Tests of relativistic energy and momentum
Tests of relativistic energy and momentum are aimed at measuring the
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.[1][2] See also Tests of special relativity for a general overview.
Overview
In classical mechanics, kinetic energy and momentum are expressed as
On the other hand,
- ,
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 "
Early experiments
First experiments capable of detecting such relations were conducted by
Electrons traveling between 0.25–0.75c indicated an increase of momentum in agreement with the relativistic predictions, and were considered as clear confirmations of special relativity. However, it was later pointed out that although the experiments were in agreement with relativity, the precision wasn't sufficient to rule out competing models of the electron, such as the one of Max Abraham.[3][4]
Already in 1915, however, Arnold Sommerfeld was able to derive the Fine structure of hydrogen-like spectra by using the relativistic expressions for momentum and energy (in the context of the Bohr–Sommerfeld theory). Subsequently, Karl Glitscher simply substituted the relativistic expression's for Abraham's, demonstrating that Abraham's theory is in conflict with experimental data and is therefore refuted, while relativity is in agreement with the data.[5]
Precision measurements
In 1940, Rogers et al. performed the first electron deflection test sufficiently precise to definitely rule out competing models. As in the Bucherer-Neumann experiments, the velocity and the charge-mass-ratio of beta particles of velocities up to 0.75c was measured. However, they made many improvements, including the employment of a Geiger counter. The accuracy of the experiment by which relativity was confirmed was within 1%.[6]
An even more precise electron deflection test was conducted by Meyer et al. (1963). They tested electrons traveling at velocities from 0.987 to 0.99c, which were deflected in a static homogenous magnetic field by which p was measured, and a static cylindrical electric field by which was measured. They confirmed relativity with an upper limit for deviations of ~0.00037.[7]
Also measurements of the charge-to-mass ratio and thus momentum of protons have been conducted. Grove and Fox (1953) measured 385-MeV protons moving at ~0.7c. Determination of the angular frequencies and of the magnetic field provided the charge-to-mass ratio. This, together with measuring the magnetic center, allowed to confirm the relativistic expression for the charge-to-mass ratio with a precision of ~0.0006.[8]
However, Zrelov et al. (1958) criticized the scant information given by Grove and Fox, emphasizing the difficulty of such measurements due to the complex motion of the protons. Therefore, they conducted a more extensive measurement, in which protons of 660 MeV with mean velocity of 0.8112c were employed. The proton's momentum was measured using a Litz wire, and the velocity was determined by evaluation of Cherenkov radiation. They confirmed relativity with an upper limit for deviations of ~0.0041.[9]
Bertozzi experiment
Since the 1930s, relativity was needed in the construction of particle accelerators, and the precision measurements mentioned above clearly confirmed the theory as well. But those tests demonstrate the relativistic expressions in an indirect way, since many other effects have to be considered in order to evaluate the deflection curve, velocity, and momentum. So an experiment specifically aimed at demonstrating the relativistic effects in a very direct way was conducted by William Bertozzi (1962, 1964).[10][11]
He employed the
Undergraduate experiments
Various experiments have been performed which, due to their simplicity, are still used as
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Particle accelerators
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.[2] 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.[24]
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 11-GeV electrons and visible light, setting an upper limit of velocity differences of .[25] Another SLAC experiment conducted by Guiragossián et al. (1974) accelerated electrons up to energies of 15 to 20.5 GeV. They used a radio frequency separator (RFS) to measure time-of-flight differences and thus velocity differences between those electrons and 15-GeV gamma rays on a path length of 1015 m. They found no difference, increasing the upper limit to .[26]
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 6-GeV pions traveling at 0.99975c. If Newtonian momentum were valid, those gamma rays should have traveled at superluminal speeds. However, they found no difference and gave an upper limit of .[27]
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.[28]
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 20-GeV 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%.[29] However, the experimentalists alluded to the fact, that calorimetric tests with 10-GeV electrons were executed already in 1969. There, copper was used as beam dump, and an accuracy of 1% was achieved.[30]
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.[28]
Annihilation and pair production
Relativistic energy and momentum can also be measured by studying processes such as
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 (i.e. the sum of their rest energy and kinetic energy) is significantly increased to about 1500 MeV each. When those particles collide, other particles such as the
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 1 TeV), the Relativistic Heavy Ion Collider (up to 200 GeV), and most recently the Large Hadron Collider (up to 7 TeV) in the course of searching for the Higgs boson.
Nuclear reactions
The relation can be tested in
A particularly sensitive test was carried out in 2005 in the
References
- ^ ISBN 0-7167-2327-1.
- ^ S2CID 53334246
- S2CID 121179531
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- .
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- ^ Zrelov, V. P.; Tiapkin, A. A.; Farago, P. S. (1958). "Measurement of the mass of 600 MeV protons". Soviet Physics JETP. 7 (3): 384–387.
- ^ Bertozzi, William (1962), The Ultimate Speed - An Exploration with High Energy Electrons https://www.youtube.com/watch?v=B0BOpiMQXQA
- ^ arXiv:1108.5977 [physics.ed-ph].
- doi:10.1119/1.12973
- S2CID 122167869
- doi:10.1119/1.17611
- doi:10.1119/1.15902
- doi:10.1119/1.12659
- ISBN 978-981-02-2749-4.
- OSTI 1443188
- .
- ^ .
- OSTI 1446354.
- OSTI 4752864.
- ^ Burton Richter (1976). "From the Psi to Charm – The Experiments of 1975 and 1976". Nobel lecture 1976.
- hdl:2066/124399
- ^ Carlo Rubbia (1984). "Experimental Observation of the Intermediate Vector Bosons W+, W- and Z0". Nobel lecture 1984.
- ISSN 1521-3889.
- .
- .
- NIST. 2005.
- S2CID 4426118.
External links
- Physics FAQ: List of SR tests