Check out Feynman's Lectures on Gravitation. He has a succinct discussion at the beginning of Lecture 3. Reasoning is by analogy: Spin 0 Scalar potential, Spin 1 Vector potential, Spin 2 Symmetric tensor potential, the latter required by general relativity.

Thanks.

Just as I suspected, the source (how gravitons are associated with spin-2) is related to the absence of the momenta-force field associated with gravity. If one were to associate the momenta force field with gravity, it gives rise to a vector potential.

In a similar analogy, if we haven't discovered the Magnetic field, we are forced to conclude that there is no vector potential associated with the charge force fields and thus it should be modeled with a tensor potential, in order to account for the force fields arising between moving mass bodies.

Quantum gravity may provide a more entuitive theory then String Theory.

Gravity is no doubt massless spin 2 field. This comes from the representation theory. Following Wigner, all the fields propagating in Minkowski space are in one to one correspondence with unitary irreducible representations of Monkowski isometry group, which is Poincare group ISO(d-1,1). In the simplest case of d=4 (our space) it is ISO(3,1). To study its unitary irreducible representations one should use so-called Wigner induced representation techniques. Roughly speaking it imples that there are two possibilities: massless and massive particles. To see that gravity is massless one should just linearise it, fix gauges (gauge away divergence of g and its trace) and discover that it satifies equation of the form

Box g_{mn}=0,

where Box is delambertian. It means that gravity is massless (momentum p squares to zero).

Once we are done with momentum, we should study how gravity transforms with respect to the remaining part of the group ISO(3,1), that leaves p invariant. This group is called Wigner liitle group and in the case of interst it is SO(2) (leaving aside some subtleties). In the given gauge gravity is discribed by symmetric traceless tensor 2 x 2. One can apply a infenitesimal rotation along one of the axis and see that the eigen values of the symmetric traceless rank 2 tensor are +2 and -2. These are helicities of gravitatilnal field and these values mean that the given field is a spin 2 field. It is pretty much similar to quantum mechanics, where psi function with momentum squared L^2 has eigen values starting from - L to L. The difference with graviton is 1) graviton is massless, so instead of expected spectrum of eigen values -2, -1, 0, 1, 2 one has only -2 and 2, 2) in quantum mechanics the momentum is related with the rotation in space, whereas for graviton it is associated with internal degrees of freedom (it has two tensor indices).

If you need more comprehensive answer, you can find it, for example in

http://arxiv.org/abs/hep-th/0611263

(at least first 3 sections) or from Weinberg Quantum Theory of Fields, vol. 1 chapter 2 I guess.

Well it is a bit more complicated. Gravity is not only an actor, it is also the director of the universe. You see, if you apply the known gauge principle to gravity, you do not find General Relativity, but you find GR plus torsion. Secondly remember that the other 3 fundamental interactions work in flat Minkowski space.

Moreover, for me the interesting question is not what is the spin of gravity (which is probably 2), but what is the classical graviton. You see, classical ElectroMagnetism can be equivalently described using the electric or magnetic field, or the electromagnetic potential. But we know that quanummechanically the photon is A_\mu. This is what is quantized.

So even if we know that gravity has spin2, the question is what is the graviton? It can be the metric, the vierbein, or the connection. All these work classically (metric formalism,teleparallel formalism, Palatini formalism). But quantummechanically only one of these pictures is correct. The graviton can be only one of them (for example in loop quantum gravity they try to quantize the connection).

Thanks guys. I am quite aware of the above mentioned work.

However, all of he work mentioned above do not take into account the existence of a dynamic momenta force associated with gravity. Therefore, my concerns are , if there exists a dynamical momenta force field for gravity , similar to the magnetic force field in charge force field domain, how that would effect all the models mentioned above?

As per my understanding, it would turn out that the gravitons too would become spin-1 instead of spin-2.

Please explain what you mean by dynamic momenta force.

>> it would turn out that gravitons too would be spin-1 instead of spin-2

Hi Dinesh - how can a spin-1 field couple with the stress-energy tensor? If it doesn't interact with stress-energy I don't think you can call it a gravitational field...

Hi Gerard,

Dynamic momenta force field is a unique force field arising between mass bodies in relative motion, similar to the magnetic force arising between charge bodies in relative motion.

you could read the paper entitled "On the Temporally Orthogonal Energies of Charge and Mass Bodies in Motion", which I have uploaded here.

