Tests Of Special Relativity Research Articles

Special relativity optical cavity experiments explained from the perspective of the rotating frame

In this paper, we present an explanation of a fundamental test of special relativity from the perspective of the frame co-moving with a rotating observer. The test in cause is based on the frequency comparison between two optical resonating cavities. The solution is of great interest for real-time applications because certain experiments, such as the optical resonator tests of Lorentz invariance, rely on rotating setups. We present the derivation of the optical resonator experiments from the perspective of the rotating device as compared to the inertial device. We explain the improved tests that use two rotating resonators mounted on the same substrate.

Ultra-stable 1064-nm neodymium-doped yttrium aluminum garnet lasers with 2.5 × 10−16 frequency instability

Cavity-stabilized ultra-stable optical oscillators are one of the core ingredients in the ground-based or spaceborne precision measurements such as optical frequency metrology, test of special relativity, and gravitational wave observation. We report in detail the development of two ultra-stable systems based on 1064-nm neodymium-doped yttrium aluminum garnet lasers and 20-cm optical cavities. The optical cavities adopt ultra-low-loss silica mirrors with compensating rings. An electro-optic crystal with a wedged angle is used to reduce the residual amplitude modulation. Using two-stage thermal control, long-term stabilities of 100 µK are achieved for the outer wall of the vacuum chamber housing the optical cavity. Two additional thermal shields increased the time constant of the optical cavities to 70 h. By operating the optical cavity at the temperature of zero coefficient of thermal expansion, the frequency stability reaches 2.5 × 10-16 at 10s averaging time and remains below 5 × 10-16 with an extended time of 1000s after removing the first- and second-order drifts. The dependence of the laser linewidth on the measurement time is tested against a simplified theoretical model.

Perspectives of double beta and dark matter search as windows to new physics

Nuclear double beta decay provides an extraordinarily broad potential to search for beyond Standard Model physics, probing already now the TeV scale, on which new physics should manifest itself. These possibilities are reviewed here. First, the results of present generation experiments are presented. The most sensitive one of them - the Heidelberg-Moscow experiment in the Gran Sasso - probes the electron mass now in the sub eV region and has reached recently a limit of ~ 0.1 eV. This limit has striking influence on presently discussed neutrino mass scenarios. Basing to a large extent on the theoretical work of the Heidelberg Double Beta Group in the last two years, results are obtained also for SUSY models (R-parity breaking, sneutrino mass), leptoquarks (leptoquark-Higgs coupling), compositeness, right-handed W boson mass, test of special relativity and equivalence principle in the neutrino sector and others. These results are comfortably competitive to corresponding results from high-energy accelerators like TEVATRON, HERA, etc. One of the enriched 7Ge detectors also yields the most stringent limits for cold dark matter (WIMPs) to date by using raw data. Second, future perspectives of ßß research are discussed. A new Heidelberg experimental proposal (GENIUS) will allow to increase the sensitivity for Majorana neutrino masses from the present level of at best 0.1 eV down to 0.01 or even 0.001 eV. Its physical potential would be a breakthrough into the multi-TeV range for many beyond standard models. Its sensitivity for neutrino oscillation parameters would be larger than of all present terrestrial neutrino oscillation experiments and of those planned for the future. It could probe directly the large angle, and for almost degenerate neutrino mass scenarios even the small angle solution of the solar neutrino problem. It would further, already in a first step using only 100 kg of natural Ge detectors, cover almost the full MSSM parameter space for prediction of neutralinos as cold dark matter, making the experiment competitive to LHC in the search for supersymmetry. Finally GENIUS could be used as the first real time detector of solar pp neutrinos.

