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We consider the problem of testing the Einstein Equivalence Principle (EEP) by measuring the gravitational redshift with two Earth-orbiting stable atomic clocks. For a reasonably restricted class of orbits we find an optimal experiment configuration that provides for the maximum accuracy of measuring the relevant EEP violation parameter. The perigee height of such orbits is $\sim$~1,000~km and the period is 3--5~hr, depending on the clock type. For the two of the current best space-qualified clocks, the VCH-1010 hydrogen maser and the PHARAO cesium fountain clock, the achievable experiment accuracy is, respectively, $1\times10^{-7}$ and $5\times10^{-8}$ after 3 years of data accumulation. This is more than 2 orders of magnitude better than achieved in Gravity Probe A and GREAT missions as well as expected for the RadioAstron gravitational redshift experiment. Using an anticipated future space-qualified clock with a performance of the current laboratory optical clocks, an accuracy of $3\times10^{-10}$ is reachable., Comment: 13 pages, 5 figures

In this article we discuss a regional recovery of gravity disturbances at the mean geocentric sphere approximating the Earth over the area of Central Europe from satellite gravitational gradients. For this purpose, we derive integral formulas which allow converting the gravity disturbances onto the disturbing gravitational gradients in the local north-oriented frame (LNOF). The derived formulas are free of singularities in case of r ≠ R . We then investigate three numerical approaches for solving their inverses. In the initial approach, the integral formulas are firstly modified for solving individually the near- and distant-zone contributions. While the effect of the near-zone gravitational gradients is solved as an inverse problem, the effect of the distant-zone gravitational gradients is computed by numerical integration from the global gravitational model (GGM) TIM-r4. In the second approach, we further elaborate the first scenario by reducing measured gravitational gradients for gravitational effects of topographic masses. In the third approach, we apply additional modification by reducing gravitational gradients for the reference GGM. In all approaches we determine the gravity disturbances from each of the four accurately measured gravitational gradients separately as well as from their combination. Our regional gravitational field solutions are based on the GOCE EGG_TRF_2 gravitational gradients collected within the period from November 1 2009 until January 11 2010. Obtained results are compared with EGM2008, DIR-r1, TIM-r1 and SPW-r1. The best fit, in terms of RMS (2.9 mGal), is achieved for EGM2008 while using the third approach which combine all four well-measured gravitational gradients. This is explained by the fact that a-priori information about the Earth’s gravitational field up to the degree and order 180 was used.

The present work investigates the practical consequences of the recent experimental observations, achieved with the help of the tightly synchronized atomic clocks in orbit, on the current view about the nature of the gravitational fields. While clocks, stationary within gravitational fields, show exactly the gravitational slowing predicted by General Relativity (GR), the GPS clocks, in orbit round earth and moving with earth round the sun, do not show the gravitational slowing of the solar field, predicted by GR. This absence can only mean that the orbital motion of earth cancels this gravitational slowing, which obviously cancels too the spacetime curvature. On the other hand, the Higgs theory introduces the Higgs Quantum Space (HQS) giving mass to the elementary particles by the Higgs mechanism. The HQS thus necessarily governs the inertial motion of matter-energy and is locally their ultimate reference for rest and for motions. Motion with respect to the local HQS and not relative motion is what causes clock slowing, light anisotropy and all the, so-called relativistic effects. Non-uniform motion of the HQS itself necessarily creates inertial dynamics, which, after Einstein’s equivalence of gravitational and inertial effects, is gravitational dynamics. The absence of the gravitational slowing of the GPS clocks by the solar field, together with the null results of the light anisotropy experiments on earth, demonstrates that earth is stationary with respect to the local HQS. This can make sense only if the HQS is moving round the sun according to a Keplerian velocity field, consistent with the planetary motions. This Keplerian velocity field of the HQS is the quintessence of the gravitational fields and is shown to naturally and accurately create the gravitational dynamics, observed on earth, in the solar system, in the galaxy and throughout the universe, as well as all the observed effects of the gravitational fields on light and on clocks.

