What is the Major Mathematical Equation of Dipole Gravity?

The material in the blog is difficult to navigate, in the sense that it deals with so many seemingly different subjects, so, for those who wants to know what dipole gravity is, in a nut shell, and also to clear the misconception if dipole gravity is purely a speculation, the main mathematical expression is presented here which was already shown in the introduction page.




The parameter etha in equation (17) is necessary to smooth the mathematical artifacts of the singularities at the distance R/2 and -R/2 along the Z direction, which are the center of mass of the individual hemispheres in the rest frame and V(r) is the Newtonian gravity from the rotating spherical shell.

The above functional expression is the three dimensional dipole gravity potential which is responsible for the jets and the dark matter problem. It is noted that this dipole term doesn't exist in the traditionally known theory of general relativity. The jets and the dark matter problem are two different sides of the same coin of dipole gravity. One can not be explained without the other. Numerical simulation and the various curve fitting will start from the equation above. The information related to the rotational frequency and the longitudinal asymmetry of the object is contained in the parameter representing the gravitational dipole moment dz/2, where dz is given by the total mass M times delta rc.



where R is the radius of the rotating spherical shell and c the speed of light for a slow limit of rotational frequency(v/c<<1). For a fast rotational frequency, the following expression can be used for the shift of the center of mass which applies to the rotating spherical shell.




However, in most of the applications, it would be difficult to tell if the core of the rotating galaxy can be represented by a spherical shape or by something totally different. Regardless of the detailed shape, the rotational frequency and the asymmetry(asymmetricity) of the geometrical configuration of the source is reflected in the gravitational dipole moment dz. Hemisphere is only one of the many possible geometrical shapes that can create gravitational dipole moment. The importance of the dipole gravity potential may be in the overall topological consistency, when it comes to the explanation of the large scale cosmological problems, which means if the functional form has all the necessary coordinations to predict the correct results.

Response to Questions from Colleagues(On the Covariance of Dipole Gravity)

Dear Eue J,

Is the theory covariant? Does it account for gravitational lensing? Can it explain the bullet cluster? These are all the sorts of questions people are probably asking you. I'm sure you have answers.
Best wishes,
daniel

Hi Daniel,

Thanks for your email with the questions. Let me try as best as I can. If you ask if Newtonian gravity is covariant, the answer will be no. Probably it's the same with dipole gravity. It's just a linearized weak field limit solution. But one may try to formulate a specific tensor metric to study the strong field regime of dipole gravity and then the question of covariance will become important. Just like Newtonian gravity becomes a black hole in the strong field regime of Schwarzschild metric, the result will be a predictable extension from the weak field limit behavior. One possible reason that it may be hard to find a tensor metric for dipole gravity will be that it is not a stable gravitational system. The system will not be local. In other words, in the strong relativistic field regime, the gravitational dipole moment will not be at the local spot where one expects it to be because of the extremely strong accelerating force it experiences from the rest of the universe. Theoretically, in such a case, how one can devise a tensor metric where the acceleration can be so strong that the locality of the system can not be well defined. If it is a moving system with a constant speed, it will be trivial, but how one can devise a tensor metric specifically for a constantly accelerating system while the constancy of the acceleration depends on the intrinsic(spin angular momentum and the longitudinal asymmetry) properties of the mechanical system under investigation. But I'm sure someone will come up with an answer. Basically, it's a metric where the source is a rotating hemispherical type (longitudinally asymmetric) rotor. Of course, nice thing about the linearized theory is that one can get a glimpse of the strong field regime without actually finding the metric sorely representing the gravitational dipole moment.

The jets from the rotating ultra compact stellar object is just as common as the winds and storms in the earth environment. And the matters ejected from the poles can take a long route to come back to the center by following the gravito magnetic force lines. Those matters in their transit toward the center of the rotating stellar object form dark matter halo in the surrounding space and the gravitational lensing becomes a natural consequence of it. It is surprising that the dark matters are actually found by studying the bullet clusters colliding with the stationary galaxy.

Regarding the bullet cluster, if a small galactic system has started with the initial condition in such a way that it has a longitudinally asymmetric configuration with non zero spin angular momentum, the cluster will run in one direction accelerating as predicted by dipole gravity. As the longitudinal asymmetricity flattens out as time goes by, due to many possible reasons, the constancy of the velocity will be set in and it becomes a bullet cluster.

The major development in the process of publishing the blog was the finding of the sign error in the Lens-Thirring force. After the correction, it flood gated all the subsequent understandings, ie, the consistent gravito magnetic force lines, the dark matter halo and the details of the intricate black hole jet engine mechanism.

Best Regards,

Eue J Jeong


==Answer to the question regarding the covariance of dipole gravity prepared earlier==

It looks like this is a common question in the minds of astro physicists as I have encountered more than several times. When Einstein's field equation is linearized, the individual terms are not by themselves covariant. For example, Newtonian (monopole) gravity will not be covariant by itself. Neither is dipole gravity. While they are parts of the solution to Einstein's field equation, the exact validity of it will be diminished substantially as the system goes into the extreme relativistic regime.

