# A relativistic quantum theory of gravity

Hello,

I would like to submit my own "crazy" theory of quantum gravity for discussion. The relevant paper was posted in the ArXiv recently

E.V. Stefanovich "A relativistic quantum theory of gravity"
http://www.arxiv.org/physics/0612019 [Broken]

Let me make sure I haven't ignored any of the posting guidelines.

1. The opening post must contain an abstract stating the results obtained and how the new theory is at variance with currently accepted theories.

Here is the abstract from the paper:

A relativistic quantum theory of gravity is proposed in which the gravitational interaction between particles is represented by distance- and velocity-dependent potentials. The Poincare invariance, the cluster separability, and the causality of this approach are established. The Hamiltonian for interacting massive particles and photons is formulated within the c$$^{-2}$$ approximation. The classical limit of this theory reproduces well-known relativistic gravitational effects, including the anomalous precession of the Mercury's perihelion, the light bending by the Sun's gravity, the radar echo delay, the gravitational time dilation, and the red shift.

The main point of "variance" with "accepted theories" is that gravity is not treated as a space-time curvature. This is important for making my theory compatible with the laws of quantum mechanics. Moreover, it appears that all classical predictions of general relativity can be reproduced within this simple potential-based approach. The theory, as presented, is an approximation. However, the message is that a full and exact approach may be based on the same principles.

2. The opening post must contain a section that either cites experiments that have been done that decide between the new and old theories, or it must propose experiments that could be done to decide between the two. If the submission contains a theory that is empirically equivalent to an existing theory, then this section may be substituted with a section that demonstrates the empirical equivalence and that compares and contrasts the insights gained from the submitted and existing theories.

As I mentioned above, the new theory agrees with all classical tests of general relativity. There are some observations, like frame dragging or orbital decay of binary pulsars, which are not mentioned in the paper, mainly due to my ignorance in these matters. My approach predicts some new effects. The most significant is the dependence of the gravitational acceleration of particles on their velocity. I believe that this effect contradicts the principle of equivalence. However, its magnitude is too small to be observed by modern experimental techniques.

3. All references to relevant prior work must be documented in the opening post.

The paper has 70 references

4. Quantitative predictions must be derived, wherever appropriate, and mathematical expressions and equations must be presented legibly, using LaTeX whenever necessary. For instructions and sample code see this thread. This should be done in the opening post.

I guess that link to the arXiv article covers this requirement.

5. New theories must not be already strongly inconsistent with the results of prior experiments.

6. If a new theory is strongly inconsistent with prior experiments, but the theorist is insisting that the experiments were either misconducted or misinterpreted by the scientific community, then the thread will be rejected. Instead the theorist should rebut the contradicting scientists in an appropriate journal.

No, I didn't claim that.

7. Theories containing obvious mathematical or logical errors will not be accepted.

If there are such errors in my paper, I am eager to learn about them.

8. Threads which contain obvious misrepresentations or gross misunderstanding of basic accepted science, especially when used in attempt to compare one's personal theory to currently accepted science, will not be accepted.

I hope I didn't do that.

9. External links will be permitted only for lengthy derivations and for diagrams. Any other expository text pertaining to the submitted theory must be posted at Physics Forums. Please note that this is a temporary Guideline that will remain in place only while we work on enlarging the maximum allowable attachment size in the IR Forum. Once that happens, we will require that all material pertaining to the theory be either posted at Physics Forums or attached to the thread.

I think this 29 pages paper can be regarded as "lengthy derivation and diagrams". So, providing an external link should be OK. If this is a problem I can attach a PDF file.

If a submitted thread with external links is approved, then the content of those links must not be altered unless approved by me. Failure to comply may result in a locked or deleted thread.

I believe it is OK to make minor modifications to the text posted in arXiv, like adding references. Is it so?

Thank you very much for providing this opportunity to share my work with scientific community.

Best regards.
Eugene Stefanovich.

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Arguably the bible on orbital alternatives to GR is Robertson Noonan Relativity and Cosmology, which has generalized the various approaches to perihelion advance and light deflection.

