly used, equivalent to the above-mentioned relativistic mass. Since in modern texts is the concept of " relativistic mass " hardly used, these experiments can be described according to the above definitions as tests of the relativistic momentum or energy, because it is:
The results of the experiments of Bucherer and Neumann gave a decrease of the charge - to-mass ratio with increasing speed, and consequently an increase of the pulse in quantitative agreement with the theory of special relativity. Later was shown, however, that the measurements were only qualitative agreement, and too inaccurate to exclude certain competing models, as the model of Max Abraham.
However, Arnold Sommerfeld was in 1915, the fine structure of the hydrogen spectrum by means of the relativistic expressions for momentum and energy can be derived ( in the context of the Bohr -Sommerfeld theory). Then Karl Glitscher replaced the relativistic expressions in the derivation of the hydrogen spectrum with those of the theory of Abraham. He showed that Abraham's theory was in contrast to the theory of relativity incompatible with the observations.
Precision measurements
Rogers et al. (1940 ) conducted the first deflection experiments with electrons with sufficient accuracy to refute the competing models conclusive. As in the experiments, the Bucherer -Neumann- charge - to-mass ratio was measured, and the electron velocities of up to 0.75 C was obtained. They improved the measurement method, for example by using a Geiger counter. The possible deviations were only about one percent.
A more accurate experiment led Meyer et al. (1963 ) by. They observed electrons with speeds from 0.987 to 0.99 c. The distractions made it in a static- homogeneous magnetic field was measured with the p, and was in a static- cylindrical electric field measured with the. They confirmed the theory of relativity, with an upper limit for deviations of ~ 0.00037.
As measurements of the charge -to-mass ratio, and hence the momentum of protons were performed. Grove and Fox ( 1953) observed 385 MeV protons moving at ~ 0.7 c. By determining the angular frequencies of the magnetic field and the charge - to-mass ratio could be determined. This, and the measurement of the magnetic center allowing the confirmation of the relativistic prediction with an accuracy of ~ 0.0006.
However Zrelov et al turned. (1958 ) so that the information provided by Grove and Fox were too sparse and such experiments are exposed to considerable difficulties due to the complex motion of the protons. Therefore led Zrelov et al. an extended measurement with 660 - MeV protons, which reached an average speed of 0.8112 c. The speed of the protons was measured by evaluation of the Cherenkov radiation, the pulse of the method of the current flowing through the thin wire, which takes the same form as a corresponding particle path in the magnetic field. The relativistic calculation was confirmed with an upper limit for deviations of ~ 0.0041.
Bertozzi experiment
In particle accelerators, the energy - momentum relation of special relativity was needed in the 1930s, since its introduction, and the above measurements of momentum and velocity confirmed the energy - momentum relation of the theory of relativity also with high precision, so that no doubt was its accuracy. However, the determination of pulse rate and deflection in curves also depends on additional factors and effects that have to be considered together. Therefore led William Bertozzi (1964) An experiment to demonstrate the relativistic effects most clearly, by direct measurement of the velocity and the kinetic energy of electrons.
He used the electron accelerator at MIT for five experimental passages in which electrons were generated with energies between 0.5 and 15 MeV from a Van de Graaff accelerator and 8.4 meters back loaded until they met on an aluminum disc. First, the flight time and thus the velocity of the electrons in all five passages was measured - these data were in close agreement with the theory of special relativity (see image ). The kinetic energy was initially determined indirectly, at this stage by the accelerating fields. Therefore Bertozzi measured the heat ( calorimetry ), which generated electrons between 1.6 to 4.8 MeV on the aluminum plate, and found agreement within an error limit of 10%.
Experiments for the undergraduate studies
Meanwhile, measurements of relativistic energy and the momentum in a simple form in university laboratories, which are suitable for the undergraduate studies, are performed. Three methods are mainly used: a) Experiments with beta radiation, for example, to detect the pulse during deflection in a magnetic field, or the kinetic energy at impact on the detector; b) the Compton effect, the electrons can be brought to relativistic velocity; c) positron annihilation, where the energy and momentum of the resulting radiation can be checked.
High-energy experiments in particle accelerators
In modern particle accelerators, the predictions of special relativity are confirmed routinely at high energies and are needed for design and analysis of collision experiments. For example, the time dilation of moving particles is observed in the decay of unstable particles, and the relativistic addition theorem of velocities is necessary to understand the distribution of the synchrotron radiation. Similarly, the relativistic energy - momentum relation was confirmed in velocity measurements and numerous high-energy experiments.
