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29-560: In the past, the apparent violation of the GZK limit has inspired cosmologists and theoretical physicists to suggest other ways that circumvent the limit. These theories propose that ultra-high energy cosmic rays are produced near our galaxy or that Lorentz covariance is violated in such a way that protons do not lose energy on their way to our galaxy. The limit was independently computed in 1966 by Kenneth Greisen , Georgy Zatsepin , and Vadim Kuzmin based on interactions between cosmic rays and

58-496: A higher energy than ordinary electron-positron pair production (lepton production) from protons impacting the CMB, which starts at cosmic-ray proton energies of only about 10  eV . However, pion production events drain 20% of the energy of a cosmic-ray proton, as compared with only 0.1% of its energy for electron–positron pair production. This factor of 200 = ⁠ 20%  / 0.1%  ⁠ comes from two causes: The pion has

87-403: A mass only about ~130 times the leptons, but the extra energy appears as different kinetic energies of the pion or leptons, and results in relatively more kinetic energy transferred to a heavier product pion, in order to conserve momentum . The much larger total energy losses from pion production result in pion production becoming the process limiting high-energy cosmic-ray travel, rather than

116-561: A mixture of elements, which is getting heavier with increasing energy. The Telescope Array Project , a joint effort from members of the HiRes and AGASA collaborations, agrees with the former HiRes result that these cosmic rays look like protons. The claim is based on data with lower statistical significance, however. The area covered by Telescope Array is about one third of the area covered by the Pierre Auger Observatory, and

145-562: A suppression in the UHECR spectrum at just the right energy, observing only 13 events with an energy above the threshold, while expecting 43 with no suppression. This was interpreted as the first observation of the GZK limit. Auger confirmed the flux suppression, but did not claim it to be the GZK limit: instead of the 30 events necessary to confirm the AGASA results, Auger saw only two, which are believed to be heavy-nuclei events. The flux suppression

174-498: Is also known as GZK horizon. The precise GZK limit is derived under the assumption that ultra-high energy cosmic rays , those with energies above 1 × 10  eV , are protons. Measurements by the largest cosmic-ray observatory, the Pierre Auger Observatory , suggest that most ultra-high energy cosmic rays are heavier elements known as HZE ions . In this case, the argument behind the GZK limit does not apply in

203-496: Is also true for the third class, which is furthermore protected from radiative corrections as one still has an exact (quantum) symmetry. Even though there is no evidence of the violation of Lorentz invariance, several experimental searches for such violations have been performed during recent years. A detailed summary of the results of these searches is given in the Data Tables for Lorentz and CPT Violation. Lorentz invariance

232-616: Is also violated in QFT assuming non-zero temperature. There is also growing evidence of Lorentz violation in Weyl semimetals and Dirac semimetals . Akeno Giant Air Shower Array The Akeno Giant Air Shower Array ( AGASA ) was an array of particle detectors designed to study the origin of ultra-high-energy cosmic rays . It was deployed from 1987 to 1991 and decommissioned in 2004. It consisted of 111 scintillation detectors and 27 muon detectors spread over an area of 100 km . It

261-534: The Δ {\displaystyle \Delta } resonance , or Pions produced in this manner proceed to decay in the standard pion channels – ultimately to photons for neutral pions, and photons, positrons, and various neutrinos for positive pions. Neutrons also decay to similar products, so that ultimately the energy of any cosmic ray proton is drained off by production of high-energy photons plus (in some cases) high-energy electron–positron pairs and neutrino pairs. The pion production process begins at

290-666: The AGASA experiment that there is no suppression was overruled. It remains controversial whether the suppression is due to the GZK effect. The GZK limit only applies if ultra-high-energy cosmic rays are mostly protons. In July 2007, during the 30th International Cosmic Ray Conference in Mérida, Yucatán, México, the High Resolution Fly's Eye Experiment (HiRes) and the Pierre Auger Observatory (Auger) presented their results on ultra-high-energy cosmic rays (UHECR). HiRes observed

319-543: The Fermi Gamma-ray Space Telescope (formerly GLAST) will also provide data that will help resolve these inconsistencies. Lorentz covariance In relativistic physics , Lorentz symmetry or Lorentz invariance , named after the Dutch physicist Hendrik Lorentz , is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay

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348-698: The Standard Model . Irrelevant Lorentz violating operators may be suppressed by a high cutoff scale, but they typically induce marginal and relevant Lorentz violating operators via radiative corrections. So, we also have very strict and severe constraints on irrelevant Lorentz violating operators. Since some approaches to quantum gravity lead to violations of Lorentz invariance, these studies are part of phenomenological quantum gravity . Lorentz violations are allowed in string theory , supersymmetry and Hořava–Lifshitz gravity . Lorentz violating models typically fall into four classes: Models belonging to

377-492: The University of Utah . The Telescope Array , a merger of the AGASA and High Resolution Fly's Eye (HiRes) groups, and the Pierre Auger Observatory have improved on the results from AGASA by building larger, hybrid detectors and collecting greater quantities of more precise data. 35°47′13″N 138°28′34″E  /  35.786966°N 138.47625°E  / 35.786966; 138.47625 This article about