I would draw your attention to section 6.6, Vector theory of Gravitation p160-163, which generalizes the vector approach.
Your equation 15 is identically equivalent to R&N,s 6-42b with certain parameters chosen. Namely beta =0 alpha = -1/2 and the integration constant a = -1/2.

According to R&N the proper perihelion advance for this equation occurs when alpha =9/4, beta -5/4, and for this set of equations there is no deflection.

It is not say that you have not overcome the R&N parameters, and put fourth a consistent theory. It would be important, however to draw the distinction between your theory, and the R&N generalizations, and specifically how they are overcome. DTF

Arguably the bible on orbital alternatives to GR is Robertson Noonan Relativity and Cosmology, which has generalized the various approaches to perihelion advance and light deflection.

I would draw your attention to section 6.6, Vector theory of Gravitation p160-163, which generalizes the vector approach.
Your equation 15 is identically equivalent to R&N,s 6-42b with certain parameters chosen. Namely beta =0 alpha = -1/2 and the integration constant a = -1/2.

According to R&N the proper perihelion advance for this equation occurs when alpha =9/4, beta -5/4, and for this set of equations there is no deflection.

It is not say that you have not overcome the R&N parameters, and put fourth a consistent theory. It would be important, however to draw the distinction between your theory, and the R&N generalizations, and specifically how they are overcome. DTF
Thank you very much for the reference. I'll need to find this book before making any comments.

Eugene.

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sweetser
Gold Member
Hello Eugene:

In my scan of the article, I saw you are trying to dodge the issue of spin by saying there is no experimental data involving gravity and spin (page 4). That is not an accurate. To be an attractive force, the particles that mediate gravity must be even spin. To bend light which has a trace of zero, the particles must have a spin greater than zero. That leaves a spin 2 particle as the minimum. In classical gravity, masses attract and light is subject to gravity, therefore a theory must demonstrate how spin 2 particles are part of the Hamiltonian. It took me a while to figure this out for my Lagrangian, but it something you are required to do, even for a classical proposal. Professionals will dismiss your proposal out of hand for this solitary reason.

doug

Hello Eugene:

In my scan of the article, I saw you are trying to dodge the issue of spin by saying there is no experimental data involving gravity and spin (page 4). That is not an accurate. To be an attractive force, the particles that mediate gravity must be even spin. To bend light which has a trace of zero, the particles must have a spin greater than zero. That leaves a spin 2 particle as the minimum. In classical gravity, masses attract and light is subject to gravity, therefore a theory must demonstrate how spin 2 particles are part of the Hamiltonian. It took me a while to figure this out for my Lagrangian, but it something you are required to do, even for a classical proposal. Professionals will dismiss your proposal out of hand for this solitary reason.

doug
Hi doug,

I am afraid you missed the main point of this article. The idea is that all gravity effects, including light bending, can be explained without assuming exchanges of spin-2 gravitons. These hypothetical particles have not been seen in experiment, and their absence in my approach is not a bug, it is a feature.

In my approach, gravitational interactions are described by direct action-at-a-distance potentials. So, it is an alternative to both QFT-based theories and to general relativity.

Eugene.

sweetser
Gold Member
Hello Eugene:

You appear to have missed my point: professional physicists will ignore your work for this reason alone. Claiming to have a "relativistic quantum theory" and not caring about the particles that mediate the force makes no sense to me.

doug

Hello Eugene:

You appear to have missed my point: professional physicists will ignore your work for this reason alone. Claiming to have a "relativistic quantum theory" and not caring about the particles that mediate the force makes no sense to me.

doug
Hello Doug,

I think I've shown in the paper that this approach is formulated in full accordance with the rules of quantum mechanics. In addition, it realizes a unitary representation of the Poincare group in the Hilbert space. So, it is both quantum and relativistic.

Yes, there are no force-mediating carriers in this approach. But I don't think there exists a rigorous proof that a relativistic quantum theory must involve exchanges of virtual particles. I know that many "professional physicists" believe in this statement. My work is a counterexample for these beliefs.