International audience; We present the result of the analysis of the GREAT (Galileo gravitational Redshift test with Eccentric sATellites) experiment. An elliptic orbit induces a periodic modulation of the fractional frequency difference between a ground clock and the satellite clock, partly due to the gravitational redshift, while the good stability of Galileo clocks allows one to test this periodic modulation to a high level of accuracy. GSAT0201 and GSAT0202, with their large eccentricity and on-board H-maser clocks, are perfect candidates to perform this test. Satellite laser ranging data allows us to partly decorrelate the orbit perturbations from the clock errors. By analyzing several years of Galileo tracking data, we have been able to improve the Gravity probe A test (1976) of the gravitational redshift by a factor of 5.6, providing, to our knowledge, the first reported improvement since more than 40 years.

We report on a new test of the gravitational redshift and thus of local position invariance, an integral part of the Einstein equivalence principle, which is the foundation of general relativity and all metric theories of gravitation. We use data spanning 1008 days from two satellites of Galileo, Europe's global satellite navigation system (GNSS), which were launched in 2014, but accidentally delivered on elliptic rather than circular orbits. The resulting modulation of the gravitational redshift of the onboard atomic clocks allows the redshift determination with high accuracy. Additionally specific laser ranging campaigns to the two satellites have enabled a good estimation of systematic effects related to orbit uncertainties. Together with a careful conservative modelling and control of other systematic effects we measure the fractional deviation of the gravitational redshift from the prediction by general relativity to be $(+0.19 \pm 2.48)\times10^{-5}$ at 1 sigma, improving the best previous test by a factor~5.6. To our knowledge, this represents the first reported improvement on one of the longest standing results in experimental gravitation, the Gravity Probe A hydrogen maser rocket experiment back in 1976., 6 pages, 4 figures, published in Phys. Rev. Lett. 121, 231101

The paper proposes a lecture experiment that can be demonstrated when studying the equivalence principle formulated by Albert Einstein. The demonstration consists of creating stroboscopic photographs of a ball moving along a parabola in Earth's gravitational field. In the first experiment, a camera is stationary relative to Earth's surface. In the second, the camera falls freely downwards with the ball, allowing students to see that the ball moves uniformly and rectilinearly relative to the frame of reference of the freely falling camera. The equivalence principle explains this result, as it is always possible to propose an inertial frame of reference for a small region of a gravitational field, where space-time effects of curvature are negligible.

Einsteins theory of General relativity is a popular theory, but unfortunately it cannot account for all the observable gravity in the universe. This paper presents a new force predicted through the McMahon field theory (2010) [1], which is refered to in McMahon field theory (2010) [1] as Mahona (pronounced “Maa-naa”), which appears to be gravitational. In this paper, I draw upon the McMahon field theory (2010) [1], and use it to explain why mass appears gravitational, as well as the source of the excess gravity that General relativity cannot account for. I will do this in simplistic terms for the benefit of the reader. Thus with the understanding presented here, any vechicle utilising this new force called “Mahona” shall have gravitational capability.

In this paper we use a dynamic form of modified Newtonian gravity to reformulate the equations for gravitational time dilation. Here we introduce the generic equations for gravitational time dilation. It is shown that these equations agree exactly with gravitational time dilation in satellite navigation systems. The equations are also in agreement with a reanalysis of observations of gravitational red shifts in black hole accretion discs. Using these equations, we translate the time dilation into a finite value at the black hole event horizon. Thus this reformulation resolves the difficulties of the existence of black hole singularities. Importantly these dynamic gravitational equations provide testable predictions in the vicinity of black holes.

Gravitational waves have been detected in the centenary year of Einstein’s formulation of general theory of relativity that predicts these waves. It has been heralded as a landmark discovery, since it not only confirms various predictions of the theory, but also opens up a new window of observing the universe. I will discuss a few basic characteristics of gravitational waves in this article, and a few astrophysical implications.