Special relativity experiments explained from the perspective of the rotating frame

In this paper, we present an explanation of several fundamental tests of special relativity from the perspective of the frame co-moving with a rotating observer. The solution is of great interest for real-time applications because Earth-bound laboratories are inertial only in approximation. We present the derivation of the Sagnac, Michelson–Morley, Kennedy–Thorndike and the Hammar experiments as viewed from the Earth-bound uniformly rotating frame or, as in the case of the Mossbauer rotor experiments, from the perspective of the rotating device. An entire section is dedicated to length/time measurement and to clock synchronization and another one to the Doppler effect and aberration on uniformly rotating platforms. This paper brings new information in the following areas: – new approach for clock synchronization on a rotating platform – new approach for length measurement in rotating frames – new explanation of the Doppler effect and of the Mossbauer rotor experiment – new explanation of the Kennedy–Thorndike experiment. The main thrust of this paper is to give a consistent explanation of various tests of special relativity as judged from the perspective of the rotating frame of the experimental setup. In addition, we correct certain misconceptions relative to clock synchronization and length measurement that have survived a long time in the specialty literature. A special chapter is dedicated to the derivation of the Doppler effect and of aberration in rotating frames. It is shown that such derivation is far from being trivial.

Relativistic Astronomy. III. Test of Special Relativity via Doppler Effect

Abstract The “Breakthrough Starshot” program is planning to send transrelativistic probes to travel to nearby stellar systems within decades. Because the probe velocity is designed to be a good fraction of the light speed, Zhang & Li recently proposed that these transrelativistic probes can be used to study astronomical objects and to test special relativity. In this work, we propose some methods to test special relativity and constrain photon mass using the Doppler effect with the images and spectral features of astronomical objects as observed in the transrelativistic probes. We introduce more general theories to set up the framework of testing special relativity, including the parametric general Doppler effect and the Doppler effect with massive photons. We find that by comparing the spectra of a certain astronomical object, one can test Lorentz invariance and constrain photon mass. Additionally, using the imaging and spectrograph capabilities of transrelativistic probes, one can test time dilation and constrain photon mass. For a transrelativistic probe with velocity v ∼ 0.2c, aperture D ∼ 3.5 cm, and spectral resolution R ∼ 100 (or 1000), we find that the probe velocity uncertainty can be constrained to σ v ∼ 0.01c (or 0.001c), and the time dilation factor uncertainty can be constrained to (or 0.001), where is the time dilation factor and γ is the Lorentz factor. Meanwhile, the photon mass limit is set to m γ ≲ 10−33 g, which is slightly lower than the energy of the optical photon.

Relativistic Astronomy. II. In-flight Solution of Motion and Test of Special Relativity Light Aberration

Abstract The Breakthrough Starshot project aims to send centimeter-sized, gram-scale “StarChip” probes to Alpha Centauri at a speed of ∼0.2 c. On the other hand, Zhang & Li recently proposed that transrelativistic cameras may be sent to any direction to study astronomical objects and test special relativity. To conduct such “relativistic astronomy,” one needs to solve the motion of the probe in flight. We solve the motion of the probe (including the moving direction and the velocity) by comparing the positions of three or more point sources observed in the Earth rest frame and in the probe’s comoving frame. When the positions of enough point sources are taken into account, the motion of the probe can be solved with an error that is even smaller than the diffraction limit of the transrelativistic camera. After solving the motion, when the measurement of the position of an additional point source is introduced, one can use the data to test the light aberration effect in special relativity. The upper limit of the photon mass can be placed from the deviation of aberration to slightly lower than the energy of the photon, e.g., ∼1 eV.

The light speed versus the observer: the Kennedy\u2013Thorndike test from GRAAL-ESRF

High precision tests of the light speed constancy for all observers as a empirical basis of Special Relativity have continuously been among the goals of advanced experimental studies. Based on the Compton edge method proposed by us (Gurzadyan and Margarian in Phys Scr 53:513, 1996), a constraint on the one-way light speed isotropy and Lorentz invariance violation has been obtained at the dedicated GRAAL experiment at European Synchrotron Radiation Facility (ESRF, Grenoble) (Gurzadyan et al. in Mod Phys Lett A 20:1, 2005, Nuovo Cimento 122:515, 2007, Proceedings of the XII M. Grossmann meeting on general relativity, vol B. World Scientific, p 1495. arXiv:1004.2867, 2012; Bocquet et al. in Phys Rev Lett 104:241601, 2010). Using the GRAAL data we now get a new constraint on one of the key tests of Special Relativity—the Kennedy–Thorndike experiment (Kennedy and Thorndike in Phys Rev 42:400, 1932) in probing light speed invariance with respect to the velocity of the observer (apparatus). Our analysis takes advantage of GRAAL’s setup where two separate energy scales are involved: first, via the position of the Compton edge determining the light speed in the reference frame of incident 6 GeV electrons within the tagging system, second, in the calorimeter via the 1.27 MeV photons of the ^{22}Na source. The two energy scales are engaged to each other through production of eta mesons by tagged laser Compton backscattered gamma -rays. The accuracy of the calibration and stability of energies reached in each section enable us to obtain the limit of 7 times 10^{-12} for the Kennedy–Thorndike test, which improves the currently existing limits by three orders of magnitude.

