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Lorentz-violating Electrodynamics
Searches for Lorentz violation involving photons provide one possible test of relativity. Examples range from modern versions of the classic Michelson–Morley experiment that utilize highly stable electromagnetic resonant cavities to searches for tiny deviations from ''c'' in the speed of light emitted by distant astrophysical sources. Due to the extreme distances involved, astrophysical studies have achieved sensitivities on the order of parts in 1038. Minimal Lorentz-violating electrodynamics The most general framework for studies of relativity violations is an effective field theory called the Standard-Model Extension (SME). Lorentz-violating operators in the SME are classified by their mass dimension d. To date, the most widely studied limit of the SME is the minimal SME, which limits attention to operators of renormalizable mass-dimension, d=3,4, in flat spacetime. Within the minimal SME, photons are governed by the Lagrangian density : \mathcal = -\textstyle\,F_F^ +\te ...
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Michelson–Morley Experiment
The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 1887 by American physicists Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year. The experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The result was negative, in that Michelson and Morley found no significant difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles. This result is generally considered to be the first strong evidence against the then-prevalent aether theory, as well as initiating a line of research that eventually led to special r ...
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Resonant Cavities
A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator can be either electromagnetic or mechanical (including acoustic). Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency. A cavity resonator is one in which waves exist in a hollow space inside the device. In electronics and radio, microwave cavities consisting of hollow metal boxes are used in microwave transmitters, receivers and test equipment to control frequency, in place of the tuned circuits which are used at lower frequ ...
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Electrodynamics
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electricity and magnetism, two distinct but closely intertwined phenomena. In essence, electric forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between ''moving'' charged particles. These two effects combine to create electromagnetic fields in the vicinity of charge particles, which can exert influence on other particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force. The electromagnetic force is responsible for many o ...
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Test Theories Of Special Relativity
Test theories of special relativity give a mathematical framework for analyzing results of experiments to verify special relativity. An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of relativity. For example, a test theory may have a different postulate about light concerning one-way speed of light vs. two-way speed of light, it may have a preferred frame of reference, and may violate Lorentz invariance in many different ways. Test theories predicting different experimental results from Einstein's special relativity, are ''Robertson's test theory (1949)'', and the ''Mansouri–Sexl theory (1977)'' which is equivalent to Robertson's theory. Another, more extensive model is the Standard-Model Extension, which also includes the standard model and general relativity. Robertson–Mansouri–Sexl framework Basic principles Howard Percy Robertson (1949) extended the L ...
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Tests Of Special Relativity
Special relativity is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as gravitation is not significant. Many experiments played (and still play) an important role in its development and justification. The strength of the theory lies in its unique ability to correctly predict to high precision the outcome of an extremely diverse range of experiments. Repeats of many of those experiments are still being conducted with steadily increased precision, with modern experiments focusing on effects such as at the Planck scale and in the neutrino sector. Their results are consistent with the predictions of special relativity. Collections of various tests were given by Jakob Laub, Zhang, Mattingly, Clifford Will, and Roberts/Schleif. Special relativity is restricted to flat spacetime, ''i.e.'', to all phenomena without significant influence of gravitation. The latter lies in the domain of general relativity and the corresponding tests of ge ...
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Lorentz-violating Neutrino Oscillations
Lorentz-violating neutrino oscillation refers to the quantum phenomenon of neutrino oscillations described in a framework that allows the breakdown of Lorentz invariance. Today, neutrino oscillation or change of one type of neutrino into another is an experimentally verified fact; however, the details of the underlying theory responsible for these processes remain an open issue and an active field of study. The conventional model of neutrino oscillations assumes that neutrinos are massive, which provides a successful description of a wide variety of experiments; however, there are a few oscillation signals that cannot be accommodated within this model, which motivates the study of other descriptions. In a theory with Lorentz violation, neutrinos can oscillate with and without masses and many other novel effects described below appear. The generalization of the theory by incorporating Lorentz violation has shown to provide alternative scenarios to explain all the established experim ...
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Atomic Clocks
An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions between such states they interact with a very specific frequency of electromagnetic radiation. This phenomenon serves as the basis for the International System of Units' (SI) definition of a second:The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, \Delta \nu_\mathsf, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be when expressed in the unit Hz, which is equal to s−1. This definition is the basis for the system of International Atomic Time (TAI), which is maintained by an ensemble of atomic clocks around the world. The system of Coordinated Universal Time (UTC) that is the basis of civil time implements leap seconds to allow cloc ...
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Particle Accelerator
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle physics. The largest accelerator currently active is the Large Hadron Collider (LHC) near Geneva, Switzerland, operated by the CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5  TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV. Other powerful accelerators are, RHIC at Brookhaven National Laboratory in New York and, formerly, the Tevatron at Fermilab, Batavia, Illinois. Accelerators are also used as synchrotron light sources for the study of condensed matter physics. Smaller particle accelerators are used in a wide variety of applications, including particle therapy for oncological purposes, radioisotope production for medical diagnostics, ion ...
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Optical Cavities
An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that forms a cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers. Light confined in the cavity reflects multiple times, producing modes with certain resonance frequencies. Modes can be decomposed into longitudinal modes that differ only in frequency and transverse modes that have different intensity patterns across the cross-section of the beam. Many types of optical cavity produce standing wave modes. Different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them. Flat mirrors are not often used because of the difficulty of aligning them to the needed precision. The geometry (resonator type) must be chosen so that the beam remains stab ...
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Microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ranges as microwaves; the above broad definition includes both UHF and EHF (millimeter wave) bands. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz (wavelengths between 0.3 m and 3 mm). In all cases, microwaves include the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum. Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, Ku, K, or Ka band, or by similar NATO or EU designations. The prefix ' in ''microwave'' is not meant to suggest a wavelength in the micrometer range. Rather, it indicates that microwaves are "small" (having shorter wavelengths), compared to the radio waves used prior to microwave te ...
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