The paper proves that due to the existence of electromagnetic interaction, the experiments of LIGO cannot detect gravitational waves. This is also the reason why Weber’s experiments of gravitational waves failed. In fact, the formulas of general relativity that gravitational waves affect distances are only suitable for particles in vacuum. LIGO experiments are carried out on the earth. The laser interferometers are fixed on the steel pipes on the earth’s surface in the balanced state of electromagnetic force. Electromagnetic force is 1040 times greater than gravity. Gravitational waves are too weak to overcome electromagnetic force and change the length of steel pipes. Without considering this factor, the design principle of LIGO experiment has serious problem. The experiments to detect gravitational waves should move to space to avoid the influence of electromagnetic interaction. Besides, LIGO experiments have the following problems. 1) No explosion source of gravitational waves is really founded. 2) The argument that the Einstein’s theory of gravity is verified is a vicious circle and invalid in logic. 3) The results of experiments cause sharp contradiction for the energy currents of gravitational waves. The difference reaches to 1024 times and is unacceptable. 4) The method of numerical relativity causes great errors due to the existence of singularities. The errors are enlarged by the effect of butterfly due to the non-linearity of Einstein’s equation of gravity. 5) The so-called change of length 10-18 m between two glasses of interferometers detected in the experiment exceeds the ability of current technique. This kind of precise has entered micro-scalar. The uncertain principle of quantum mechanics makes it impossible. The signs appeared in LIGO experiments are not caused by distance change. 6) LIGO experiments have not detected gravitational waves. What detected may be the signs of disturbances coming from the middle region between two laser interferometers.

According to the equivalence principle, the accelerating field and the gravitational field are considered to be completely equivalent. But after carefully studying the two most classic acceleration systems,i.e. the uniform acceleration elevator and the uniform rotating disc, the author has discovered that there is only partial equivalence instead of complete equivalence between the above two acceleration systems and the gravitational field.

On August 22, 2014, the satellites GSAT-0201 and GSAT-0202 of the European GNSS Galileo were unintentionally launched into eccentric orbits. Unexpectedly, this has become a fortunate scientific opportunity since the onboard hydrogen masers allow for a sensitive test of the redshift predicted by the theory of general relativity. In the present Letter we describe an analysis of approximately three years of data from these satellites including three different clocks. For one of these we determine the test parameter quantifying a potential violation of the combined effects of the gravitational redshift and the relativistic Doppler shift. The uncertainty of our result is reduced by more than a factor 4 as compared to the values of Gravity Probe A obtained in 1976., Comment: 6 pages, 3 figures, published in Phys. Rev. Lett. 121, 231102

We present an approach to testing the gravitational redshift effect using the RadioAstron satellite. The experiment is based on a modification of the Gravity Probe A scheme of nonrelativistic Doppler compensation and benefits from the highly eccentric orbit and ultra-stable atomic hydrogen maser frequency standard of the RadioAstron satellite. Using the presented techniques we expect to reach an accuracy of the gravitational redshift test of order $10^{-5}$, a magnitude better than that of Gravity Probe A. Data processing is ongoing, our preliminary results agree with the validity of the Einstein Equivalence Principle., Comment: Submitted to Physics Letters A

Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyze experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators to the effects of gravity. The main observable -- maximal energy of the scattered photons -- would experience a significant shift in the ambient gravitational field even for otherwise negligible violation of the equivalence principle. We confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of resolution and expect our work to be a starting point of further high-precision studies on current and future accelerators, such as PETRA, European XFEL and ILC., Comment: 5+ pages. Published version. Description of experimental setup is drawn from arXiv:1401.3720 by another author

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the “dark matter” and “dark energy” we are looking for to explain this excess gravity doesn’t exist.

