# Vector theory of Gravity

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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......

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.

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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.

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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.

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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 by beecee

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15 minutes ago, beecee said:

The following is research being undertaken testing the true nature of GW's and of course GR..

Thank you for the information, though I think we still have a very long way to go in grappling with this subject.

IMHO we are still trying to extrapolate far too much from far too little information.

So the process of 'refinement' will go on.

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34 minutes ago, studiot said:

Thank you for the information, though I think we still have a very long way to go in grappling with this subject.

IMHO we are still trying to extrapolate far too much from far too little information.

So the process of 'refinement' will go on.

Totally agree.

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I'm not quite sure how many times (I think it was three) Einstein fundamentally changed the equations of GR and 'experts' are still arguing over which version is 'correct'.
Note I don't mean the solutions, I mean the equations themselves.

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Its an interesting paper, I am still reading it atm.  Its too early to form an opinion of the papers accuracy, some of the postulates are rather different to say the least. In particular the graviton being a fermion/antifermion pair. However that is just me lol.

Anyways I have seen far too many alternative theories proposed that I will wait and see what happens. Far too often promising theories never succeed in the face of further evidence.

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16 minutes ago, Mordred said:

Its an interesting paper, I am still reading it atm.  Its too early to form an opinion of the papers accuracy, some of the postulates are rather different to say the least. In particular the graviton being a fermion/antifermion pair. However that is just me lol.

Anyways I have seen far too many alternative theories proposed that I will wait and see what happens. Far too often promising theories never succeed in the face of further evidence.

Would "LISA" be any more precise in ability to analyse and have the necessary sensitivity that the present ground based  interferometers do not have? [at this point in time]

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LISA would allow us to detect a spectrum of GW wavelengths that we would not be able to detect on Earth. In order for LIGO or LISA to work the arm lengths are critical to capture the required frequencies. In order to detect a wave the arm length must match a quarter of the wavelength the longer the arms the longer the wavelengths that can be detected. In essence LISA would be far more accurate in so far as it will be able to measure an extremely smaller amount of strain. It should also capture a greater number of events than LIGO.

In essence it is the same for any antenna, the frequencies that the antenna can detect depend on the length of the antenna. Ideally the optimal sensitivity is to match the length to a quarter wave. If you pick up a half wave the strength of the detection drops as the two quarter waves that make up the half way will interfere with each other causing a loss in wattage.

The reason for the L shape is that GW waves a quadrupole waves whereas your antenna at home your antenna will only pick up dipolar waves ie electromagnetic

Edited by Mordred
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18 minutes ago, Mordred said:

LISA would allow us to detect a spectrum of GW wavelengths that we would not be able to detect on Earth. In order for LIGO or LISA to work the arm lengths are critical to capture the required frequencies. In order to detect a wave the arm length must match a quarter of the wavelength the longer the arms the longer the wavelengths that can be detected. In essence LISA would be far more accurate in so far as it will be able to measure an extremely smaller amount of strain. It should also capture a greater number of events than LIGO.

In essence it is the same for any antenna, the frequencies that the antenna can detect depend on the length of the antenna. Ideally the optimal sensitivity is to match the length to a quarter wave. If you pick up a half wave the strength of the detection drops as the two quarter waves that make up the half way will interfere with each other causing a loss in wattage.

The reason for the L shape is that GW waves a quadrupole waves whereas your antenna at home your antenna will only pick up dipolar waves ie electromagnetic

Thanks Mordred.

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Your welcome and its an excellent question to ask. I got curious as the expected strain and frequencies LISA would be sensitive to so I did some digging. Here is the mission proposal with those specifications.

Edited by Mordred
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1 hour ago, Mordred said:

LISA would allow us to detect a spectrum of GW wavelengths that we would not be able to detect on Earth. In order for LIGO or LISA to work the arm lengths are critical to capture the required frequencies. In order to detect a wave the arm length must match a quarter of the wavelength the longer the arms the longer the wavelengths that can be detected. In essence LISA would be far more accurate in so far as it will be able to measure an extremely smaller amount of strain. It should also capture a greater number of events than LIGO.

As can be easily seen from the chart shown here: https://en.wikipedia.org/wiki/Gravitational-wave_astronomy
current aLIGO actually has a peak GW strain detection sensitivity around an order of magnitude greater than that projected for the vastly larger and still future LISA array.
So factors other than arm length evidently play a crucial role in actual instrument capabilities.