However, one can assume with great confidence that the major property of either monopole or dipole gravity will not change drastically as the system develops into the strong field regime. Black hole's gravity potential is different from the linearized weak field monopole(Newtonian) gravity, only in the way its functional variation over the close distances. The fundamental radial character of the monopole gravity force will not change. For example, the monopole gravity will not change suddenly into the dipole gravity just because the system goes into the strong field regime.

So, one can see that dipole gravity is a totally new entity. Its weak field limit property will not change into something else(other than dipole gravity itself) even if the system goes to the extreme relativistic regime.

One can see that there can be two different ways to perform research in general relativity to discover a new physics. One is trying to find a totally new metric tensor that may reveal some type of new physics in general relativity, which is the way most of the gravitational physicists are focused into these days. The other method is to find an actual mechanical system that can be calculable in the weak field limit of general relativity, which is presented in the theory of dipole gravity as well as in the quadrupole gravitational radiation research, the path of which is limited and has not been sought by many physicists. While some type of metric tensors that have been found may not represent the actual universe, the linearized weak field solution found directly from the mechanical system will represent a part of the actual universe at least in the regime of the weakly gravitating source.


PS; If we look back at the development of general relativity, it is not hard to see that dipole gravity is the true crown jewel of general relativity. Because the first term from the linearized theory which is the monopole(Newtonian) gravity was a totally expected one that can not surprise anybody and the third term which is the radiative type of gravitational quadruple moment is two orders of (v/c) magnitude weaker than the monopole gravity, which makes it extremely difficult to detect its effect. And none of these two known terms of gravitation seems to explain the most prominent cosmological problems of today, namely, the jets and the dark matter problem.

The second term in the linearized theory which is the dipole gravity was a totally unexpected one since it doesn't exist in the context of the classical gravitational physics. And it was not obvious if it does exist and meaningful within general relativity either, so it was generally considered non existent and that the dipole term in general relativity was considered physically meaningless, although many hints were there suggesting that it could exist and be real. For example, Lens-Thirring force should have been taken more seriously because it carries the signature of dipole gravity. And also, since acceleration of mass creates gravitational field, according to the equivalence principle, the gravitational field from the rotating sphere should have been looked at more carefully.

Pioneer 10/11 Anomaly

The astrophysics community has been baffled by the apparent anomalous behavior of Pioneer 10/11, as they have been observed to be attracted toward the sun slightly more than predicted by the force given by Newtonian gravity.

The anomalous Pioneer 10/11 acceleration (8.74 +/- 1.33) * 10^-8 cm/s^2 has been reported. For more info, visit http://www.planetary.org/programs/projects/pioneer_anomaly/ .

The acceleration of the Earth in its orbit is 0.593 cm/s^2 on average (1 AU)*(2*pi/yr)^2 making this anomalous acceleration 1.5*10^-7 of that.

However, Pioneer 10 was 67 AU from the Sun in 1997, when its mission was downgraded to a sort of background status, and Pioneer 11 was 40 AU from the Sun when contact with it was lost in 1995. This means that the anomalous acceleration is ~10^-4 of the Sun's acceleration of them at that distance.

Finally, it is noted that calculated nongravitational effects, such as radiation reaction from the spacecraft's radio transmissions and the glow of the RTG's, are not much smaller than the anomalous acceleration itself, suggesting that one may have to model such effects more carefully.

Also, there are no similar effects reported for the Voyager spacecraft, so these may be due to some quirk of the Pioneers.

The following is a quote from the report from NASA at JPL and LANL.
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Dispassionately, the most likely cause of the anomalous acceleration of the Pioneer spacecraft is on-board systematics, but the smoking gun has not yet been found. The only other possibility is the existence of new physics. This dichotomy represents a healthy win-win situation because either one of these two explanations for the Pioneer anomaly would constitute an extremely important discovery. (Author Slava Turyshev and John Anderson are at the NASA Jet Propulsion Laboratory, Pasadena and Michael Martin Nieto at the Los Alamos National Laboratory, US)
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One possible explanation of this anomaly may be found within the theory of dipole gravity. Since the rotating parabolic antenna of Pioneer represents a dipole gravity rotor, the observed additional acceleration toward the sun can be explained if the antenna is focused toward the sun which means the wider (open) side of the parabola faces the sun. And Pioneer is reported to be spinning at 14.1 sec per revolution which makes it spinning at 4.25 rpm. However, since the effect was not observed from Voyager as prominently(if at all) as it was observed from Pioneer, this may still be an open question.

If Voyager has different mechanical parameter (it also has parabolic antenna) compared to that of Pioneer in such a way that the dipole gravity effect is minimal (for example, the spinning rate is lower and it has more longitudinal axially symmetric configuration), then the mystery could be resolved. For this purpose, the detailed mechanical configuration including the rate of the spin rotation for both Pioneer and Voyager may be needed. This data may be found in the detailed original engineering design in terms of the mass distributions inside the craft.