Exploring Einstein's theories of relativity in quantum systems, for example by using atomic clocks at high speeds can deepen our knowledge in physics. However, many challenges still remain on finding novel methods for detecting effects of gravity and of special relativity and their roles in light-matter interaction. Here we introduce a scheme of x-ray quantum optics that allows for a millimeter scale investigation of the relativistic redshift by directly probing a fixed nuclear crystal in Earth's gravitational field with x-rays. Alternatively, a compact rotating crystal can be used to force interacting x-rays to experience inhomogeneous clock tick rates in a crystal. We find that an association of gravitational or special-relativistic time dilation with quantum interference will be manifested by deflections of x-ray photons. Our protocol suggests a new and feasible tabletop solution for probing effects of gravity and special relativity in the quantum world., Comment: 17 pages, 4 figures, 1 table and Supplemental Materials

The history of experimentation relevant to general relativity covers the time post-1928. Classes of investigation are the weak equivalence principle (equivalence of inertial and gravitational mass and gravitational redshift), orbital precession of a body in gravitational fields (the relativistic perihelion advance of the planets, the relativistic periastron advance of binary pulsars, geodetic precession and Lense-Thirring effect), light propagation in gravitational fields (gravitational optical light deflection, gravitational radio deflection due to the Sun, gravitational lensing, time dilation and atomic clocks) and strong gravity implications (Nordtved effect and potential gravitational waves). The results of experiments are analysed to conclude to what extent they support general relativity. A number of questions are then answered: (a) how much evidence exists to support general relativity, (b) is it a reasonable way of thinking and (c) what is the niche it may occupy?

I argue that the best spacetime setting for Newtonian gravitation (NG) is the curved spacetime setting associated with geometrized Newtonian gravitation (GNG). Appreciation of the ‘Newtonian equivalence principle’ leads us to conclude that the gravitational field in NG itself is a gauge quantity, and that the freely falling frames are naturally identified with inertial frames. In this context, the spacetime structure of NG is represented not by the flat neo-Newtonian connection usually made explicit in formulations, but by the sum of the flat connection and the gravitational field.

The recent LIGO detection of gravitational waves from black-hole binaries offers the exciting possibility of testing gravitational theories in the previously inaccessible strong-field, highly relativistic regime. While the LIGO detections are so far consistent with the predictions of General Relativity, future gravitational-wave observations will allow us to explore this regime to unprecedented accuracy. One of the generic predictions of theories of gravity that extend General Relativity is the violation of the strong equivalence principle, i.e. strongly gravitating bodies such as neutron stars and black holes follow trajectories that depend on their nature and composition. This has deep consequences for gravitational-wave emission, which takes place with additional degrees of freedom besides the tensor polarizations of General Relativity. I will briefly review the formalism needed to describe these extra emission channels, and show that binary black-hole observations probe a set of gravitational theories that are largely disjoint from those that are testable with binary pulsars or neutron stars., 8 pages. Submitted to the proceedings of the 3rd International Symposium on "Quest for the Origin of Particles and the Universe", 5-7 January 2017, Nagoya University, Japan

The direct detection of gravitational waves provides the opportunity to measure fundamental aspects of gravity which have never been directly probed before, including the polarization of gravitational waves. In the context of searches for continuous waves from known pulsars, we present novel methods to detect signals of any polarization content, measure the modes present and place upper-limits on the amplitude of non-tensorial components. This will allow us to obtain new model-independent, dynamical constraints on deviations from general relativity. We test this framework on multiple potential sources using simulated data from three advanced-era detectors at design sensitivity. We find that signals of any polarization will become detectable and distinguishable for characteristic strains $h\gtrsim 3\times10^{-27} \sqrt{1~{\rm yr}/T}$, for an observation time $T$. We also find that our ability to detect non-tensorial components depends only on the power present in those modes, irrespective of the strength of the tensorial strain., Comment: 27 pages, 23 figures

The test of the Einstein Equivalence Principle (EEP) is of crucial importance as a deviation from it could hint to quantum effects in gravity or to unification with the other fundamental forces. One aspect of EEP is the local position invariance (LPI), which can be tested by measuring the gravitational red-shift. As an example of a possible space mission which could test the EEP, we will discuss a recently proposed satellite experiment, Einstein Gravitational RedShift Probe (E-GRIP), with the aim to test LPI using an hydrogen maser atomic clock on a highly elliptic orbit around Earth and compare the on-board clock to clocks located on Earth via a microwave link.