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The amplitude of the of the GW frequency and how closely the antenna resonates at  given frequency will give rise to the amount of strain. Greater strain is easier to detect than a smaller strain. The strain is the amount of change in arm lengths this will always depend on the frequency of the signal as well as the sensitivity the antenna is to that particular frequency.

$h=\frac{\Delta L}{L}$ this is the basic strain formula that applies however your correct that other factors are involved. Such factors are the direction of the signal to the arm in terms of polarizations $h_+, h_x$ the cross section. Photon shot noise also plays a factor in laser interferometers

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16 minutes ago, Mordred said:

The amplitude of the of the GW frequency and how closely the antenna resonates at  given frequency will give rise to the amount of strain. Greater strain is easier to detect than a smaller strain. The strain is the amount of change in arm lengths this will always depend on the frequency of the signal as well as the sensitivity the antenna is to that particular frequency.

h=ΔLL this is the basic strain formula that applies however your correct that other factors are involved. Such factors are the direction of the signal to the arm in terms of polarizations h+,hx the cross section. Photon shot noise also plays a factor in laser interferometers

There is no disputing the obvious fact measured strain is defined as fractional length change, or that, all other things being equal, it's directly proportional to incident GW amplitude (not power density i.e. intensity). However laser interferometers are not built on a resonance principle like the earlier generation resonant bar and similar detectors.

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Why do you think I mentioned photon shot noise ?

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11 minutes ago, Mordred said:

Why do you think I mentioned photon shot noise ?

I'd have to guess. Both aLIGO and LISA will try their best to deal with it. Is this your way of a backdoor admission that my reference to 'factors other than arm length' re greater peak strain sensitivity of aLIGO vs LISA is obviously true? So how well shot noise is handled will be one key factor in overall sensitivity. And without my wasting a lot of time pouring over technical data, it's a fair bet aLIGO can do it a lot better than LISA can. For whatever technical reasons. There are other charts available that illustrate the various contributions to overall sensitivity for the different GW detectors, but I'm not interested in chasing one down right now.

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1 hour ago, Mordred said:

however your correct that other factors are involved. Such factors are the direction of the signal to the arm in terms of polarizations h+,hx the cross section. Photon shot noise also plays a factor in laser interferometers

did you miss this part when I already stated your correct on other factors being involved ? However your incorrect on LIGO being better than LISA. One other factor I didn't yet mention is seismic interference which wouldn't occur in space this is a serious limitation for LIGO.

Edited by Mordred
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16 minutes ago, Mordred said:

did you miss this part when I already stated your correct on other factors being involved ? However your incorrect on LIGO being better than LISA. One other factor I didn't yet mention is seismic interference which wouldn't occur in space this is a serious limitation for LIGO

Er sorry yes I did miss that, maybe because the content in relevant email notification was what I responded to, and that had not included a later edit.

But I'm puzzled why you now evidently claim LIGO (currently - aLIGO) is overall less sensitive than what LISA is projected to be. You dispute accuracy of that chart in Wikipedia article I linked to earlier? All contributions to final detection sensitivity are implicitly contained in those curves. No?!

[PS - re seismic interference. I know they should have, but wonder how well LISA crowd have allowed for e.g. micro-meteorite bombardment, or random solar flares.]

Edited by Q-reeus
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strain isn't a measure of the detectors sensitivity. LISA will be able to detect much lower frequencies than LIGO. One related formula is the gravitational wave energy flux $F\sim f^2h^2$ as LISA will be able to detect roughly $10^5$ lower frequency this will correspond to roughly $10^{10}$ greater sensitivity.

higher frequencies are easier to detect the energy flux is greater

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2 hours ago, Mordred said:

strain isn't a measure of the detectors sensitivity. LISA will be able to detect much lower frequencies than LIGO. One related formula is the gravitational wave energy flux Ff2h2 as LISA will be able to detect roughly 105 lower frequency this will correspond to roughly 1010 greater sensitivity.

higher frequencies are easier to detect the energy flux is greater

I could strongly dispute the correctness and/or relevance of every single statement made there, but am content to let it stand as a record against your name - assuming special editing permissions are not exercised later on. Best imo to now end this sidetrack off of main topic. Hopefully the disputed GR vs Vector Gravity GW results referred to earlier will be unambiguously resolved sooner rather than later - to both parties mutual agreement.