In the mean time, the following information has been available which can be very significant.
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Is the same effect seen with the Voyager spacecraft?
The Pioneers are spin-stabilized spacecraft. The Voyagers are three-axis stabilized craft that fire thrusters to maintain their orientation in space or to slew around and point their instruments. Those thruster firings would introduce uncertainties in the tracking data that would overwhelm any effect as small as that occurring with Pioneer.

This difference in the way the spacecraft are stabilized actually is one of the reasons the Pioneer data are so important and unique. Most current spacecraft are three-axis stabilized, not spin stabilized.
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If the above information is true, in the three-axis stabilized spacecraft case, the anomalous effect would have been automatically canceled or diluted, because of the continuous adjustment of the orientation of the craft. However, in the case of the spin-stabilized craft, the dipole gravity effect will not be corrected which will make the effect prominently visible.

The following information is exactly what can be expected from a dipole gravity rotor placed in the empty space.
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What really puzzles scientists, Turyshev said, is that the anomaly is constant with respect to time and distance from about 1 1/2 billion miles away from the sun to about 6 1/2 billion miles out. The anomalous behavior has been observed in other deep space vehicles such as Voyager and Ullyses.
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The magnitude of anomaly seems larger than one would expect from a spin rotation of 4.25 rpm regardless of the size of the rotor. But the exact mechanical configuration of the craft is not yet available at the moment. And there is an uncertainty on the average distance and the amount of the mass of the universe which are not well defined relative to the location of the dipole gravity rotor. So, in case a terrestrial experiment is planned for the second confirmation, the Pioneer data will make a good starting point.

In a sense, the alternative experiment that has been proposed for the test of dipole gravity in the page http://dipoleantigravity.blogspot.com/2007/04/alternative-method-of-detecting-dipole.html may have already been done in the space without our knowledge.

Dipole Gravity and The Big Bang Cosmology

Some people in the field may engage into immediate expansive thoughts on what will be the consequence of this result on the current understanding of the big bang cosmology. Since the inflationary theory of cosmology depends largely on the ideas of the elementary particle physics, one has to assume that the current understanding of the theoretical elementary particle physics is complete and infallible to put 100 percent faith on it.

However, as I mentioned in the digression page, it must be emphasized that the exact physical nature of the neutrinos, which are the most mysterious particles in elementary particle physics today, is still controversial, although there is a great chance that they are tachyons. And such assumption doesn't seem to contradict the nature of dipole gravity, instead it helps understanding the cause of the gravity in general. Furthermore, the number of such supporting empirical evidences seems to be growing.

If neutrinos are tachyons, the homogeneity and the isotropy of the universe will be guaranteed at any time in the past and in the future. One doesn't have to worry about if some globular clusters may be older than the age of the universe predicted by the big bang theory.

The reason for the continuous expansion of the universe may be answered if neutrinos are magnetic monopoles themselves as well. It also explains the missing dark energy problem. Will there be final crunch after all these expansions? No one will be able to tell for sure at the moment. We are not certainly in the stage of science being able to contemplate any possibility after the complete expansion of the universe, if there is such a thing as complete expansion.

One thing that can be stated for sure is that there are stages of development of science where certain conjectures can be made on certain questions of the nature. Since no one survived to tell what happened at the time of big bang, most of the features of the theory must be categorized as speculations.

Our visible part of the universe may be expanding but no one knows what is happening to the other invisible part of the universe. So, our ability to foretell the mechanism of the universe is severely limited by our own limitations. As our science progresses to the higher level to be able to physically reach far out side of our own galaxy, our ability to predict the future of the universe will grow as well and become more reliable.

Response to Email Letter from Prof. McGaugh

----- Original Message -----
From: "Stacy McGaugh" (ssm@astro.umd.edu)
To: "ejeong" (ejeong1@sbcglobal.net)
Sent: Wednesday, May 23, 2007 5:49 PM
Subject: Re: Dark Matter is Real

> Yes, it is well known that in MOND there must be more mass than meets the
> eye (about a factor of two, presumably in some mundane baryonic form).
> The recent cluster press releases merely confirm this; they don't shed any
> light on the nature of the unseen mass (baryonic or non-baryonic) which
> makes all the difference.

> Professor Stacy McGaugh
> Department of Astronomy ssm@astro.umd.edu


I think the whole matter will eventually boil down to the priority issue. We haven't exhausted the known theory of gravitation, ie, general relativity. It looks like there are plenty of rooms for the dark matter problem to be taken care of within general relativity without the fundamental destruction of the existing Newtonian mechanics.

That's a humongous assumption. Occam's razor makes it a little bit hard for us to take it in.

Dipole gravity also demands the overhaul of Newtonian mechanics but not in such an arbitrary way. There is a clear cut path to the revision dictated by general relativity.

There is no ad hoc assumption in dipole gravity. It is general relativity itself.

Does MOND predict jets and provide the elaborate jet engine mechanism also? I don't think so. Does it provide any remote clues to the mechanism of creating the macroscopic wormhole, the ultimate method of space travel? No.

I don't know why anyone would want to stick to MOND after the revelation of dipole gravity other than based purely on the sentimental values, which scientists must avoid.

EJJ