The space radio telescope “RadioAstron” is equipped with a high performance hydrogen maser frequency standard and thus provides a unique opportunity for a gravitational redshift test. We consider various modes of operation of the on-board scientific equipment and their impact on accuracy of the anticipated experiment. We find that the accuracy of the test is limited by ∼10−2 for the hardware configuration routinely used in radio astronomical observations, which is a consequence of using ballistic data to remove the nonrelativistic Doppler frequency shift from the analyzed signal. On the other hand, the so-called “Semi-coherent” mode of the on-board hardware provides for combining the space and ground maser signals in such a way that the resulting signal carries information about the useful effect but is free from the nonrelativistic Doppler and tropospheric frequency shifts. The proposed compensation scheme, which is different from the one used in the Gravity Probe A experiment, allows for testing the gravitational redshift effect with ∼10−6 accuracy.

The principle of equivalence between acceleration and gravity of general relativity is reviewed in a thought experiment of two bodies, aligned according to the perpendicular, under the reciprocal action of their gravity, in free fall, inside of an uniformly accelerated reference system, in the vacuum. The result is that the two bodies fall with a different acceleration. This result invalidates such principle.

We define passive and active gravitational mass operators of the simplest composite quantum body - a hydrogen atom. Although they do not commute with its energy operator, the equivalence between the expectation values of passive and active gravitational masses and energy is shown to survive for stationary quantum states. In our calculations of passive gravitational mass operator, we take into account not only kinetic and Coulomb potential energies but also the so-called relativistic corrections to electron motion in a hydrogen atom. Inequivalence between passive and active gravitational masses and energy at a macroscopic level is demonstrated to reveal itself as time dependent oscillations of the expectation values of the gravitational masses for superpositions of stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by macroscopic ensemble of hydrogen atoms, moved by small spacecraft with constant velocity in the Earth's gravitational field. We suggest the corresponding experiment on the Earth's orbit to detect this radiation, which would be the first direct experiment where quantum effects in general relativity are observed., 10 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1304.6106, arXiv:1311.2627, arXiv:1205.3134

In the present paper, gravitational lensing is described as the electromagnetic influence from gravity waves on light waves. Previous reports have described the dynamic electromagnetic processes of the atom, the photon and gravity. Results from these reports have been compiled into a theoretical model. The theoretical model describes the mechanism which results in gravitational lensing. The study also displays how the electromagnetic characteristics of gravity waves and light waves and the mechanism creating gravitational lensing are measured.

Through the contributions of Galileo, Newton, and Einstein, we recall the universality of free fall (UFF), the weak equivalence principle (WEP), and the strong equivalence principle (SEP), in order to stress that general relativity requires all test masses to be equally accelerated in a gravitational field; that is, it requires UFF and WEP to hold. The possibility of testing this crucial fact with null, highly sensitive experiments makes these the most powerful tests of the theory. Following Schiff, we derive the gravitational redshift from the WEP and special relativity and show that, as long as clocks are affected by a gravitating body like normal matter, measurement of the redshift is a test of UFF/WEP but cannot compete with direct null tests. A new measurement of the gravitational redshift based on free-falling cold atoms and an absolute gravimeter is not competitive either. Finally, we compare UFF/WEP experiments using macroscopic masses as test bodies in one case and cold atoms in the other. We conclude that there is no difference in the nature of the test and that the merit of any such experiment rests on the accuracy it can achieve and on the physical differences between the elements it can test, macroscopic proof masses being superior in both respects.