Analogue special and general relativity by optical multilayer thin films: the Rindler space case

In this paper, to obtain an analogy between the curved spaces and the linear optics, we expand the idea of Sánchez-Soto and co-workers [Phys. Rep.2012,513, 191; Phys. Rev. A 2011,84, 023830] to the multilayer films. We investigate effects of thickness and index of refraction of the films on the Lorentzian transformations. In addition, by using the multilayer films, we suggest a very simple experimental set-up which can serve as an analogue computer for testing special relativity. Finally, we draw an analogy between the Rindler space, as an example of the curved spaces, and a suitable multilayer film.

On measuring the one-way speed of light

The crucial problem of how to synchronize clocks and measure the one-way speed of light was originally discussed by Poincare and Einstein. After being neglected for many decades, the Poincare-Einstein problem of synchronization revived in 1977 with the work of Mansouri and Sexl, by which the one-way speed remains undetermined, allowing for unequal values of the speed of light in opposite directions. We review this problem in the framework of relativistic theories that assume clock-retardation and rod-contraction. We show that, for preferred frame theories, convection or “open” currents yield a magnetic field that depends on the velocity v with respect to the preferred frame S o . We also outline an experiment, based on Faraday’s law of induction, that can determine the velocity v, identify S o , and test special relativity versus preferred frame theories. This result resolves the Poincare-Einstein problem and shows that, in principle, the one-way speed c can be measured.

PENTATRAP: a novel cryogenic multi-Penning-trap experiment for high-precision mass measurements on highly charged ions

The novel five-Penning-trap mass spectrometer Pentatrap is developed at the Max-Planck-Institut für Kernphysik (MPIK), Heidelberg. Ions of interest are long-lived highly charged nuclides up to bare uranium. Pentatrap aims for an accuracy of a few parts in 1012 for mass ratios of mass doublets. A physics program for Pentatrap includes Q-value measurements of β-transitions relevant for neutrino physics, stringent tests of quantum electrodynamics in the regime of extreme electric fields, and a test of special relativity. Main features of Pentatrap are an access to a source of highly charged ions, a multi-trap configuration, simultaneous measurements of frequencies, a continuous precise monitoring of magnetic field fluctuations, a fast exchange between different ions, and a highly sensitive cryogenic non-destructive detection system. This article gives a motivation for the new mass spectrometer Pentatrap, presents its experimental setup, and describes the present status.

Cosmic rays and tests of fundamental principles

It is now widely acknowledged that cosmic rays experiments can test possible new physics directly generated at the Planck scale or at some other fundamental scale. By studying particle properties at energies far beyond the reach of any man-made accelerator, they can yield unique checks of basic principles. A well-known example is provided by possible tests of special relativity at the highest cosmic-ray energies. But other essential ingredients of standard theories can in principle be tested: quantum mechanics, uncertainty principle, energy and momentum conservation, effective space-time dimensions, hamiltonian and lagrangian formalisms, postulates of cosmology, vacuum dynamics and particle propagation, quark and gluon confinement, elementariness of particles... Standard particle physics or string-like patterns may have a composite origin able to manifest itself through specific cosmic-ray signatures. Ultra-high energy cosmic rays, but also cosmic rays at lower energies, are probes of both "conventional" and new Physics. Status, prospects, new ideas, and open questions in the field are discussed. The Post Scriptum shows that several basic features of modern cosmology naturally appear in a SU(2) spinorial description of space-time without any need for matter, relativity or standard gravitation. New possible effects related to the spinorial space-time structure can also be foreseen. Similarly, the existence of spin-1/2 particles can be naturally related to physics beyond Planck scale and to a possible pre-Big Bang era.

