# A relativistic quantum theory of gravity

by meopemuk
Tags: gravity, quantum, relativistic, theory
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 P: 1,473 Eugene - I think I know where you got the idea - in part 3, Selleri refers to the "velocity of a point source light signal ..." he is talking about the velocity of the light signal, not the velocity of the point source - remember these are translated from Italian probably originally ...if you read the rest of the paragraph it is clear he is not referring to the velocity of the sources but rather the velocity of the signal emitted by the point sources as they would be measured in different frames w/o relativity.
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 Quote by yogi I dont know how you arrived at the conclusion that inertial transforms depend upon the source velocity. Selleri takes the position that the velocity of light is c in free space - his transforms avoid the postulate of one way light velocity - he embraces the proven part of the SR experiments - namely that MMx, Kennedy Thondyke etc are experiments confirming two way velocity Can you direct me to the paragraph or words which you have relied upon to arrive at the above criticism?
Hi Yogi,

Special relativity postulates that the speed of light is independent on the velocity of the observer (who measures this speed) and on the velocity of the light source. This postulate is embodied in the Lorentz transformations

$$x' = \frac{x - vt}{\sqrt{1-v^2/c^2}}$$
$$t' = \frac{t - vx/c^2}{\sqrt{1-v^2/c^2}}$$

where $(x,t)$ are space-time coordinates of a certain event from the point of view of observer O, and $(x',t')$ are space-time coordinates of the same event from the point of view of observer O', which moves with velocity $v$ with respect to O.

The reason why these transformations preserve the speed of light is simple. Assume that a light pulse was emitted from the space-time point $(x_1,t_1)$ and absorbed at the space-time point $(x_2,t_2)$ (the measurements were done by the observer O). Then the interval between these points is always zero

$$s^2 \equiv c^2 (t_2 - t_1)^2 - (x_2 - x_1)^2 = 0$$

which is just another way of saying that the speed of propagation of light is c.

It is not difficult to show that Lorentz transformations preserve this interval, i.e., from the point of view of O' the interval is zero as well

$$(s')^2 \equiv c^2 (t'_2 - t'_1)^2 - (x'_2 - x'_1)^2 = s^2 =0$$

Therefore, from the point of view of O', the speed of light is c as well

Applying these considerations to gamma quanta studied in the paper of Alvager et al., we can say that if their speed is c with respect to the moving particles, which emitted them, then their speed must be c with respect to the ground laboratory as well. That's what experiment has confirmed with great precision.

Now, if we accept Selleri's modification of Lorentz transformations

$$x' = \frac{x - vt}{\sqrt{1-v^2/c^2}}$$
$$t' = \frac{t }{\sqrt{1-v^2/c^2}}$$

we must conclude that they do not preserve the interval between the light emission and absorption events. Therefore, according to him, the speed of light is different in different reference frames. Alvager's experiment should have detected this difference. But it didn't.

Eugene.
 P: 1,473 Alvager's experiment showed that the speed of light doesn't depend upon the velocity of the source - something already known from de Sitter. But that is not the only way one can arrive at different one way velocities for light in different reference frames - Selleri Transforms are based upon a preferred frame and therefore the one way velocity of light will be different if the observer is moving wrt to the preferred frame. Selleri is not introducing a ballistic theory - but rather restoring a form of Lorentz ether which has never been falsified. You are correct, using Selleri tranforms, the speed of light (one way) will be different in different reference frames, but not because of the source velocity. The one way velocity proposed by Einstein in SR has never been measured, and it is this aspect of the theory that leads to the counter intuitive aspects of the Special Theory, Don't want to get to side-tracked by Selleri - I raised it because I felt it related to your theory and perhaps potential criticism of causalty that always arises in FTL communications Best Yogi
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 Quote by yogi The one way velocity proposed by Einstein in SR has never been measured
Hi Yogi,

Isn't it true that time-of-flight experiments measure the one-way velocity?

 Quote by yogi Don't want to get to side-tracked by Selleri - I raised it because I felt it related to your theory and perhaps potential criticism of causalty that always arises in FTL communications
I agree that SR Lorentz transformations forbid any kind of FTL signals due to the violation of causality. So, any theory claiming faster-than-light propagation of interactions (including my theory) must involve some modifications of Lorentz formulas.

I think that both Einstein's and Selleri's approaches have one important weakness. They presume that Lorentz (or "inertial") transformations are universal, i.e., they are the same for all particles and events, independent on their nature and involved interactions. In my opinion, this is very strong and unjustified assumption. To show its limitations, let us apply this assumption to time translations instead of Lorentz boosts. (Both time translations and boosts are members of the Poincare group of inertial transformations, so we may expect some similarities between them). Then the assumption of universality would lead us to the conclusion that time translations have exactly the same effect on positions of all particles

$$\mathbf{R}(t) = \mathbf{R}(0) + \mathbf{V}t$$......(1)

which is definitely not true for interacting particles.