In this letter, we first consider the famous non-vacuum solution of general relativity for a static spherically symmetric charged object, i.e. the Reissner-Nordstrom solution. Afterwards, by adopting an isotropic coordinate system, we derive the equivalent form of this solution in the so-called geometry. Then we discuss the gravitational redshift in the consequent spacetime.

In the context of the teleparallel equivalent of general relativity (TEGR) we investigate the role of local observers, associated with tetrad fields, in the description of the gravitational interaction through the concepts of the gravitoelectric (GE) and gravitomagnetic (GM) fields. We start by analyzing the gravitoelectromagnetic (GEM) fields obtained from an observer freely falling in Schwarzschild space-time. Then, we investigate whether it is possible to distinguish between this situation and that of an observer at rest in Minkowski space-time. We conclude that, although there are non-zero components of the fields obtained in the case of a free fall, its dynamical effect, measured by the gravitational Lorentz force, is zero. Moreover, the gravitational field energy obtained from the GEM fields for an observer freely falling in Schwarzschild spacetime, is zero. These results are in complete agreement with the equivalence principle.

Two significant findings compel a rethink of physical theories. First, using a 7-billion-year-old gamma-ray burst, Nemiroff (2012) showed that quantum foam could not exists. And second, Solomon (2011) showed that gravitational acceleration is not associated with the gravitating mass, that gravitational acceleration g is determined solely by τ the change in time dilation over a specific height multiplied by c2 or g = τc2. Seeking consistency with Special Theory of Relativity, as means to initiate this rethink, this paper examines 12 inconsistencies in physical theories that manifest from empirical data. The purpose of this examination is to identify how gravitational theories need to change or be explored, to eliminate these 12 inconsistencies. It is then proposed that spacetime is much more sophisticated than just a 4-dimensional continuum. And, that the Universe consists of at least two layers or “kenos” (Greek for vacuous), the 4-dimensional kenos, spacetime (x, y, z, t) and the 3-dimensional kenos, subspace (x, y, z) that are joined at the space coordinates (x, y, z). This explains why electromagnetic waves are transverse, and how probabilities are implemented in Nature. This paper concludes by proposing two new instruments and one test, to facilitate research into gravitational fields, the new torsion-, tension- and stress-free near field gravity probe, the gravity wave telescope, and a non-locality test.

The interaction of electromagnetic and gravitational fields and gravitational super-compressibility were investigated experimentally. Dynamic emitter provides conditions for the generation of eigenfunctions with eigenvalues for the various fields, including: acoustic, gravitational and electromagnetic. We observe the gravitational waves in gas flowing from the dynamic emitter and their interaction with electromagnetic waves. The gravitational field energy was decreasing when electromagnetic field was emitted through the excitation of condensed medium. The direction of maximum change of the emitted energy of excited medium was strongly opposed to gravity vector at that point. The frequency of radiation against the gravity vector in given point of space exceeded radiation frequency of same source in opposite direction.

We examine gravitational wave memory in the case where sources and detector are in an expanding cosmology. For simplicity, we treat the case where the cosmology is de Sitter spacetime, and discuss the possibility of generalizing our results to the case of a more realistic cosmology. We find results very similar to those of gravitational wave memory in an asymptotically flat spacetime, but with the magnitude of the effect multiplied by a redshift factor.