Preparatory measurements for a test of time dilation in the ESRThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010.

We present preparatory measurements for an improved test of time dilation at the experimental storage ring (ESR) at GSI in Darmstadt. A unique combination of particle accelerator experiments and laser spectroscopy is used to perform this test with the highest precision. 7Li+ ions are accelerated to 34% of the speed of light at the GSI Helmholtzzentrum für Schwerionenforschung and stored in the experimental storage ring. The forward and backward Doppler shifts of an electric dipole transition of these ions are measured with laser spectroscopy techniques. From these Doppler shifts, both the ion velocity β = ν/c and the time dilation factor [Formula: see text] can be derived for testing Special Relativity. Two laser systems have been developed to drive the 3S1→3P2 transition in 7Li+. Moreover, a detector system composed of photomultipliers, both to monitor the exact laser ion beam overlap as well as to optimize fluorescence detection, has been set up and tested. We investigate optical-optical double-resonance spectroscopy on a closed Λ-type three-level system to overcome Doppler broadening. A residual, broadened fluorescence background caused by velocity-changing processes in the ion beam is identified, and a background subtraction scheme implemented. At the present stage the experimental sensitivity, although already comparable with previous measurements on slower ion beams at the TSR storage ring that led to [Formula: see text] < 8.4 × 10–8, suffer from a poor signal-to-noise ratio. Modifications of the ion source as well as the detection system are discussed that promise to improve the sensitivity by one order of magnitude.

Experiment for testing special relativity theory

An experiment aimed at testing special relativity via a comparison of the velocity of a nonmatter particle (annihilation photon) with the velocity of the matter particle (Compton electron) produced by the second annihilation photon from the decay 22Na (β+)22Ne is proposed.

Analytical Solution for the Deformation of a Cylinder under Tidal Gravitational Forces

AbstractQuite a few future high precision space missions for testing Special and General Relativity will use optical resonators which are used for laser frequency stabilisation. These devices are used for carrying out tests of the isotropy of light and of the universality of the gravitational redshift. As the resonator frequency not only depends on the speed of light but also on the resonator length, the quality of these measurements is very sensitive to elastic deformations of the optical resonator itself. As a consequence, a detailed knowledge about the deformations of the cavity is necessary.In this note we derive for the first time an analytical solution for the problem of an elastic, isotropic, homogeneous free–flying cylinder in space under the influence of a tidal gravitational force. A detailed derivation can be found in [4]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analytical solution for the deformation of a cylinder under tidal gravitational forces

Quite a few future high precision space missions for testing special and general relativity will employ optical resonators which are used for laser frequency stabilization. These devices are basic for carrying out modern tests of the isotropy of light (Michelson–Morley experiment) and of the universality of the gravitational redshift. As the resonator frequency not only depends on the speed of light but also on the resonator length, the quality of these measurements is very sensitive to elastic deformations of the optical resonator itself. As a consequence, a detailed knowledge about the deformations of the cavity is necessary. Therefore, in this paper, we investigate the modelling of optical resonators in a space environment. Usually, for simulation issues, the finite element method (FEM) is applied in order to investigate the influence of disturbances on resonator measurements. However, for a careful control of the numerical quality of FEM simulations, a comparison with an analytical solution of a simplified resonator model is beneficial. In this paper we present an analytical solution for the problem of an elastic, isotropic, homogeneous free-flying cylinder in space under the influence of a tidal gravitational force. The solution is gained by solving the linear equations of elasticity for special boundary conditions. The applicability of using FEM codes for these simulations shall be verified through the comparison of the analytical solution with the results gained within the FEM code.

Experimental test of special relativity by laser spectroscopy

The Doppler-free laser-spectroscopic frequency measurement of Doppler-shifted optical lines in forward and backward direction of a fast ion beam permits a sensitive test of the relativistic Doppler-formula and, hence, the relativistic time dilation factor γ SR=(1−ν 2/c 2)−1/2. An experiment on metastable 7Li+, stored at a velocity of ν=0.064c in the Heidelberg heavy-ion storage ring TSR, has confirmed time dilation with unprecedented accuracy. Latest tests at two different ion-velocities (ν=0.03c and ν=0.064c) will enhance these measurements. An improved version of this experiment will be carried out at the experimental storage ring (ESR) at the Gesellschaft fur Schwerionenforschung (GSI) in Darmstadt. The ESR permits 7Li+ to be stored at ν=0.33c which promises an improvement of the sensitivity to deviations from γ SRby an order of magnitude. A first test at the ESR has shown the feasibility for this kind of experiment.