We know well that time translations affect particle positions in a complex way, which depends on interactions, and eq. (1) is, at best, an approximation which may work at small values of t.

Extending this analogy to boosts, it doesn't seem unreasonable that boost transformations of particle positions can depend on interactions between particles. Physical events are not abstract space-time points. They are real processes (e.g., collisions) involving real interacting particles. Therefore, it is natural to assume that boost transformations of space-time coordinates of events should not be given exactly by Lorentz formulas. There could be corrections that depend on interactions between particles. In my theory, Lorentz transformations are modified by these interaction-dependent corrections. This is how I can have instantaneous interactions and, at the same time, avoid the causality paradox.

Eugene.
 P: 1,473 I may not be interpreting your post correctly - seems if you have a pure time translation of a system of interacting particles (e.g., electrons), nothing would change unless you impose an artifical time dependent asymmetry - in other words you must introduce an epoch dependent factor that relates the forces to conditions existing in a particular era... then time symmetry is broken and so is conservation of energy a la Noether! Or maybe you are saying that time translations of relativisticly interacting particles are not symmetrical.
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 Quote by yogi I may not be interpreting your post correctly - seems if you have a pure time translation of a system of interacting particles (e.g., electrons), nothing would change unless you impose an artifical time dependent asymmetry - in other words you must introduce an epoch dependent factor that relates the forces to conditions existing in a particular era... then time symmetry is broken and so is conservation of energy a la Noether! Or maybe you are saying that time translations of relativisticly interacting particles are not symmetrical.
I am afraid that you are confusing two different issues: the invariance of the laws of nature with respect to time translations and the non-trivial time evolution of interacting systems. I will try to explain the difference:

Invariance of the laws of nature with respect to time translations. This is an absolute and exact (as fas as we know) law of nature. It basically says that if I prepare a physical system S and measure its property P today, then I will obtain exactly the same result as if I prepare the same system (in exactly the same conditions) and measure the same property tomorrow, or at any other time.

This law, however, does not mean that the time evolution of the system is trivial. For example, if the system is made of interacting particles, then positions of these particles measured at times 0 and t are related by complex formulas that depend on interactions acting between the particles

$$x_1(t) = x_1(0) + v_1(0)t + \frac{a_1(0)}{2}t^2 + \ldots$$
$$x_2(t) = x_2(0) + v_2(0)t + \frac{a_2(0)}{2}t^2 + \ldots$$

where accelerations $a_1, a_2$ are non-trivial functions of the distance between the particles and their velocities. This is what I call non-trivial time evolution of interacting systems.

Note that, according to the law if time invariance, if I prepare the same system of interacting particles tomorrow, then positions $x_1(t + 1 day)$ and $x_1(0 + 1 day)$ will be related to each other by the same non-trivial formulas as $x_1(t)$ and $x_1(0)$.

Exactly the same considerations apply to boosts. There is an exact and universal law of invariance of physical laws with respect to boost transformations of reference frames (in all moving frames of reference physical laws are the same). However, this invariance does not imply that boost transformations of observables between two moving frames of reference are given by some universal interaction-independent formulas. In fact, I am arguing that it is impossible to have universal Lorentz transformation formulas if the observed system contains interacting particles. One cannot have trivial (interaction-independent Lorentz) boost transformations of observables and a non-trivial (interaction-dependent) time evolution. This would contradict the Poincare group properties.

Eugene.
 P: 1,473 " I am arguing that it is impossible to have universal Lorentz transformation formulas if the observed system contains interacting particles" Ok - so you are saying this transitions by implication to instantaneous field propagation?
P: 1,746
 Quote by yogi " I am arguing that it is impossible to have universal Lorentz transformation formulas if the observed system contains interacting particles" Ok - so you are saying this transitions by implication to instantaneous field propagation?
Not exactly. The idea of the instantaneous propagation of interactions came from the "dressed particle" reformulation of QED. This is described in detail in http://www.arxiv.org/physics/0504062. The main idea of the dressed particle approach is that virtual particles (they are usually visualized as spontaneously created in the vacuum and forming dressing "clouds" around real particles) can be incorporated into the definition of physical particles by performing a unitary "dressing" transformation of the QED Hamiltonian. This transformation preserves the form of the S-matrix in the renormalized QED, so all results comparable with experiment remain preserved.

However the physical interpretation of the "dressed" theory is quite different from the standard interpretation of QED. Instead of virtual particles carrying interactions between real particles, we have instantaneous inter-particle potentials. In the lowest perturbation order these are usual Coulomb and magnetic potentials. In higher orders, there are radiative corrections responsible for such effects as the Lamb shift, for example.

The "quantum gravity" paper discussed here is an extension of the above ideas to gravity. I simply assume that in analogy with the "dressed particle" reformulation of QED, a similar action-at-a-distance approach should be applicable to gravity as well. The interaction-dependence of boost transformations plays its role in proving that such instantaneous interactions do not contradict the principle of causality.