406-590: The (transformational) nature of a Lorentz tensor can be identified by its tensor order , which is the number of free indices it has. No indices implies it is a scalar, one implies that it is a vector, etc. Some tensors with a physical interpretation are listed below. The sign convention of the Minkowski metric η = diag  (1, −1, −1, −1) is used throughout the article. In standard field theory, there are very strict and severe constraints on marginal and relevant Lorentz violating operators within both QED and

435-453: The GZK limit. These observations appear to contradict the predictions of special relativity and particle physics as they are presently understood. However, there are a number of possible explanations for these observations that may resolve this inconsistency. Another suggestion involves ultra-high-energy weakly interacting particles (for instance, neutrinos ), which might be created at great distances and later react locally to give rise to

464-404: The Pierre Auger Observatory the effect is statistically significant at the level of 20 standard deviations. After the flux suppression was established, a heated debate ensued whether cosmic rays that violate the GZK limit are protons. The Pierre Auger Observatory, the world's largest observatory, found with high statistical significance that ultra-high-energy cosmic rays are not purely protons, but

493-541: The fact that Telescope Array has not collected enough events yet to distinguish the pure-proton hypothesis from the mixed-nuclei hypothesis. EUSO , which was scheduled to fly on the International Space Station (ISS) in 2009, was designed to use the atmospheric- fluorescence technique to monitor a huge area and boost the statistics of UHECRs considerably. EUSO is to make a deep survey of UHECR-induced extensive air showers (EASs) from space, extending

522-476: The first two classes can be consistent with experiment if Lorentz breaking happens at Planck scale or beyond it, or even before it in suitable preonic models, and if Lorentz symmetry violation is governed by a suitable energy-dependent parameter. One then has a class of models which deviate from Poincaré symmetry near the Planck scale but still flows towards an exact Poincaré group at very large length scales. This

551-419: The latter has been running for a longer time. The controversy was partially resolved in 2017, when a joint working group formed by members of both experiments presented a report at the 35th International Cosmic Ray Conference. According to the report, the raw experimental results are not in contradiction with each other. The different interpretations are mainly based on the use of different theoretical models and

580-421: The lower-energy process of light-lepton production. The pion production process continues until the cosmic ray energy falls below the threshold for pion production. Due to the mean path associated with this interaction, extragalactic cosmic ray protons traveling over distances larger than 50  Mpc ( 163  Mly ) and with energies greater than the threshold should never be observed on Earth. This distance

609-589: The measured energy spectrum well beyond the GZK cutoff. It is to search for the origin of UHECRs, determine the nature of the origin of UHECRs, make an all-sky survey of the arrival direction of UHECRs, and seek to open the astronomical window on the extreme-energy universe with neutrinos. The fate of the EUSO Observatory is still unclear, since NASA is considering early retirement of the ISS. Launched in June 2008,

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638-484: The originally simple form: however, as Greisen noted, the giant dipole resonance also occurs roughly in this energy range (at 10 EeV/nucleon) and similarly restricts very long-distance propagation. A number of observations have been made by the largest cosmic-ray experiments Akeno Giant Air Shower Array (AGASA), High Resolution Fly's Eye Cosmic Ray Detector , the Pierre Auger Observatory and Telescope Array Project that appeared to show cosmic rays with energies above

667-490: The particles observed. In the proposed Z-burst model, an ultra-high-energy cosmic neutrino collides with a relic anti-neutrino in our galaxy and annihilates to hadrons. This process proceeds through a (virtual) Z-boson: The cross-section for this process becomes large if the center-of-mass energy of the neutrino antineutrino pair is equal to the Z-boson mass (such a peak in the cross-section is called "resonance"). Assuming that

696-409: The photons of the cosmic microwave background radiation (CMB). They predicted that cosmic rays with energies over the threshold energy of 5 × 10  eV would interact with cosmic microwave background photons γ C M B , {\displaystyle \gamma _{\rm {CMB}}\;,} relatively blueshifted by the speed of the cosmic rays, to produce pions through

725-462: The relic anti-neutrino is at rest, the energy of the incident cosmic neutrino has to be where m Z {\displaystyle m_{Z}} is the mass of the Z-boson, and m ν {\displaystyle m_{\nu }} the mass of the neutrino. A suppression of the cosmic-ray flux that can be explained with the GZK limit has been confirmed by the latest generation of cosmic-ray observatories. A former claim by

754-457: The same for all observers that are moving with respect to one another within an inertial frame . It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space". Lorentz covariance , a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings: On manifolds ,

783-493: The words covariant and contravariant refer to how objects transform under general coordinate transformations. Both covariant and contravariant four-vectors can be Lorentz covariant quantities. Local Lorentz covariance , which follows from general relativity , refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point. There is a generalization of this concept to cover Poincaré covariance and Poincaré invariance. In general,

812-580: Was operated by the Institute for Cosmic Ray Research , University of Tokyo at the Akeno Observatory . The results from AGASA were used to calculate the energy spectrum and anisotropy of cosmic rays. The results helped to confirm the existence of ultra-high energy cosmic rays ( > 5 × 10  eV ), such as the so-called " Oh-My-God " particle that was observed by the Fly's Eye experiment run by

841-482: Was previously brought into question when the AGASA experiment found no suppression in their spectrum. According to Alan Watson , former spokesperson for the Auger Collaboration, AGASA results have been shown to be incorrect, possibly due to the systematic shift in energy assignment. In 2010 and the following years, both the Pierre Auger Observatory and HiRes confirmed again a flux suppression, in case of

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