Before this work was presented, back in 1890, Oliver Heaviside proposed that there should exist such a force field associated with gravity, similar to magnetic force field. However, he proposed this force field as a hypothesis, observing the symmetry between the gravitational and electrostatic force fields. In our work, we managed to show, what Heaviside proposed is in fact correct and managed to derive the force field equations for the momenta force field arising between mass bodies in relative motion.

Christopher:

Once the momenta force field is incorporated to gravity, the stress energy tensor will be replaced with a vector potential, which will be similar to what one would obtain in charge force field domain.

So my conclusion is, if one were to incorporate the momenta force field (dynamic force field of gravitation), one could potentially obtain the following results:

1. we have successfully proved that the propagation speed of the gravity is that of the speed of light in free space. (remember, GR and all the other theorems had to conject this limit, inheriting from the STR)

2. we could potentially prove that the graviton is a spin-1 particle

3. we can show that the "frame-dragging" phenomena is a direct consequence arising from the momenta-force field.

dinesh

Again, please explain what you mean by dynamic momenta force:

What does momentum have to do with force?

Does a gravitational field have a force field or a geometrical distortion of space-time?

What is the magenetic force between charged bodies?

What does the magnetic force have to do with gravity?

And most of all what kind of nonsense are you talking about?

Gerard,

I explained above that the momenta force is the force arising between 2 charge or mass bodies in relative motion (ie. when they possess momentum).

in charge field domain, the force arising out of relative motion between charge bodies is called magnetic force. similarly, we have shown that there exist a similar force field arising between mass bodies in relative motion. (arising from their momentum).

if they are not in relative motion compared to each other, then they are associated with the static force fields between them. ie. electrostatic or gravitational force fields, which are static.

I believe, if you are to understand this discussion you must know about the magnetic force, so I am not gonna go into a lengthy discussion on defining the magnetic force.

if you had carefully gone through my explanations above, you should have understood that in charge force field domain, there exists 2 force fields arising between charge bodies in motion, namely the static component : electrostatic field , and the dynamic component : magnetic field. These two force fields give rise to electrostatic force and magnetic force between the 2 charge bodies.

Similarly, we have shown that there exist 2 force fields between mass bodies in relative motion, the static component : static gravitational field and a dynamic gravitational field.. These 2 fields will give rise to gravitational force (Newton's gravitational force between static mass bodies) and a dynamical momenta force between them.

And I am not going to answer to your last question, as I believe it shows a lot about your fluency in engaging in a constructing discussion.

dinesh.

Dinesh,

In standard terminology the fields you mention are: Electric fields, Magnetic fields, Electromagnetic fields and Gravitational fields.

Electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects (a test charge) by the electrically charged particle the field is surrounding.

Magnetic field describes the magnetic influence of electric currents and magnetic materials.

Electromagnetic field is produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field.

None of these fields are related to gravity, so you should not compare them to a Gravitational field.

Gravitational field is the influence that a massive body extends a gravitational effect into the space around it, producing a force on another body that has mass.

The Magnetic field may have two components: the B field – outside of on object and the H field as in a magnetic object which produces the magnetism of the object.

In the 1980’s there was some research to determine an additional component to the gravitational field: Modified Newtonian Dynamics (MOND).

Motivation for MOND was to explain galaxy rotation. In a solar system the farther a planet is from the star the slower it moves. However all stars in a galaxy move at the same rate around the galactic center and the galaxy structure is stable.

Today the accepted theory for the stability of galaxies is that of Dark Matter. A halo of dark matter surrounds each galaxy, thus providing stability to the galaxies (even though we are totally in the Dark as to what Dark Matter is). I am not aware of any current MOND research.

However, as far as the “dynamic momenta force” between the two gravitational fields:

Maybe I still don’t get it, but I must say that it is nonsense.

Sorry

Hi Dinesh,

from the way you are talking about electric and magnetic field, I can deduce, that you don't really pay attention to Lorentz invariance. In 1890 there were no special relativity and one could talk about electric and magnetic fields separately. One could also draw inspiration from this description to modify gravity with appropriate magnetic component. But, since special relativity has been discovered, there is no doubt it is true. And it requires electric and magnetic forces to be unified, In fact, the formula for 4-acceleration a^i reads

a^i=F^i_jv^j,

where v^j is a 4-velocity and F^i_j is a tensor imcorporating both electric and magnetic fields. The usual spacial 3-velocity is a part of 4 velocity v^j where j takes only spacial values 1,2,3, but not time value 0. So, the part of F^i_j, where i and j run over 1,2,3 multiplies velocity and is nothing but magnetic field strength.