Can you explain why my approach doesn't make sense, in your opinion? Does it contain mathematical errors? Does it contradict experimental observations?

Eugene.

sweetser
Gold Member
Hello Eugene:

Your approach does contradict the most basic property of gravity: that like charges attract. Read Brian Hatfield's introduction, and chapter 3 of "Feynman Lectures on Gravitation". I'll quote the most relevant paragraph:

Hatfield said:
In order to produce a static force and not just scattering, the emission or absorption of a single graviton by either particle must leave the particles in the same internal state. This rules out the possibility that the graviton carries half-integer spin (for example, related to the fact that it takes a rotation of 720 degrees to return to a spin-1/2 wave fuction back to itself). Therefore the graviton must have integer spin. Next, to decide which integer spins are possible, we examine the two cases where particle 2 is identical to particle 1 and where particle 2 is the antiparticle of 1, so that when charged, the two particles will carry the same and opposite charge, respectively. When the potential is computed in both cases and the appropriate limits are taken, we find that when the exchanged particle carries odd integer spin, like charges repel and opposite charges attract, just as in the example of electrodynamics. On the other hand, when the exchanged particle carries even integer spin, the potential is universally attractive (like charges and opposite charges attract). Hence, the spin of the graviton must be 0, 2, 4,... ...If we assume that the exchanged particle is spin 0, then we lose the coupling of gravity to the spin-1 photon. Since we know that light is deflected by massive objects, e.g., the Sun, then the graviton cannot be spin 0.
This is a reference to the same comments I made in #4. If your Hamilton gets the spin wrong, the proposal is wrong. The logic is that harsh (nothing personal).

Relativistic quantum field theory is all about the particles that mediate the interaction. One uses the propagator to calculate scattering angles in Feynman diagram calculations. It makes no sense to say you have a quantum field theory without a mediating particle. It's like saying one has an approach to QED without the photon. Unfortunately it implies a profound lack of understanding of the topic.

doug

Hi Doug:

Your approach does contradict the most basic property of gravity: that like charges attract.
Relativistic quantum field theory is all about the particles that mediate the interaction. One uses the propagator to calculate scattering angles in Feynman diagram calculations. It makes no sense to say you have a quantum field theory without a mediating particle. It's like saying one has an approach to QED without the photon.
That's the whole point of my article that I am not doing a quantum field theory. I am doing a theory of particles interacting by instantaneous (attractive) potentials. So, usual considerations about the spin of the force carriers do not apply here. (By the way, thank you for the quote.) Simply because there are no force carriers. The interaction between massive particles (and between massive particles and photons) is represented by usual Newtonian instantaneous potentials (plus some relativistic corrections).
The leading potential energy terms (i.e., second terms in the Hamiltonians (8) and (19)) are negative, so they correspond to attraction.

My theory does not use quantum fields at all. The usual wisdom says that such a theory cannot be relativistically invariant, but I prove by example that this wisdom is not correct. The theory is relativistically invariant, it is fully consistent with the rules of quantum mechanics, and it agrees with experimental observations.

Eugene.

sweetser
Gold Member
Hello Eugene:

First you claim to use "instantaneous potentials". This you claim releases you from an obligation to have a logically consistent field theory approach, whether you use that approach or not (and I don't agree with you on this claim - Nature is consistent no matter what - you can pick out a spin 1 particle in the classical EM Lagrange density even if that is used only to solve classical problems). Then you talk about "some relativistic corrections". In quantum field theory, that translates directly to virtual particles. Chapter 3 of the lectures does a great job of describing exactly that issue.

The problem with gravity is to get it to work seamlessly with quantum mechanics. It bothers me to see you claim to be "fully consistent with the rules of quantum mechanics." It sounds like an empty claim to me. Full consistency requires an understanding of the mediating particle.

Since we are merely repeating ourselves, I will give up. At least you know why one person sees a fundamental flaw in your work.

doug

Hi Doug,

Full consistency requires an understanding of the mediating particle.

Since we are merely repeating ourselves, I will give up. At least you know why one person sees a fundamental flaw in your work.

