Question on the Covariance of Dipole Gravity

It seems that this subject is a lingering question to many of the readers of dipole gravity. When a new metric is devised, this certainly becomes an important issue. A fully covariant field equation was expanded in the linearized theory and expressed by sums of infinite number of the individual multipole components. So in reality, the individual poles(monopole, dipole, quadrupole...etc) are not covariant by themselves, the total sum is.

Even so, it is amazing to see how much of the cosmological mysteries are solved solely by Newtonian(monopole) gravity. As the energy scale of the cosmological system gets larger, the higher order of the poles start making important contributions. The reason Newtonian gravity could not explain the jets and/or the dark matter problem was, in retrospect, because we have been working with a totally simplified, truncated non covariant field. As the more of the higher order poles are included, the overall gravity field starts to become more accurate and offer solutions to many other mysteries of the universe. Since the strength(magnitude) of the each poles decrease by the factor of c (speed of light) as the order increases, after the inclusion of the second and third terms of the linearized theory the overall sums of the field will still be accurate enough to cover most of the observable universe.

So, one can view the overall scheme of the linearized theory of general relativity by the following; the spatial translational motion is covered by Newtonian gravity(via point mass approximation), the intrinsic rotational motion of the bulk object is covered by dipole gravity and finally the intrinsic vibrational motion of the extended object is covered by the gravitational quadrupole moment.

In retrospect, I always felt that there was something fundamentally missing in our understanding of the universe. I remember looking up the text books on gravitation in 1982, even though I was not an astronomy major when I was a graduate student at the University of Michigan Ann Arbor. I was interested in the theoretical high energy physics. The most puzzling experience in this episode was when I looked up the page describing the linearized form of general relativity. There was something next to Newtonian gravity and that was the dipole gravitational moment. And it was dismissed by a reason that I thought was too much of tongue in cheek argument. The fact that one has to move the origin of the coordinate system to the center of mass of the object to remove the term seemed too convenient or/and unnatural(can't find the right word for it) because one can always set up the origin of the coordinate system at the center of mass of the object and forget about the coordinate alignment problem. I thought it was an unnecessary and non physical activity which may hide some more serious physics involved. The reason for its dismissal, I thought, was too frivolous compared to the possible importance of the term.

Because if general relativity have answers to the further mysteries of the universe, it should be in the term next to the Newtonian gravity in the linearized theory.

The conventional treatment of it made me feel suspicious of the argument. I never trusted any derivation of the physical equations in the text books in my college years until I derived it myself anyways.

It's like weighing a feather same as a gold nugget painted like a cotton.

But there was no way I could have guessed at the time that it could have something to do with the anomalous center of mass shift from the rotating hemisphere. In 1995, the puzzle was solved after 13 years since I began wondering about the strangeness of displacing the origin of the coordinate system to remove the dipole term in the linearized theory. It happened when I asked the following two questions in my mind. What is so special about the rotating hemisphere? And then how about the center of mass? The answers to these two questions answered the 13 years old questions in my mind. Hermes struck me down at the instant. The gravitational dipole moment!!!! It looks like there is no way one can avoid this solution. The jets and the dark matter problem are the two different sides of the same coin due to the dipole gravity effect from the fast rotating black holes.

At the moment, the quadrupole gravitational moment seems to be the main interest of experimental investigation in gravity. However, we missed dipole gravity altogether and there is no doubt that it should be investigated fully in the near future especially because it is much more stronger than the quadrupole moment. The extensive investigation of dipole gravity will determine the scope of the overall success of Einstein's initial revolution.

After that, when we still have too many mysteries remain unsolved, the next order of the poles will offer important clues to the problem. In this respect, the quadrupole moment will become important in the much high energy scale than that of dipole gravity, so we may be too far ahead of our steps in the adventure to the cosmological mystery.

In regard to this subject, if we assume that a big bang occurs in a much higher energy scale than that is governed by dipole gravity, it is quite conceivable that the instability arising from the vibrational oscillation of the quadrupole moment can result in the massive disintegration of the black hole in the form of a big bang. So, the extreme relativistic extension of the gravitational quadrupole moment can be a big bang which is listed as a question mark(?)in the dipole gravity chart.

How to Falsify Dipole Gravity?

Some readers of the dipole gravity article objected to the notion that there is a relativistic center of mass shift for a rotating hemispherical rotor by invoking Ehrenfest's paradox, which states that due to the length contraction effect of special relativity, the circumference of a rotating ring will be shorter than given by 2piR(the length of the radius will still be the same).

So the mass of the rotating ring should be the same regardless of the speed of the rotation according to their objection.

However, if we assume that the ring is made up of N number of atoms connected in series, each atoms will experience the special relativistic mass increase effect, and since the number of the atoms can not change due to the rotational motion, the relativistic mass increase effect for the whole ring(as well as for the whole hemisphere) should still be effective.

The next objection is from the simple comparison with the electromagnetic phenomenon. The electricity and magnetism has electric and magnetic dipole moment because there are two different charges in the theory of electromagnetism, ie, positive and negative charges of electricity and north and south poles of magnetism, but there is no negative mass in gravity so how can you have gravitational dipole moment?

While gravity and electromagnetism are both long range forces, they are fundamentally different forces of nature. In fact, the fact that there is no observed negative mass in the universe has contributed greatly to the notion that there should be no gravitational dipole moment in the physical world. However, general relativity in the linearized form only requires a physically meaningful shift(not the kind that can be eliminated by a coordinate translation) of the center of mass, not the presence of a negative mass for the existence of a gravitational dipole moment.