The Confrontation between General Relativity and Experiment.

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

First Evidence for Lepton Number Violation and of the Majorana Character of Neutrinos

Nuclear double beta decay provides an extraordinarly broad potential to search for beyond-standard-model physics. The occurrence of the neutrinoless decay (0νββ) mode has fundamental consequences: first total lepton number is not conserved, and second, the neutrino is a Majorana particle. Further the effective mass measured allows to put an absolute scale of the neutrino mass spectrum. In addition, double beta experiments yield sharp restrictions also for other beyond standard model physics. These include SUSY models (R-parity breaking and conserving), leptoquarks (leptoquark-Higgs coupling), compositeness, left-right symmetric models (right-handeld W boson mass), test of special relativity and of the equivalence principle in the neutrino sector and others. First evidence for neutrinoless double beta decay was given in 2001, by the HEIDELBERG-MOSCOW experiment. The HEIDELBERG-MOSCOW experiment is the by far most sensitive 0νββ experiment since more than 10 years. It was operating 11 kg of enriched 76Ge in the GRAN SASSO Underground Laboratory. The analysis of the data taken from 2 August 1990 - 20 May 2003, is presented here. The collected statistics is 71.7kg y. The background achieved in the energy region of the Q value for double beta decay is 0.11 events/ kg y keV. The two-neutrino accompanied half-life is determined on the basis of more than 100 000 events to be (1.74.−0.16+0.18)×1021 years. The confidence level for the neutrinoless signal has been improved to a 4.2 σ level. The half-life is T1/20ν=(1.19−0.23+0.37)×1025 years. The effective neutrino mass deduced is (0.2 - 0.6) eV (99.73% c.l.), with the consequence that neutrinos have degenerate masses. The sharp boundaries for other beyond SM physics, mentioned above, are comfortably competitive to corresponding results from high-energy accelerators like TEVATRON, HERA, etc.

FROM NUCLEAR PHYSICS TO PHYSICS BEYOND THE STANDARD MODEL: FIRST EVIDENCE FOR LEPTON NUMBER VIOLATION AND THE MAJORANA CHARACTER OF NEUTRINOS

Nuclear double beta decay provides an extraordinarily broad potential to search for beyond-standard-model physics. The occurrence of the neutrinoless decay(0νββ) mode has fundamental consequences: first, the total lepton number is not conserved, and second, the neutrino is a Majorana particle. Furthermore, the measured effective mass provides an absolute scale of the neutrino mass spectrum. In addition, double beta experiments yield sharp restrictions for other beyond-standard-model physics. These include SUSY models (R-parity breaking and conserving), leptoquarks (leptoquark-Higgs coupling), compositeness, left-right symmetric models (right-handed W boson mass), test of special relativity and of the equivalence principle in the neutrino sector and others. First evidence for neutrinoless double beta decay was reported by the HEIDELBERG–MOSCOW experiment in 2001. The HEIDELBERG–MOSCOW experiment is by far the most sensitive0νββ experiment since more than 10 years. It is operating 11 kg of enriched76Ge in the GRAN SASSO Underground Laboratory. The analysis of the data taken from 2 August 1990–20 May 2003 is presented here. The collected statistics is 71.7 kg y. The background achieved in the energy region of the Q value for double beta decay is 0.11 events/kg y keV. The two-neutrino accompanied half-life is determined on the basis of more than 100,000 events to be [Formula: see text] years. The confidence level for the neutrinoless signal has been improved to a 4.2σ level. The half-life is [Formula: see text] years. The effective neutrino mass deduced is (0.2–0.6) eV (99.73% C.L.), with the consequence that neutrinos have degenerate masses. The sharp boundaries for other beyond SM physics, mentioned above, are comfortably competitive to the corresponding results from high-energy accelerators like TEVATRON, HERA, etc.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light defl ection the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar, and new binary pulsar systems may yield further improvements. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.