In my undestanding, a theory is quantum and relativistic if it provides an unitary representation of the Poincare group in the Hilbert space of the system. I took this definition from vol. 1 of Weinberg's "The quantum theory of fields". It is true that so far most examples of quantum relativistic theories were constructed by using field approaches, which imply exchanges of virtual particles. However, there is no theorem, which would prove that alternative non-field approaches are impossible. Actually, such non-field approaches have been developed, but they are not well-known. One example is given by works of H. Kita (refs. [5] and [6] in the paper). In my paper, I just apply Kita's ideas to gravity.

Eugene.

In regard to the instantaneous propagation of gravitation there are at least two methods of analyzing motion that yield contradictory results. For example if we analyze the orbit of a planet around a star using force we find that “if” the propagation of the force isn’t instantaneous, there is a couple developed that would have a measurable effect, and since we don’t see this effect, we conclude that the force transmission has to be instantaneous. On the other hand if we analyze the same system using potential, we find that the propagation of the potential at the speed of light works just fine, yielding no anomalous motion. The answer to this paradox is probably that analyzing motion using force is an improper method, rather than that force is transmitted instantaneously at super-luminous velocities. DTF

In regard to the instantaneous propagation of gravitation there are at least two methods of analyzing motion that yield contradictory results. For example if we analyze the orbit of a planet around a star using force we find that “if” the propagation of the force isn’t instantaneous, there is a couple developed that would have a measurable effect, and since we don’t see this effect, we conclude that the force transmission has to be instantaneous. On the other hand if we analyze the same system using potential, we find that the propagation of the potential at the speed of light works just fine, yielding no anomalous motion. The answer to this paradox is probably that analyzing motion using force is an improper method, rather than that force is transmitted instantaneously at super-luminous velocities. DTF
I am not sure if there is a fundamental difference in describing interactions in terms of forces or potentials. After all, force is just a gradient of the potential, so I would expect both descriptions to be equivalent.

Regarding the issue of instantaneous vs. retarded propagation of gravity, there was a long debate partly covered by references [60] - [68] in my paper. My position is that gravity propagates instantaneously, but I have no idea how this fact can be proven (or disproven) experimentally.

Eugene.

Us old fogies are sort of super luminous action adverse

Us old fogies are sort of super luminous action adverse
Why?

The usual reason to reject superluminal propagation of interactions is based on the alleged "causality violation". In special relativity this violation is derived from Lorentz transformations for the time and position of events. However, as I tried to argue in sections 5.2 and 5.3, in the presence of interaction (gravitational or otherwise), usual Lorentz formulas become approximate. Interaction corrections to Lorentz formulas are sufficient to invalidate the usual argument that leads to the prohibition of action-at-a-distance. This line of thought is explained in more detail in section 12.1 of http://www.arxiv.org/physics/0504062 [Broken] .

Eugene.

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sweetser
Gold Member
Put me in the "old fogies" category. Gravity goes at the speed of light, no faster. There is such a volume of bad work claiming they can break the law, it has never been worth the effort to dig through and find the mistake, especially when the mistake will not be admitted.

It is not a physical model to say information go instantaneously everywhere.
doug

Hi, old fogies:

"That can not possibly be, because it could never possibly be."
Letter to a Learned Neighbor, A. P. Chekhov, 1880.

Hi Eugene

Decided to accept your invitation. First, my own views are similar - I don't think its unjustified to propose field action at a distance - logically it seems to make more sense than conjuring up spin 2 virtual particles - virtual photons all got started with Feynman as an alternative to calculating the perturbation coefficients - then it got carried over to gravity - but I cannot believe that these concepts are more that metaphorical at best.

