beecee Posted January 6, 2019 Share Posted January 6, 2019 (edited) On 12/9/2018 at 5:36 AM, studiot said: So no response to my vector field question then, and we still have to go offsite to read any replies? The following is research being undertaken testing the true nature of GW's and of course GR...... https://www.ligo.org/science/Publication-O1StochNonGR/index.php LOOKING FOR "FORBIDDEN" POLARIZATIONS IN THE GRAVITATIONAL-WAVE BACKGROUND WITH ADVANCED LIGO A century ago, Einstein revolutionized our understanding of gravity with his general theory of relativity, which explains gravitational attraction as the curvature of spacetime around massive objects. It could be the case, however, that general relativity is only an approximation of a more complete theory of gravity, much like Newtonian gravity was an approximation of Einstein's theory. To find out whether this is the case, physicists and astronomers put general relativity to the test, comparing the observed properties of gravity to the predictions made by this theory. Any disagreement between the two could signal that general relativity isn't entirely correct. The field of gravitational-wave astronomy, ushered in by Advanced LIGO's direct detection of gravitational waves, gives us opportunities to test general relativity in many new ways. One new test is the study of gravitational-wave polarizations, which describe the characteristic pattern of the wave's distortion of spacetime as it moves. General relativity makes specific predictions about the polarization of gravitational waves. In particular, Einstein's theory only allows gravitational waves to take on two "tensor" polarizations. In contrast, alternative theories of gravity allow for up to four extra gravitational-wave polarizations (called "vector" and "scalar" polarizations). Whether a gravitational wave is tensor-, vector-, or scalar-polarized determines how it distorts spacetime and what direction it can move in as it propagates. (See Fig. 1 here for more details.) According to general relativity, vector and scalar polarizations do not exist. Any experimental observation of these "forbidden" polarizations would therefore prove Einstein wrong, indicating the existence of a complete theory of gravity that is more complicated that general relativity. In this study, we have searched for any traces of the "forbidden" vector and scalar polarizations in the stochastic gravitational-wave background. Unlike the "loud" binary mergers detected by LIGO and Virgo so far, the stochastic background is a soft, persistent "hum" of gravitational waves produced by the combination of many quieter gravitational-wave sources. Although these quiet sources are too weak, too rare, or too distant to be detected individually, when they overlap they produce a long-duration background that appears as static noise in the Advanced LIGO and Virgo detectors (listen here). The strength of the stochastic background is typically described in terms of its energy density, which expresses the fraction of the total energy in the Universe in the form of gravitational waves. Advanced LIGO has previously searched for the stochastic background considering only the tensor-polarized gravitational waves allowed by general relativity. No such background has been detected yet; those searches instead yielded upper limits on the energy density (i.e. strength) of the background, over the whole sky and as a function of the sky direction. If a significant fraction of the stochastic background's energy were instead in the form of the "forbidden" polarizations, then even a loud background could have been missed by previous searches. In this latest analysis, we use data from Advanced LIGO's first scientific observing run (which took place between September 2015 and January 2016) to answer two questions. First: Has Advanced LIGO found evidence of a stochastic gravitational-wave background of any polarization ("forbidden" or not)? Second: Is there any trace of the "forbidden" vector or scalar polarizations in the stochastic background? Ultimately, we find no evidence for a stochastic background of any polarization at the sensitivity of Advanced LIGO and Virgo during the first observing run, and by extension we cannot say whether the stochastic background contains vector or scalar polarizations. What we can do, however, is to place the first upper limits on the strength of vector- and scalar-polarized gravitational waves. The figure shows our inferred probability distributions on the energy densities of tensor- (blue), vector- (red), and scalar-polarized (green) gravitational waves in the stochastic background. The shaded shapes (or probability distributions) illustrate the possible energy densities that are compatible with our measurements — the higher a distribution at a given point, the more likely it is to represent the true value in our data. Notice that each plot in the figure contains two probability distributions. These just correspond to two different initial guesses (also known as "priors") about the relative probability that the strength of the background might take for different values. Regardless of the prior used, we find that all probability distributions sink to zero above sufficiently large energy densities (towards the right side of each plot). We can therefore compute upper limits on the possible strengths of each type of polarization. 