The similar formula for gravity reads

a^i=-\Gamma^i_{jk} v^jv^k,

where \Gamma is a gravity force in a sense. Analogously to the previous formula, acceleration depends on velocities. In this sence usual formulation of gravity (general relativity) contains what you call "dynamic moment force"

Gerard,

I didn't compare the electric field, magnetic field with gravity. In fact, it was Oliver Heaviside who was one of the first to suggest a possibility of a dynamic force field associated with mass bodies in motion, similar to the magnetic fields associated with charge bodies in motion. This was later termed as "Gravito-magnetism", which I am sure that you are quite aware of.

Now, despite this claim made by Heaviside and the other pioneers who sought to develop a dynamic force field associated with mass bodies in motion, the work was based on a assumption that there exists a dynamic force field associated with mass bodies in motion, similar to the magnetic force fields associated with charge bodies in motion.

However, if you go through some of the work that I have uploaded here, we first showed that by introducing a single hypothesis, one can derive both mass-energy and charge-energy equivalences. ( On the Energy-Mass and Energy-Charge Equivalences).

Once this was achieved, we managed to show that there exists an energy-momentum relation for a charge body in motion, similar to the energy-momentum relation for a mass body in motion.

As the energy momentum relations are quadratic in nature, we then showed that the total energy of a mass or charge body in motion is associated with 2 force fields. Namely, the rest energy of the energy-momentum relation is associated with the static force field and the momentum-energy is associated with a dynamic force field. This is where the momenta force field comes in. In fact, the magnetic field itself is a momenta force-field in charge domain. We have shown that the charge-momenta (or you may call it as 'electric current') is what what gives rise to magnetic field.

This may look like nonsense, unless you go through the work to realize that this is a new approach, which could possibly reconcile the gravity and electromagnetism.

I must emphasize that the current work has no connection with MOND and I am quite aware of the work by Milgrom who suggested this hypothesis. However, the proposed work presented in our papers shows an additional centripetal acceleration exerted by a massive rotating sphere on its satellite objects orbiting around it. This could potentially help us to explain the proposed Dark-matter effect, in part or as in whole.

Also I must emphasize that we are not claiming that the momenta force field arise between 2 gravitational fields. What we had shown is, that a static mass bodies are associated with a static gravitational field, and a dynamic mass body (a mass body which is associated with momentum) is associated with both static and dynamic force fields.

I believe, you could get a glimpse of what we are proposing. Even if you don't, we can engage in a positive and constructive dialog, as I believe that will help us to understand each others views. Further, you don't have to feel sorry for not being able to understand this work, as. I don't expect one to understand others work by merely going through it.

dinesh

Hi Dmitry,

I am fully aware that GR contains what I called dynamic momenta force. There is no question about that.

However, what we are proposing is that there exists two distinguished force fields in gravity. We have only recognized the static part of it : "Newton's gravitational force field", where as the dynamic part is not recognized as a fundamental force field. On the other hand, in charge force field domain, we have recognized both the static and dynamic components and their relevant inverse square force laws.

Though, we have not recognized the dynamic part and its inverse square nature, the predictions it gives out can be shown to be in accordance with GR.

The difference is, in GR, gravity is assumed to be propagating at speed of light, where as in our approach, we manage to show the existence of the 2 separate force fields and once you combine them similar to how Maxwell combined the electric field and magnetic fields, the outcome is a wave, and we showed that its speed is that of the speed of light.

Therefore, our effort is to show the existence of a dynamic force field equation and find its force constant, and then combine the static and dynamic force fields together and obtain its properties - which shows that the combined is a wave and its speed is that of the speed of light. This we believe, giving a possible explanation to what GR had to conject : that the gravitational waves propagate at speed of light.

dinesh.

Gr does not assume that gravity propagates at speed of light. It follows from equations of motion

Dmitry

GR equations are embedded with this assumption, and therefore it will throw out the gravitational wave propagation at speed of light.

Let us divert our attention to Maxwell's work :

My understanding is, during Maxwell's time, both the electric field and magnetic field were known and he combined the two to obtain the electromagnetic field and found that the combined wave propagate at a speed which was same as the speed which was known as the speed of light , during that time. The key is, there are 2 force fields associated with 2 force constants , permittivity and permeability constants. If you go through Maxwell's work, you would observe that these 2 constants are combined, in order to obtain the electromagnetic wave propagation speed.