Anyway - phone just rang - more later

Yogi

Decided to accept your invitation. First, my own views are similar - I don't think its unjustified to propose field action at a distance - logically it seems to make more sense than conjuring up spin 2 virtual particles - virtual photons all got started with Feynman as an alternative to calculating the perturbation coefficients - then it got carried over to gravity - but I cannot believe that these concepts are more that metaphorical at best.
Hi Yogi,

You are right, virtual photons of QED are methaphorical non-observable concepts. The entire theory can be recast in the action-at-a-distance form without losing the accuracy of its predictions. This is done in a systematic way in

E.V. Stefanovich "Relativistic quantum dynamics", http://www.arxiv.org/physics/0504062 [Broken]

which is based on the "dressed" (or "clothed") particle approach first proposed in

O. W. Greenberg, S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim. 8 (1958), 378

and developed further by L. D. Faddeev, M. I. Shirokov, and few others.

Eugene.

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strangerep
Relativistic quantum field theory is all about the particles that mediate the interaction. One uses the propagator to calculate scattering angles in Feynman diagram calculations. It makes no sense to say you have a quantum field theory without a mediating particle.
For the record, relativistic QFT is not "all" about the particles that mediate
the interaction. E.g: phi^4 QFT has no mediating particle but we can still
calculate scattering amplitudes. However, the phi^4 interaction remains
local, whereas Eugene's proposed interaction is non-local.

It's like saying one has an approach to QED without the photon.
Actually, it's not really like that. In QED we can observe photons, whereas
gravitons and gravity-waves are still a bit controversial. If they are
unambiguously discovered, Eugene's theory will be in trouble and/or require
modification.

In QED we can observe photons, whereas
gravitons and gravity-waves are still a bit controversial. If they are
unambiguously discovered, Eugene's theory will be in trouble and/or require
modification.
There is an indirect proof of existence of free (not virtual!) gravitons and gravitational waves in observations of the orbital decay in binary pulsar systems, e.g.,

M. Kramer, et al. "Tests of general relativity from timing the double pulsar" http://www.arxiv.org/astro-ph/0609417 [Broken]

You are right, if graviton radiation is indeed discovered, this would mean a mild (but manageable) trouble for my theory. There would be no need to change the present (instantaneous) potential form of mass-mass and mass-photon interactions. The theory could be fixed by adding extra terms to the Hamiltonian. These terms would describe the graviton emission and absorption. In the lowest order they might have the form

a*a*aag + a*a*g*aa

where a*/a are creation/annihilation operators of massive particles and g*/g are creation/annihilation operators of gravitons. This form of the Hamiltonian would be quite similar to the QED Hamiltonian in the "dressed particle" approach discussed in my previous post.

Eugene.

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The binary pulsar decay may be a case of experimenters finding what they want to find. The problem I have with all force field communications is that there is no model of how forces can be connected this way - if a photon is emitted it travels by a well defined relationship with the properties of free space - it leaves here and it goes there - and it impacts and transfers momentum - in a field, something starts at A, travels to B - but it is still at A

Force fields cannot be imagined as particles going from A to B, yet most modern physics mathamatically models these fields the same way as light - I think Eugene's approach is a step in a direction that could lead to a holistic viewpoint of force fields in general
I am curious whether Van Flanderen published a response to Carlip's paper?

The binary pulsar decay may be a case of experimenters finding what they want to find.
There was a Nobel prize awarded for measurements and GR explanations of binary pulsar properties (including the orbital decay). That's not easy to beat.

Force fields cannot be imagined as particles going from A to B, yet most modern physics mathamatically models these fields the same way as light
I think most serious QFT practitioners do not accept virtual particles as real concepts. They are just internal lines in Feynman diagrams, or certain factors (propagators) in Feynman integrals. No more than that. The trouble arises when someone tries to "explain" Feynman diagrams to laymen. Then all this nonsense about "interaction carriers" and "virtual particle exchanges" begins.

I am curious whether Van Flandern published a response to Carlip's paper?
There is a (relatively) recent paper

T. Van Flandern, J. P. Vigier, "Experimental repeal of the speed limit for gravitational, electromagnetic, and quantum field interactions", Found. Phys. 32 (2002), 1031.

where he discusses Carlip's response. In my opinion, the debate Van Flandern - Carlip is in a dead end.