90% of the probability distribution of the strength of each polarization is contained within these limits, so the true value will be within the limit nine out of ten times. These upper limits imply that less than one millionth of the energy in the Universe comes from a gravitational-wave background of any polarization. Trying to directly measure gravitational-wave polarizations is a powerful new test of general relativity. While we have not (yet!) detected a stochastic background of gravitational waves or found evidence for the existence of "forbidden" polarizations, this work presents the first upper limits on the energy density due to vector and scalar polarizations. Continued improvements to the sensitivity of Advanced LIGO and Virgo and the construction of additional detectors will allow for better resolution of the polarization content of gravitational waves in the future. <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://arxiv.org/pdf/1802.10194.pdf The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individuallyunresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically-polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy-densities of tensor, vector, and scalar modes at 95% credibility to Ω T 0 < 5.6 × 10−8 , Ω V 0 < 6.4 × 10−8 , and Ω S 0 < 1.1 × 10−7 at a reference frequency f0 = 25 Hz. <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>> https://www.researchgate.net/publication/326874881_The_Polarizations_of_Gravitational_Waves/fulltext/5b72d6d9299bf14c6da20661/326874881_The_Polarizations_of_Gravitational_Waves.pdf?origin=publication_detail This paper is based on the talk on the International Conference on Quantum Gravity, Shenzhen, China, 26–28 March 2018. The Polarizations of Gravitational Waves† Abstract: The gravitational wave provides a new method to examine General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General Relativity, so it is important to study the polarization contents of theories of gravity to reveal the nature of gravity. In this talk, we analyze the polarization contents of Horndeski theory and f(R) gravity. We find out that in addition to the familiar plus and cross polarizations, a massless Horndeski theory predicts an extra transverse polarization, and there is a mix of pure longitudinal and transverse breathing polarizations in the massive Horndeski theory and f(R) gravity. It is possible to use pulsar timing arrays to detect the extra polarizations in these theories. We also point out that the classification of polarizations using Newman–Penrose variables cannot be applied to massive modes. It cannot be used to classify polarizations in Einstein-æther theory or generalized Tensor-Vector-Scalar (TeVeS) theory, either. 6. Conclusions In this talk, we discussed the polarization contents in several alternative theories of gravity: f(R) gravity, Horndeski theory, Einstein-æther theory, and generalized TeVeS theory. Each theory predicts at least one extra polarization states due to the additional d.o.f. provided by it. In the case of the local Lorentz invariant theories, such as f(R) gravity and Horndeski theory, the massive scalar field excites a mix of Pˆ l and Pˆ b ; the massless scalar field induces merely Pˆ b . For the local Lorentz violating theories, such as Einstein-æther theory and generalized TeVeS theory, each of the scalar d.o.f. is massless, but it propagates at speeds different from 1, so it also excites a mix of Pˆ l and Pˆ b . Einstein-æther theory and generalized TeVeS theory also have vector polarizations due to the presence of the vector fields. E(2) classification was designed to categorize the polarizations for the null GWs in the local Lorentz invariant theories, so it cannot be applied to these theories discussed in this talk. The observational tests of the extra polarizations were also discussed. The analysis showed that the interferometers are not sensitive to the longitudinal polarization which might be detected using PTAs. <<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>> ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: The above are just two examples of cosmologists and Astrophysicists continuing the research albeit difficult and as yet inconclusive of the exact nature of gravitational radiation, and the total nonsensical conspiracy approach, that science is incalcitrant, stubborn and incapable of letting go of the past and incumbent theories including GR. Obviously a Nobel awaits any successful person with a more inclusive theory then GR, that will take its place. As yet, that hasn't happened. Edited January 6, 2019 by beecee Link to comment Share on other sites More sharing options...
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