Edited by Q-reeus
and -> and/or
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1 hour ago, Mordred said:

did you miss this part when I already stated your correct on other factors being involved ? However your incorrect on LIGO being better than LISA. One other factor I didn't yet mention is seismic interference which wouldn't occur in space this is a serious limitation for LIGO.

Of course LISA while due to its nature and being in space, will be able to detect a great range of frequencies, it will be  great to see LISA aloft complimenting the work of the ground base detectors, GW's and GR.

I found another paper you may find interesting.....

Primordial Gravitational Waves with LISA:

Abstract:

Primordial Gravitational Waves are the next target of modern cosmology. They represent a window on the early Universe and the only probe of the physics and microphysics of the inflationary period. When the production of GWs happens in scenarios richer than the standard single-field slow-roll, the GW signal becomes potentially detectable also on scales smaller than the Cosmic Microwave Background. LISA will be extremely complementary to CMB experiments to extract information about primordial inflationary models and in particular to probe phases of the inflationary period for which we have very poor knowledges.

6. Conclusions

Primordial GWs are one of the next targets of modern cosmology since they represent a unique opportunity to shed light on the physics of the early Universe and in particular to probe the microphysics of inflation. An irreducible GW background is an ubiquitous prediction of all the inflationary models and this represents a smoking gun of the primordial accelerated expansion. The primary probe of primordial GW is the polarization of the CMB and in particular the curlfree polarization pattern (B-modes). When the inflationary scenario is enriched by secondary fields, besides the inflaton, or by assuming new symmetry pattern, GWs become a target also on scales smaller than CMB, and in particular for interferometers like LISA. While the GW by vacuum fluctuations is not visible by the next generation interferometers, many well-motivated inflationary scenarios produce a signal that can be visible or that can be extremely useful to reduce the parameter space of such scenarios. It becomes clear that a detection of GW signal on the small scales accessible to LISA, will offer a window on scales of inflation on which we currently have little knowledge and will become of fundamental importance in order to provide constraints on tensor perturbations complementary to the CMB.

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Primordial Gravitational Waves? Gravitational waves from the BB itself??

Conclusion:

The groundbreaking discovery of Gravitational Waves by ground-based laser interferometric detectors in 2015 has changed astronomy, by giving us access to the high-frequency regime of Gravitational Wave astronomy. By 2030 our understanding of the Universe will have been dramatically improved by new observations of cosmic sources through the detection of electromagnetic radiation and high-frequency Gravitational Waves. But in the low-frequency Gravitational Wave window, below one Hertz, we expect to observe the heaviest and most distant objects. Using our new sense to ‘hear’ the Universe with LISA, we will complement our astrophysical knowledge, providing access to a part of the Universe that will forever remain invisible with light. LISA will be the first ever mission to survey the entire Universe with Gravitational Waves. It will allow us to investigate the formation of binary systems in the Milky Way, detect the guaranteed signals from the verification binaries, study the history of the Universe out to redshifts beyond 20, when the Universe was less than 200 million years old, test gravity in the dynamical sector and strong-field regime with unprecedented precision, and probe the early Universe at TeV energy scales. LISA will play a unique and prominent role in the scientific landscape of the 2030s.

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And more confirmation re aLIGO, VIRGO and aLISA.....

extract:

Now, another detector is being built to crack this window wider open. This next-generation observatory, called LISA, is expected to be in space in 2034, and it will be sensitive to gravitational waves of a lower frequency than those detected by the Earth-bound Laser Interferometer Gravitational-Wave Observatory (LIGO).

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Current count is 11 [unless I'm missing something.]

Some outstanding cosmology ahead in the next decade or so, and I believe further precision and validation of Albert and GR.

In essence the main point I believe being made here and in the science world in general, is that individuals that whine conspiracy, incalcitrance by scientists and general inability to change according to "supposed" new evidence, have been shown to be totally wrong and in error with such accusations.

If GR is surpassed [a big big if!] it will be due to the research by the aLIGO/Virgo team, the LISA team and reputable scientists all round the world...nothing more, nothing less.

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Good article Beecee... I seriously doubt that GR will be overturned by the VR gravity... The more I read the article the less confidence I have in it

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7 minutes ago, Mordred said:

Good article Beecee... I seriously doubt that GR will be overturned by the VR gravity... The more I read the article the less confidence I have in it

Would you care to provide detailed, technically relevant reasons for that assessment?

