# A relativistic quantum theory of gravity

sweetser
Gold Member
Hello Eugene:

The Lorentz transformations are part of the machinery that characterizes the Lorentz group. That group is not approximate. It is the group that every observation ever made in regards to special relativity is based. If you decide to ditch the Lorentz group, well, you are not going to have friends. Superluminal propagation of interactions does create problems for causality. There are plenty of reasons not to like tachyon theory.

doug

Hello doug,

The Lorentz transformations are part of the machinery that characterizes the Lorentz group.
I respectfully disagree. The Lorentz group and Lorentz transformations are two separate issues, and they are not 100% equivalent

Lorentz group is a 6-parameter group of transformations between inertial observers (it includes rotations and boosts). It is a subgroup of the full 10-parameter Poincare group of inertial transformations, which, in addition, includes space and time translations. The Poincare group is an exact set of relationships. Any physical system, interacting or otherwise, must be invariant with respect to Poincare group transformations. We agree 100% about that. In quantum mechanics, this means that the Hilbert space of any physical system should carry an unitary representation of the (universal covering of the) Poincare group.

Lorentz transformations are certain formulas that connect space-time coordinates of events in different moving reference frames. For example, if observer O sees and event at point x at time t, then, according to Lorentz transformations, observer O' moving relative to O with velocity v sees the same event at the space-time point (x', t'), where

$$x' = (x -vt)(1-v^2/c^2)^{-1/2}$$..........(1)
$$t' = (t - xv/c^2)(1-v^2/c^2)^{-1/2}$$......(2)

I prefer a slightly different notation in which velocity v is replaced by rapidity $\theta$, such that $v = c \tanh \theta$. Then

$$x' = x \cosh \theta - ct \sinh \theta$$.........(1')
$$t' = t \cosh \theta - x/c \sinh \theta$$........(2')

My point is that transformations (1)-(2) or (1')-(2') do not follow immediately from properties of the Lorentz (or Poincare group). Some additional assumptions should be made to make such a derivation, and these are crucial assumptions. For example, one situation in which Lorentz transformations (1)-(2) can be rigorously proven is when particles (whose worldline points and collisions form the events in question) are non-interacting. However, transformations of space-time coordinates of such events become different from simple formulas (1)-(2) if interaction between particles is turned on. I briefly discuss this point in section 5.2 of the paper. A more detailed discussion can be found in section 10.2 of http://www.arxiv.org/physics/0504062 [Broken].

The difference between the concepts of relativistic invariance (the Lorentz and Poincare groups) and manifest covariance (Lorentz transformations) has been known for a long time. I strongly recommend this paper

D. G. Currie, T. F. Jordan, E. C. G. Sudarshan, "Relativistic invariance and
Hamiltonian theories of interacting particles", Rev. Mod. Phys., 35 (1963), 350

where these two concepts are discussed with outmost clarity. In particular, the authors prove an interesting theorem which says that in a relativistic theory of classical particles their worldlines can transform by Lorentz formulas (1)-(2) only if interaction is absent.

That group is not approximate. It is the group that every observation ever made in regards to special relativity is based. If you decide to ditch the Lorentz group, well, you are not going to have friends.
As I said I fully accept the exact and universal character of the Lorentz group. However, I do not accept the exact and universal character of Lorentz transformations for space-time coordinates of events. I don't think there is a contradiction in my position.

Superluminal propagation of interactions does create problems for causality.

The problems with causality arise if one applies Lorentz transformations (1)-(2) (which are strictly valid for non-interacting systems only) to an interacting system. If one properly takes into account the interaction-dependence of boost transformations, then these problems disappear. I briefly discuss this point in section 5.3 of the paper. A more detailed discussion can be found in section 10.2 of http://www.arxiv.org/physics/0504062 [Broken].

There are plenty of reasons not to like tachyon theory.
I don't like tachyon theory as well. However, note that we have discussed the superluminal propagation of interactions, not particles. Interactions can propagate superluminally, particles can't.

Eugene.

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"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."

As I understand the results, they were very close to the desired fit on only one pulsar pair - maybe there are more recent tests.

If your action at a distance theory is correct, there is no justification for gravitational waves. But of course you are already aware of that.

"....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."

It gives very close correlation to the measured values - but It is ad hoc from the standpoiint of a physical explanation.

With regard to the Lorentz tranforms cited by sweetser - I have yet to see an experiment that establishes the truth of those parts of the transforms that are the result of the one way velocity of light - what is proven is the invarience of the interval - but this is easily obtained from Minkowski unification which leads to the result that the two way velocity is constant.

Selleri spend most of his later years reviewing the known experiments dealing with SR time dilations and concluded they could all be easily explained with simple inertial transforms without reference to the xv/c^2 term that arises from the one way constancy postulate. While Lorentz-Einstein transforms may be correct, there needs to be a distinguishing experiment one that invalidates either Selleri or Einstein. I raise this because it bears on the issue of synchronization and consequently causality ...when information travels faster than light, the causalty issue does not occur in Selleri transforms.