Speed
Far more than the energy values of the Bertozzi experiment addition of-flight measurements were performed to determine differences in velocity between electrons and light through the Stanford Linear Accelerator Center ( SLAC ). Brown et al. (1973 ) found no difference here and determined an upper limit for the speed differences between 11- GeV electrons and visible light from. Guiragossian et al. (1974) In a further experiment, the accelerated electrons from 15 to 20.5 GeV. They used a Radiofrequenzseparator (RFS ) to measure flight time differences between these electrons and 15 GeV gamma radiation at a distance of 1015 m. Again, no difference was found by a maximum upper limit.
Previously led Alväger et al. (1964 ) at the CERN proton synchrotron by a time of flight measurement to test the Newtonian momentum relationship, as it is valid, for example, in the emission theory. This gamma rays arising from the dismemberment of 6 GeV pions at a rate of 0.99975 c. For validity of the Newtonian relationship the gamma rays would have to be much faster than light. However, no such effect was found, with a maximum ceiling of.
Energy and Calorimetry
The penetration sufficiently fast particles in a particle is accompanied by electron-positron annihilation, Compton scattering, Cherenkov radiation, etc., so that a cascade of effects in the formation of new particles (photons, electrons, neutrinos, etc.) leads. The energy of this Teilchenschauers corresponds to the relativistic kinetic energy and the rest energy of the penetrating particles. Based on the interactions with the detector, this energy can be measured, for example by specially designed calorimeter, this measurement can be effected electrically, optically, thermally or acoustically.
Calorimetric measurements of the relativistic energy to thermal base as described above were already carried out by Bertozzi. It was followed by further measurements by SLAC, where the heat of 1982 accelerated to 20 GeV electrons was measured; calorimeter was used as a water-cooled absorber ( beam dump ) made of aluminum. It was consistent with the relativistic energy-momentum relationship found, but only accurate to 30%. The experimenters pointed out, however, that as early as 1969 calorimetric measurements were performed with 10 GeV electrons. The beam absorber while copper was used, and the theory was confirmed with a far greater accuracy of 1 %.
In modern calorimeters ( which are referred to the type of interaction as either electromagnetically or hadronically ) the energy of the shower particles is often determined by measuring the ionization caused by them. It also comes to suggestions ( scintillation ) in the detector, leading to the emission of light, which is measured by scintillation counter. Similarly, the Cherenkov radiation can be evaluated. These methods implies that the measured energy is proportional to the initial particle.
Annihilation and pair production
Relativistic energy and momentum occur directly in processes such as annihilation and pair formation in appearance. For example, the rest energy of the electron and positron is 0.51 MeV, respectively. Now, when a photon interacts with an atomic nucleus, electron-positron pairs can be formed when the photon has the necessary threshold energy of 1.02 MeV. When the photon energy is larger, the surplus energy is converted into kinetic energy of the particles. The reverse process occurs, for example in electron-positron annihilation at low energies, where photons arise correspond to their total energy and momentum of the initial particles. These are direct examples of the equivalence of mass and energy according to.
Much clearer enter these relationships on at much larger energies where relativistic kinetic energy is converted into rest energy. 1974 accelerated the SLAC accelerator both electrons and positrons to relativistic speeds where their relativistic energy (the sum of the rest energy and kinetic energy ) was approximately 1500 MeV, respectively. In collisions ( see Colliding Beam Experiment) of these particles originated J / ψ mesons with a rest energy of about 3000 MeV. Much larger energies were obtained from 1989 at the Large Electron-Positron Collider, where electrons and positrons were accelerated to 45 GeV, respectively, which W bosons and Z- bosons could arise with rest energies 80-91 GeV. Later energies up to 200 GeV have been achieved, so that these particles could occur in pairs. This high-energy bosons have already created ( 1984) in the Super Proton Synchrotron proton -antiproton collisions. The rest energy of these particles is 0.938 GeV, respectively. You have now accelerated to about 270 GeV, so that the center of mass energy was 540 GeV in the collision. This energy was needed to ensure that their constituents, quarks and anti-quarks, the necessary energy and momentum given to produce W and Z bosons.
In addition to these examples, a large number of experiments were carried out where both solid particles, such as protons and electrons, as well as a large number of unstable particles were produced. In addition to these institutions achieve especially Hadron Collider enormous energies: HERA (up to 920 GeV ), the Tevatron (up to 1 TeV ), the Relativistic Heavy Ion Collider (up to 200 GeV ) and especially the Large Hadron Collider (up to 7 TeV ).