Having said that, one must understand that, knowing only ONE force field (static part) and its constant would NOT enable us to find the wave propagation speed. One must know both the force equations and force constants, in order to obtain the wave propagation speed. On the other hand, if you ONLY know the existence of a ONE force field and its force constant (static part in this case), one could only conject that there exists a wave which propagated at speed of light. So, we need both the static and dynamic parts, in order to obtain the wave propagation speed.

Similarly, if we haven't quite found the magnetic field and its force field equations, one could still develop a GR like dynamical theory, and conject that there exists a wave that propagates at speed of light. Obviously, then you would end up with a theory which predicts all the predictions one could obtain from the magnetic force field, without actually knowing its (magnetic field) existence.

Now lets get back to our current discussion related to dynamic momenta force field and GR :

As I have pointed out above, one must first recognize the existence of both the static and dynamic force fields and their force constants, in order to obtain the wave propagation speed. As with the electromagnetic case outlined above, both the parts are mandatory (force constants), in order to obtain the wave propagation speed of gravity. Currently we only have the static part : the Newton's universal gravitational constant and its force field equations. So our claim is that, only when one finds the dynamical part, one can truly show the wave nature associated with gravity and its speed is that of the speed of light, by combining the static and dynamic parts. (similar to what Maxwell did).

We are not contesting GR, but we are giving a mathematical proof for the wave nature associated with gravity and its propagation speed is that of the speed of light, without having to resort to an assumption, inherited from STR , where nothing can propagate faster than light.

dinesh.

Dinesh,

I understand what you are saying because I read your paper:) It is good that you don't afraid to do something new, but you cannot solve all the problems of physics by making series of unsupported conjectures. I believe that first you should learn what was done at least in the beginning of 20th century. Then you will discover, that most of them has been already solved. In your paper you rely on results of 19th century!! After that a lot has been done. You also refer to works of Einstein, but in fact, you contradict them.

What you have done there --- you basically said, that gravity is just another copy of electro-magnetic field. Which means that you treat gravity as another non-intaracting spin-1 field. But the gravity is much more complicated and interesting. The main thing is that it underlies geometry of space, whole Riemannian geometry. Value of gravitational field influences measurements of time and length. And it is indeed obseved, for example in gravitational red shifts. Also, it interacts with light, which is observed experimentally. You have nothing of that in your theory. GR is checked on numerous experiments qualitatively and quantitatively.

And gravity do propagates with the speed of light as any massless field does. It doesn't require any side conjectures. Instead it follows from Einstein's equations. To translate in your language, in GR gravity contains not only Newtons potential, but also other 9 components, which in some sense play role of your dynamic force field, but in a completely different way. However, in the end the speed of gravity waves is speed of light. By the way, do you think that fitting of the new interaction constant such that its product with Newton's constant gives speed of light sqared is a good scientific method to show that gravity propagates with the speed of light in your theory?

Dmitry,

Its nice to know that you have gone through the said paper.

Based on our work, we showed that, not just gravity, but the electromagnetic fields also influences the measurements of time and length.

With regards to the new interaction constant, we haven't define it, so that the product gives rise to the speed of light, as you have mentioned above. In fact what we said was, the proposed relation should hold true in Planck units, and from that we obtained the constant. (Before that, we showed that all the other 3 relations do hold true when applied with Planck units.)

Dinesh,

It does not matter who proposed a relationship between an electromagnetic field and a gravitational field. The point is that no one has been able to correlate them as a unified field.

I am still not sure what you mean by a dynamic force field associated with mass bodies in motion. Gravitational fields are associated with mass, not with the motion of the masses. And most of all what is a momentum force?

The concept of momentum force is something you need to explain explicitly, since we all know that momentum is not a force. We know that impulse is force multiplied by time, however I’m sure that is not what you mean.

Hi Gerard,

Yes, you are right. The present work related to momenta force is not about the impulse.

In the present context, dynamic force field / momenta force field are both the same. What this states in general

1. Two charge bodies at rest are associated with a static Coulomb force field between them.

2. Two charge bodies in relative motion are associated with both Coulomb force field (static part) and a magnetic force field (dynamical part).