The Einstein Equivalence Principle (EEP) requires that clocks in free fall, when observed by other clocks in free fall, show no frequency variations. To some approximation, clocks on the surface of the Earth can be considered freely falling in the solar gravitational potential, and one would expect to find no frequency variations between the clocks as the Earth's rotation modulates the potential experienced by each clock. We investigate the attainable limits of a search for such a frequency variation using satellites, parameterized as a fraction of the expected differential gravitational redshift of a clock pair not in free fall. Under the most optimistic of assumptions, a 3-sigma limit to the EEP violation of 10−4 may be possible in the future, although the uncertainties we present are an order of magnitude higher, with an upper limit to an EEP violation of

In Nature Phys. 11, 668 (2015) (Ref. [1]), a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field is shown to undergo a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's Equivalence Principle to be valid, we demonstrate, first in a Lorentz frame with accelerating detectors, and then directly in the Lab frame with uniform gravity, that the dephasing between the different internal states arise not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Ref. [1], where we propose that gravity plays a kinematic role in the loss of fringe visibility by giving the detector a transverse velocity relative to the particle beam; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the Equivalence Principle is violated., 5 pages, 3 figures

The detection of gravitational waves is challenging researchers since half a century. The relative precision required, \(10^{-21}\), is difficult to imagine, this is \(10^{-5}\) the diameter of a proton over several kilometres, using masses of tens of kilograms, or picometres over millions of kilometres. A theoretical description of gravitational radiation and its effects on matter, all consequence of the general theory of relativity, is given. Then the astrophysical phenomena that are candidates of gravitational wave emission are discussed, considering also amplitudes and rates. The binary neutron star system PSR1913\(+\)16, which provided the first evidence for energy loss by gravitational radiation in 1975, is briefly discussed. Then comes a description of the experimental developments, starting with ground-based interferometers, their working principles and their most important sources of noise. The earth-wide network that is being built describes how these instruments will be used in the observation era. Several other detection techniques, such as space interferometry, pulsar timing arrays and resonant detectors, covering different bands of the gravitational wave frequency spectrum complete these lectures.

A conservative constraint on the Einstein Weak Equivalence Principle (WEP) can be obtained under the assumption that the observed time delay between correlated particles from astronomical sources is dominated by the gravitational fields through which they move. Current limits on the WEP are mainly based on the observed time delays of photons with different energies. It is highly desirable to develop more accurate tests that include the gravitational wave (GW) sector. The detection by the advanced LIGO/VIRGO systems of gravitational waves will provide attractive candidates for constraining the WEP, extending the tests to gravitational interactions, with potentially higher accuracy. Considering the capabilities of the advanced LIGO/VIRGO network and the source direction uncertainty, we show that the joint detection of GWs and electromagnetic signals could probe the WEP to an accuracy down to $10^{-10}$, which is one order of magnitude tighter than previous limits, and seven orders of magnitude tighter than the multi-messenger (photons and neutrinos) results by supernova 1987A., Comment: Accepted for publication in PRD

Within the framework of the five-dimensional geometric theory, the problem of gravitational interaction of a vortex gravitational and scalar fields is investigated. A solution of the five-dimensional Einstein vacuum equations is derived. The results obtained are compared with those obtained previously within the framework of the four-dimensional theory.

A new method for processing the output signal from a gravitational wave direction finder in the measurement problem of detecting and identifying gravitational waves from binary relativistic astrophysical objects is discussed and studied.

For detecting gravitational waves in space, deep-space laser ranging using drag-free spacecraft is a common method. Deep space provides a large arena and a long integration time. Laser technology provides measurement sensitivity, while drag-free technology ensures gravitational phenomenon to be measured with least spurious noises. In this talk, we give an overview of motivations and methods of various space missions/proposals for detecting gravitational waves, and refer them to various references.

The relationship between energy, time and space is still not solved in an appropriate manner. According to Newton's concept of time and space, both have to be taken as absolute. If we follow Leibniz and his arguments, space and time are relative. Since Einstein's theory of relativity we know at least that energy, time and space are deeply related. Albert Einstein originally predicted that time is nothing absolute but something relative, time changes and can change. Especially, time and gravitational field are related somehow even in detail if we still don’t know how. According to the gravitational time dilation, the lower the gravitational potential, the more slowly time passes and vice versa. Somehow, it appears to be that the behaviour of time is directly linked to the behaviour of the gravitational field. The aim of this publication is to work out the interior logic between time and gravitational field and to make the proof that time is equivalent to the gravitational field and vice versa.