The question on why this shift implicated in the linearized theory of general relativity should be identified with the relativistic shift of the center of mass of a rotating longitudinally asymmetric object may be entirely a matter of faith. There is no reason it should be identified as such. But then there is also no reason it should not. At least it confirmed the result calculated by a different method of analytic integration performed by Lens-Thirring.

As in the Dirac's equation of the relativistic theory of positrons, a mathematical equation can be interpreted by predicting a certain new physical reality.
The entire justification of such an interpretation totally remains in its predictive power of the physical nature.

So the last resort to falsify dipole gravity remains in the test of its fundamental predictions since all the features of the dipole gravity potential have been consistent with the observed cosmological data.

Newtonian gravity started from the conceptual extension of the force that was observed from a falling apple(the real story behind will be much more complicated and deeper than can be described by such a simple story), the same force is exerted in the planetary system as well as in our daily lives. It seems clear that the massive cosmological phenomena like the jets and the dark matter problems should have a similar counter part in our daily lives so that we can observe it. Since dipole gravity is the second order effect from general relativity, its strength should be much weaker than Newtonian gravity and as such its effect will be much harder to detect in the terrestrial environment. But it is certainly within our current technological reach to test it as shown in the previous pages.

What if the test disproves the prediction?

I think it is possible, but it will ultimately mean the disproof of general relativity.

Rocketless Propulsion by Dipole Gravity

The theoretical explanation of the mysteries in cosmology may be the least exciting part of the consequences of dipole gravity. Apart from the obvious engineering difficulties associated with finding materials that can withstand the enormous centrifugal force that can tear up the whole structure of the rotor, dipole gravity is a practical and efficient method of propulsion in space travel.

Once a certain level of rotational speed of the dipole rotor is reached, it will start propelling the ship with an ever increasing speed without any additional expenditure of energy according to the theory of dipole gravity. The ship travels in space like falling down a constant gravity field except that there is no fixed source of a gravity center. The ship propelled by dipole gravity will travel the space like sliding down hill as it creates its own slope of the hills which depends on the rotational frequency of the dipole gravity rotor.

In theory, there is no limit of the speed of travel in this propulsion method.

What happened to special relativity that limits the speed of travel to the speed of light?

Special relativity applies when there is no curvature in space time, meaning when there is no gravity field. In terms of the tachyonic world picture, it means in the region where the density of the tachyonic neutrinos are uniform. Motion in space in this mode is like that of running against the blowing wind, not with the wind. The atomic nuclei of the material in motion in this mode suffers dislocation and huge resistance due to the enormous collision with the tachyonic particles. This is the main cause of the increase of energy(mass) as the object travels faster and faster in space by Newton's third law of motion. Any living organisms will not be able to withstand the stress without getting destroyed. The integrity of the structure of the material is not supported in this mode of travel as the speed gets close to the speed of light.

However, in the mode of the dipole gravity propulsion, the ship is enveloped inside the tachyonic aether's clothing. The ship is naturally following the density gradient of the spacetime curvature itself. In other words, the front side of the space of the dipole gravity propulsion device is an artificially created aether vacuum while the back side of it is a compressed aether space.

Alcubierre devised a metric that resembles this configuration in spacetime.

So, in the dipole gravity propulsion scheme, the imbalance of the surrounding tachyonic aether pressure is the one responsible for the acceleration of the ship itself. So the nuclei of the material inside the aether gradient doesn't suffer the massive pressure against the tachyonic neutrinos. The ship is traveling fast, even faster than the speed of light, but there is no increased aetheric pressure associated with it and thereby the structural and biological integrity of the ship is preserved.

After all, the black hole is a blob of space where tachyonic neutrinos can not penetrate. In a sense, it is a gigantic localized aether vacuum where all the material objects close to it are bound to fall into.

It's no suprise that the extreme relativistic extension of dipole gravity becomes a one way transversabe worm hole while that of Newtonian(monopole) gravity a black hole.

The Length of the Jets from Dipole Gravity

The lengths of the jets are determined by the peak of the repulsive dipole gravity potential on both poles of the rotation axis. The strength of dipole gravity falls more rapidly than the Newtonian gravity, so at certain point of the distance from the center, the attractive force of Newtonian gravity will dominate over the repulsive force of dipole gravity, which is the cause of the return trajectory and the brightly lit jets observed from the black hole accretion disks.


Essentially, the property of the linear trajectory is a function of the rotational frequency, total mass and the geometrical shape of the galactic core which determine the magnitude of the length element of the relativistic center of mass shift. Since the geometrical shape of the core can not be determined apriori, and also since its observation is out of the reach of the currently known method, the gravitational dipole moment will need to be treated as an adjustable parameter. One can assume a certain shape for the core, its mass(density as well) and the rotational frequency to estimate the actual length of the jets. It is noted that the length of the jets are very sensitive to the peak height of the repulsive dipole gravity potential. Due to the thermal fluctuation of the molten core material before the ejection, it is expected that there will be corresponding fluctuations on the length on the jets and also on the population density of the dark matter halo. The estimated dark matter population density function predicted by dipole gravity is 1/r. However, this density function suggests an infinite wise distribution which can not be true. So at certain point at the far out distance, the density distribution function is expected to decrease more rapidly than 1/r, because the density distribution can not suddenly be truncated to zero at distance r=ro(ro is the distance where the density distribution deviates from 1/r). In this sense, NFW's proposal of 1/r^3 dependency on the density distribution beyond certain distance limit r=ro is justified. (I'm indebted to Prof. Joel Primack for providing me with this information).
It would be interesting to see if the property of the thermal distribution of the molten core material could be related to the 1/r^3 dependency in the population density of the dark matter halo at the far out stretch as the compressed molten material would not all have the same kinetic energy at the peak height of the repulsive dipole gravity potential.