3. Two mass bodies at rest are associated with a static Newtonian force field between them.

we then showed that, there exists a force field, such that :

4. Two mass bodies in relative motion are associated with BOTH Newtonian force field (static part) and the momenta force field (dynamical part).

The key to understand this work is to first go through the energy-equivalences paper (On the Mass-Energy and Charge-Energy Equivalences), in which both mass-energy and charge energy equivalences are formulated from a single hypothesis. This gives rise to a relativistic energy-momentum relations for BOTH mass and charge bodies in motion. The results are in accordance with the special theory of relativity for mass bodies in motion.

Once we have the energy-momentum relations for both charge and mass bodies in motion, we can show that their exists two independent force fields for each domain (gravitational or electromagnetic) associated with their rest-energy and momentum-energy components.

From this we can show:

1. Static Coulomb force arise between the rest-energy components of two charge bodies (as the rest charge is a measure of a charge body's rest energy)

2. Static Newton's force arise between the rest-energy components of two mass bodies.(as the rest mass is a measure of a mass body's rest energy)

3. Magnetic or Dynamical momenta force (electromagnetic) arise between momentum-energy components of two charge bodies

4. Similarly, a Dynamical momenta force(gravitational) arise between momentum-energy components of two mass bodies.

So in a sense, even the magnetic force is a dynamical/momenta force, but electromagnetic in nature. Whereas the proposed dynamical/momenta force is a gravitational counterpart of the magnetic force.

I trust the above explanations might help you to understand the proposed work, its scope and finally what is meant by 'dynamical/momenta force field'.

Note: If one carefully go through the work presented, one can see how all the 4 force equations are combined to give a single equation : Force-energy equation, which encapsulates all the 3 known force equations (Newton's Gravitational, Coulomb and Magnetic) and the newly proposed dynamical/momenta (gravitational) force equation.

regards,

dinesh.

Dinesh,

I think that you do have a relevant theory and you should publish it in a refereed journal.

If you will allow me to provide a suggestion, play down the relationship between mass and charge.

I wish you all the best.

Gerard

Hi Gerard,

Thank you for your wishes. I will make a note of your suggestion and I know why you suggested that. Thank you again.

With regards to publishing, we both know that when it comes to publishing a new hypothesis, and if you are relatively unknown to the academia, well your chances are almost zero. This is the hard fact that I have to face.

Actually other than the 2 papers I have uploaded here at researchgate, there is another paper which is currently going through the peer-review process in a reputed journal. However, I would like to get it reviewed by a few more individuals like you to get their opinions and test the validity of the hypothesis presented in that paper, which is quite novel. If you are interested in going through this work, kindly advise me your email ID to which I can fwd you a copy. (or for that matter anyone who is experienced in reviewing a paper related to relativity and quantum physics, could get in touch with me @ [email protected], and I would be more than happy to engage myself with them for a constructive discussion).

I appreciate your efforts in going through this work (momenta force field) and trying to understand its significance.

regards,

dinesh.

Dinesh:

Permit me to discuss work that dovetails with the notion that gravitons would have spin 2.

My attempted research in math and physics features math solutions (to quantum isotropic harmonic oscillator equations) for which some solutions correlate with all known elementary particles (and their fields, some particle properties, and some interactions in which particles participate) and other solutions might correlate with yet-to-be-found elementary particles (and … similar to previous list in parenthesis).

One solution, which I denote by 44G4& would correlate with properties (including zero-mass, 2 polarizations, and spin 2) and roles people might expect of gravitons.

For further information, you might want to look at (at least) sections 1.1, 1.2, and 1.3 of "Physics Math Correlations." (I attach an extract that includes this material.)

More generally, I suggest that the "G-family" of zero-mass bosons includes 22G2& (photons), 44G4&, and other particles. I suggest that some of these other particles drove the big bang and regulate the rate of expansion of the universe.

In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be mass less (because the gravitational force has unlimited range) and must be a spin-2 boson. This is because the source of gravitation is the stress-energy tensor, a second-rank tensor, compared to electromagnetism, the source of which is the four-current, a first-rank tensor. Additionally, it can be shown that any mass less spin-2 field would be indistinguishable from gravitation, because a mass less spin-2 field must couple to (interact with) the stress-energy tensor in the same way that the gravitational field does. This result suggests that, if a mass less spin-2 particle is discovered, it must be the graviton, so that the only experimental verification needed for the graviton may simply be the discovery of a massless spin-2 particle.