Van Flandern basically says (rephrased): "there is no aberration in gravitational interaction, i.e., the force of gravity points to the instantaneous position of the source, not to the retarded position. Therefore, the propagation of gravity must be instantaneous"

Carlip replies (rephrased): "Yes, there is no aberration of gravity (this is an experimental fact), but this doesn't prove the instantaneous propagation of gravity. In GR, if you take into account velocity dependent terms of higher orders in $c^{-2}$, then, due to some lucky compensation, the total force does not have aberration, even though all terms are retarded."

I think that Carlip is right. Aberration does not necessarily implies the superluminal propagation of the force. So, one cannot decide one way or the other by looking only at aberration.

You are probably aware of Fomalont and Kopeikin recent measurements of the light deflection by Jupiter. They claimed that they have measured the speed of gravity that coincided with c. There is a lot of responses to this result (some references are in my paper), which argue that the speed of light was actually measured, rather than the speed of gravity. I am lacking deep knowledge of GR, so I can't appreciate the arguments in this debate. I was thinking about calculating this effect within my theory. This should be a good independent check of its validity. What do you think?

Eugene.

Yes - I am aware of the Kopeikin claim - and also the criticisms thereof.

If you can come up with numbers, critics take notice. I do not have your article in front of me at present - have you included a critique of Einstein's explanation of the perihelion precession of Mercury's orbit. I have read some criticism of how he used this to validate the c velocity of gravitational propagation - I need to reread your paper on this. In any event - you are in for an uphill battle.

Had not realized the binary pulser data got a Nobel - I would say premature. Feynman got one too - as he said: "For sweeping the infinities under the rug" One of the problems in handing out such awards is that it blesses the work with an air of infallibility

There are several issues that arise in connection with G fields - one is how fast the new position of an object is communicated to other masses when it moves, or when it accelerates or when the accelertion changes. Another is, if a particle is destroyed - how fast is this information communicated. These may each involve different kinds of propagation mechanisms. Then there is the interesting question of what is the nature of the de Broglie wave when matter is accelerated.

Think how boring physics would be if all the problems were solved. How lucky we are to be able to ponder these questions.

Hi, Yogi,

I do not have your article in front of me at present - have you included a critique of Einstein's explanation of the perihelion precession of Mercury's orbit. I have read some criticism of how he used this to validate the c velocity of gravitational propagation - I need to reread your paper on this. In any event - you are in for an uphill battle.
No, I don't discuss or criticize Einstein's general relativity in the paper. I also believe that predictions made in GR are perfectly consistent within this approach. This theory made a huge number of correct predictions without any fitting parameters. This is truly amazing! And this makes so much harder to come up with an alternative theory.

Nevertheless, I believe that GR is built on wrong physical premises (the 4D space-time manifold) and sooner or later this will show up in disagreements with experiments. For example, I discuss possible violations of the equivalence principle in section 5.1.

Had not realized the binary pulser data got a Nobel - I would say premature. Feynman got one too - as he said: "For sweeping the infinities under the rug" One of the problems in handing out such awards is that it blesses the work with an air of infallibility

In 1993 Taylor and Hulse received the Nobel prize for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation. This was a remarkable piece of work, and I wouldn't say that the prize was premature. Likewise, the development of the renormalized QED in the late 1940's was probably the greatest advance in theoretical physics after formulation of quantum mechanics in 1926. Of course, this doesn't mean that the final judgement has been pronounced on these matters.

There are several issues that arise in connection with G fields - one is how fast the new position of an object is communicated to other masses when it moves, or when it accelerates or when the accelertion changes. Another is, if a particle is destroyed - how fast is this information communicated. These may each involve different kinds of propagation mechanisms.
I believe that gravitational interactions propagate instantaneously, however, I don't know any convincing way to demonstrate that experimentally. I think, there is much greater chance to confirm the superluminal propagation of electromagnetic interactions. In recent years there has been a large number of experiments pointing in this direction.

Think how boring physics would be if all the problems were solved. How lucky we are to be able to ponder these questions.
I thank "Supreme Being" everyday for the privilege to live in such interesting times.

Eugene.