Eugene.
 P: 1,746 Many thanks to Juan R. Gonzalez-Alvarez and Eugene Shubert who took time to read the paper and sent me their comments. From their input I realized that my description of the principle of equivalence is not accurate. It is not correct to think that in an accerated elevator cabin all bodies move with the same acceleration independent on their velocity. There is a dependence of acceleration on the velocity, which can be calculated from the relativistic law of addition of velocities. I corrected this place and several other inaccuracies in the paper and uploaded the new text in http://www.arxiv.org/abs/physics/0612019 (v6). I should note also that these changes, however significant, do not modify the major conclusions made in the paper. Eugene.
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 Quote by dtfroedge 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. DTF
Hi DTF,

a few comments:

As I wrote in my previous post, I found a few important mistakes in the original version of my paper. The latest text (v6) is considerably revised. Eq. (15) in the earlier version is now replaced by eq. (24) which doesn't look like eq. (6-42b) from R&N anymore.

I am not sure whether I want to compare my results with scalar, vector, and tensor theories of gravity described in the R&N book. First, I have many objections regarding their presentation of relativistic interacting dynamics. For example, I am absolutely convinced that any relativistic interacting theory must realize a representation of the Poincare Lie algebra either by commutators (in the quantum case) or by Poisson brackets (in the classical case). This is just a mathematical representation of the principle of relativity. They use a different approach, whose validity is not clear to me yet.

Another difference is that I use different Hamiltonians for gravitational interactions of massive particles and photons. R&N obtain equations for light rays by simply setting particle speed to c.

So, my theory is very different from "special-relativistic gravitational theories" described in R&N. A fair comparison with my approach would require a lot of work, and could be a subject of a separate paper or two. I am not sure what would be the significance of this work, since the theories described in chapter 6 of R&N are considered "dead" anyway.

Thanks for your input.
Eugene.
P: 27
 Quote by meopemuk Hi DTF, So, my theory is very different from "special-relativistic gravitational theories" described in R&N. A fair comparison with my approach would require a lot of work, and could be a subject of a separate paper or two. I am not sure what would be the significance of this work, since the theories described in chapter 6 of R&N are considered "dead" anyway. Thanks for your input. Eugene.
Yes; and I didn’t want to imply that R&N was a definitive treatises on the subject. In terms of the current state of the art, it is way behind the times. It’s just that when a new theory is presented, it’s hard to persuade a skeptical audience to even wade through the material, unless it is contrasted with previously well known work. So when a proper perihelion advance etc., is predicted, it’s a good for the audience to have a familiar starting point.

Moving back and forth between the assumptions and the predicted results, which you have done, is the essence of developmental physics. Philosophically, however theories won’t get much traction in the community, unless at some point there is a prediction of something that has been predicted wrong, or not within the scope of other concepts. Developing something that is more intellectually elegant doesn’t move this audience much.

I am inclined to agree with you on the validity of the Poincare Lie algebra as being at least part of the proper mathematical apparatus for dynamical systems; it makes sense. At this point however the algebra itself is not a theory, and neither is a selected Hamiltonian, it’s only an indicator of a direction to go. Sourcing the empirically arrived at Hamiltonian on the other hand would move it up a notch. DTF
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 Quote by dtfroedge Yes; and I didn’t want to imply that R&N was a definitive treatises on the subject. In terms of the current state of the art, it is way behind the times. It’s just that when a new theory is presented, it’s hard to persuade a skeptical audience to even wade through the material, unless it is contrasted with previously well known work. So when a proper perihelion advance etc., is predicted, it’s a good for the audience to have a familiar starting point.
Hi DTF,

I got your point (at least I think so). I think you are right. It wouldn't hurt if I briefly discuss previous "flat spacetime" theories of gravity and how my approach is different. I don't need to go into full detailed comparison, but a few sentences and references would help to place my work into context. Thanks for the idea. I'll do that.

Eugene.
P: 44
 Quote by sweetser 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 Doug,

It may be true that "In classical gravity, masses attract" but it is also true that gravitation can't be described exactly by any classical theory so it does not need to be an attractive force. It is an attractive force only in certain (mis)interpretations of Newtonian math that assume that masses attract each other.

In general relativity though it is only an inertial force generated by direct push from other particles trying to push the particle out of its geodesic worldline in spacetime which can be observed as tidal force. Furthermore, in Einstein's gravitation this force must be mediated by photons since an atom loses/gains photons when its gravitational energy diminishes/increases by the energy of a photon (as demonstrated indirectly by Landau in his "Theory of fields", which BTW might be relevant for your own theory of equivalence of EM and gravitation, which I tried to write you about already since you have the same problem with the spin of graviton and photon, and I'm curious how you have solved it).
P: 1,746
 Quote by JimJast ... it is also true that gravitation can't be described exactly by any classical theory

That's exactly the point of my paper that gravitation *can* be described by classical Newtonian theory. One can do fine without curved space-time or spin-2 "interaction carriers".

Eugene.

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