A relativistic quantum theory of gravity

  1. Jul 4, 2007 #1

    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"

    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[tex]^{-2}[/tex] 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.

    I mentioned that already.

    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.
  2. jcsd
  3. Jul 23, 2007 #2
    Enjoyed reading your paper, would like to make a few comments.

    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. :smile: DTF
  4. Jul 23, 2007 #3
    Thank you very much for the reference. I'll need to find this book before making any comments.

    Last edited: Jul 23, 2007
  5. Jul 24, 2007 #4
    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.

  6. Jul 24, 2007 #5
    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.

  7. Jul 24, 2007 #6
    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.

  8. Jul 24, 2007 #7
    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?

  9. Jul 24, 2007 #8
    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:

    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.

  10. Jul 24, 2007 #9
    Hi Doug:

    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.

  11. Jul 24, 2007 #10
    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.

  12. Jul 24, 2007 #11
    Hi Doug,

    Yes, we are repeating ourselves. Thanks for your comments, anyway.

    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.

  13. Jul 25, 2007 #12
    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.:smile: DTF
  14. Jul 25, 2007 #13
    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.

  15. Jul 25, 2007 #14
    Us old fogies are sort of super luminous action adverse
  16. Jul 25, 2007 #15

    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 .

  17. Jul 26, 2007 #16
    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.
  18. Jul 26, 2007 #17
    Hi, old fogies:

    I see your point.

    "That can not possibly be, because it could never possibly be."
    Letter to a Learned Neighbor, A. P. Chekhov, 1880.
  19. Jul 27, 2007 #18
    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

  20. Jul 27, 2007 #19
    Hi Yogi,

    thank you for your support.

    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

    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.

  21. Jul 27, 2007 #20


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    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.

    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
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