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Well for one thing LIGO has identified the sources of the GW waves it has detected. The paper clearly mentions that there is a distinct difference in the polarization angles for the $h_+$ and the $h_x$ components between the 45 degree detection and the perpendicular to the detectors. Yet gravity waves have been detected by several detectors and those results can be compared to find the polarization angles with the current datasets available to distinquish between the two.

The theory also requires both photons and gravitons to be fermion/antifermion pairs yet the photon has spin characteristics of spin 1 which is different that the spin 2 characteristics detected by LIGO. The very design of the detector is specific to detecting a spin 2 quadrupole rather than a spin 1 dipolar wave. Gravitons and GR in general regardless of whether or not the graviton actually exists has successfully follow all the spin 2 characteristics

The paper claims to agree with the LIGO results but one has to ask how is this possible with such a distinctive difference in detectable polarization angles....

edit side note the paper also reminds me too much of vector electrogravity that I read back in the 90's

also the polarization angles detected by LIGO were used to identify the GW wave sources

Edited by Mordred
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14 minutes ago, Mordred said:

Well for one thing LIGO has identified the sources of the GW waves it has detected. The paper clearly mentions that there is a distinct difference in the polarization angles for the h+ and the hx components between the 45 degree detection and the perpendicular to the detectors. Yet gravity waves have been detected by several detectors and those results can be compared to find the polarization angles with the current datasets available to distinquish between the two.

The theory also requires both photons and gravitons to be fermion/antifermion pairs yet the photon has spin characteristics of spin 1 which is different that the spin 2 characteristics detected by LIGO. The very design of the detector is specific to detecting a spin 2 quadrupole rather than a spin 1 dipolar wave. Gravitons and GR in general regardless of whether or not the graviton actually exists has successfully follow all the spin 2 characteristics

The paper claims to agree with the LIGO results but one has to ask how is this possible with such a distinctive difference in detectable polarization angles....

edit side note the paper also reminds me too much of vector electrogravity that I read back in the 90's

also the polarization angles detected by LIGO were used to identify the GW wave sources

Every objection there has been comprehensively dealt with in either the main published article, or subsequently in the updated arXiv article challenging validity of LIGO_Virgo analysis of NS-NS merger event GW170817. I find it telling that afaik no spokesperson(s) for LIGO_Virgo team have to date publicly responded to that challenge. Which imo is extraordinary.

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I don't find it extraordinary at all there is literally 100's of alternative theories competing against GR. Is it LIGO's job to counter them or is it the physics community in general ?

The staff at LIGO's duty is to collect the data....

Edited by Mordred
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51 minutes ago, Mordred said:

Good article Beecee... I seriously doubt that GR will be overturned by the VR gravity... The more I read the article the less confidence I have in it

18 minutes ago, Mordred said:

Well for one thing LIGO has identified the sources of the GW waves it has detected. The paper clearly mentions that there is a distinct difference in the polarization angles for the h+ and the hx components between the 45 degree detection and the perpendicular to the detectors. Yet gravity waves have been detected by several detectors and those results can be compared to find the polarization angles with the current datasets available to distinquish between the two.

The theory also requires both photons and gravitons to be fermion/antifermion pairs yet the photon has spin characteristics of spin 1 which is different that the spin 2 characteristics detected by LIGO. The very design of the detector is specific to detecting a spin 2 quadrupole rather than a spin 1 dipolar wave. Gravitons and GR in general regardless of whether or not the graviton actually exists has successfully follow all the spin 2 characteristics

The paper claims to agree with the LIGO results but one has to ask how is this possible with such a distinctive difference in detectable polarization angles....

edit side note the paper also reminds me too much of vector electrogravity that I read back in the 90's

also the polarization angles detected by LIGO were used to identify the GW wave sources

Well put Mordred, and as supported by the papers.....

Quote

The paper claims to agree with the LIGO results but one has to ask how is this possible with such a distinctive difference in detectable polarization angles....

Speaking for the authors of a couple of papers supporting VG4 gravity, I suppose just as any Mother believes her child to be the most beautiful, would be a good explanation. I repeat though, contrary to some pushing the VG4, and their baseless claims re incalcitrance in mainstream circles, that has been absolutely shown to be total whining and baseless excuses.

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