Major predictions of General Relativity, unforeseen at the beginning of the preceding century, are now under investigation. The existence of black holes of any mass from tens to billions of solar masses is now established, and the physics around these objects begins to be studied through direct observations in a wide electromagnetic spectrum from visible light to X-rays. General relativity, however, provides an extra medium which carries more information on the regions of intense gravitational field, namely gravitational waves (GWs). Due to their extremely weak coupling to matter, GWs are precisely generated in those regions of spacetime undergoing strong curvature, which is very exciting for modern astrophysics. On the other hand, this weak coupling makes it difficult for GWs to cause appreciable effects in human made instruments. This is why technology of GW detectors took such a long time to reach a sensitivity level consistent with GW amplitudes predicted by theoretical models of sources. In the present status, apart from resonant solid detectors, two large interferometric antennas (LIGO in the USA and the French-Italian Virgo) are beginning to produce data, and a joint ESA-NASA space mission, resulting from a wide effort of European and American groups, is reaching a crucial approval phase. The aim of the present review is to give the theoretical bases of GW detectors using light.

We present an orientational quantum interferometer sensitive to gravitational waves that is based on orienting quantum objects like molecules, atoms, or nuclei in space. The detection principle is based on inducing non-sphericity to the corresponding wave functions by light-pulses. In the field of a gravitational wave these objects then possess spectra that depend on their orientation in space. In our measurement scheme we investigate the adiabatic influence of a monochromatic gravitational wave over a quarter gravitational wave period and compare the corresponding frequencies at instances with maximal and vanishing gravitational wave elongation. We therefore explore the effect over a quarter gravitational wave period (or wavelength) and the resulting frequency shift scales with the binding energy of the system times the amplitude of the gravitational wave. In particular, a gravitational wave with amplitude h = 10−23 will induce a frequency shift of the order of 110 μHz for an atom interferometer based on a 91-fold charged uranium ion.

We propose TS-like class of gravitational wave solutions in 4D Einstein gravity. TS1-like gravitational wave solution is analyzed in detail. On the axis, the gauge potential changes from a finite value to zero at t = τ. The spacetime on the axis approaches the flat one as t → ∞. It is found that by an appropriate parameter substitution and coordinate transformation TS-like gravitational wave solutions in 4D Einstein gravity may be obtained from TS solutions.

An expression for the gravitational deflection angle of a high-energy massless scalar boson is computed using the JWKB method. The resulting expression depends on the energy of the scalar boson or, equivalently, on its wavelength, even to first order in [Formula: see text], where G is Newton's constant, M is the mass of the gravitational source, and b is the impact parameter. On the other hand, combining the expressions for the magnification of two images obtained from a gravitational lens with the classical expression for the cross section, it is found that for purely gravitational scatterings the gravitational cross sections are proportional to the relative intensities. As a consequence of this remarkable proportionality and of the fact that the deflection angle obtained via the JWKB method is energy dependent, we come to the conclusion that chromatic effects in the gravitational lenses at the semiclassical level are possible, which violates the classical equivalence principle. The probability of detecting this tiny effect in the foreseeable future is discussed.

Gravitational bending of light is a spectacular prediction of Einstein's general relativity, tested and observed in numerous situations. We examine the fine structure of gravitational bending in new light to obtain insights pertaining to some deep links between gravity and quantum mechanics. The new results include quantum-theoretical interpretation of part of the light bending, making a good case for gravity encompassing wave–particle duality, perhaps a new insight for quantum gravity itself. We reiterate the mutual compatibility of the equivalence principle and quantum dynamics in a simple proof. Finally, we address certain unresolved issues regarding the gravitational bending of ultraslow light and tunneling photons in the context of experiments that might pose fresh challenges for the interface of the two century-old theories.