"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."

As I understand the results, they were very close to the desired fit on only one pulsar pair - maybe there are more recent tests.
Yes, more binary systems were discovered since then, including those in which both neutron stars are seen as pulsars from Earth. A lot of new data has been accumulated, all of which is consistent with GR. Check this recent reference:

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

If your action at a distance theory is correct, there is no justification for gravitational waves. But of course you are already aware of that.
Yes, gravitational waves are not needed in my approach. However, there is still a puzzle related to the observed orbital decay of binary pulsar systems. This seems to be a real effect, which indicates that energy gets radiated away in some form. There was no direct observation of this radiation, so we don't know what it is. The usual viewpoint is that this is the gravitational radiation. It could be also possible that this is a low-energy electromagnetic radiation. Both these possibilities can be, in principle, accomodated within my approach by adding extra terms to the Hamiltonian. (I discussed this point in post #21.) I would prefer the latter possibility, because I don't like the idea of introducing new particles (gravitons).

"....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."

It gives very close correlation to the measured values - but It is ad hoc from the standpoiint of a physical explanation.
I have a much higher opinion about renomalized QED of Tomonaga-Schwinger-Feynman. I expressed my views in detail in chapters 9 and 12 of http://www.arxiv.org/physics/0504062 [Broken].

Briefly, I think the trouble began already in the original formulation of QED (late 1920's). The Hamiltonian of this theory was derived from vague analogies with Maxwell's electrodynamics, and this Hamiltonian didn't satisfy some very important physical principles (the stability of vacuum and 1-particle states). This Hamiltonian was useless for S-matrix calculations beyond the leading perturbation order, because of infinities.

Tomonaga, Schwinger, and Feynman fixed a part of this problem in the late 1940's. They added infinite counterterms to the original Hamiltonian in such a way that all infinities in the S-matrix canceled out and very precise agreement with experiment could be achieved. However, as you said, they "swept infinities under the rug". This rug was the Hamiltonian. In renormalized QED, the Hamiltonian has infinite terms, so it is useless for anything but S-matrix calculations.

Another improvement of QED is needed in order to obtain both reasonable Hamiltonian and accurate S-matrix. This can be done by using the "dressed particle" approach. This approach has been known for a long time

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

Unfortunately, it didn't get much traction in modern quantum field theories.

Selleri spend most of his later years reviewing the known experiments dealing with SR time dilations and concluded they could all be easily explained with simple inertial transforms without reference to the xv/c^2 term that arises from the one way constancy postulate. While Lorentz-Einstein transforms may be correct, there needs to be a distinguishing experiment one that invalidates either Selleri or Einstein. I raise this because it bears on the issue of synchronization and consequently causality ...when information travels faster than light, the causalty issue does not occur in Selleri transforms.
Unfortunately, it is very difficult to verify Lorentz transformations themselves. Experiments can only probe some of their consequences, such as the time dilation. I haven't heard about Selleri's works. Do you have a reference?

ADDED: Perhaps the most important idea that I had in my works is that there can be no unique and universal formula for boost transformations of particle observables (such as the formula for Lorentz transformations). Boost transformations should depend on the system in which these transformations are measured and on interactions acting in the system. That's why I am sceptical about attempts to find a universal transfrormation.

Thanks.
Eugene.

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Hi Eugene - from your post 23:

"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."

I recalled that you had derived the perihelion motion - so I pulled up your article and re-read that part - you have treated this and found your derivation consistent with the observations - that is a big plus. I guess my only suggestion would be to de-emphasize the action at distance premise since you have alternatives. But you raise a good point in that, while there is slowing of binary systems, - it doesn't mean necessarily that it takes the form of gravitational radiation - for all we know it the energy may be absorbed in some form of dark matter

My own view is consistent with GR in part - in that masses condition space - they do not act directly upon one another. As you probably know, there are several authors including Sciama, that have developed theories to explain inertia in terms of Mach's principle - all such theories require instant action at a distance - so you might want to read some of these if you have not already done so. I will send you a link to one of Selleri's articles. Selleri is not accepted by main stream, nor as you know, is Van Flanderen. Selleri however, has a list of accomplishments a mile long, so he can't be ignored summarily

I recalled that you had derived the perihelion motion - so I pulled up your article and re-read that part - you have treated this and found your derivation consistent with the observations - that is a big plus.

Yes, I used a fairly simple instantaneous potential Sun-Mercury, which consisted of the usual Newtonian part plus small velocity-dependent correction. The important part was to make sure that this potential satisfies the principle of relativistic invariance (commutation relations of the Poincare Lie algebra). Otherwise, it was simply fitted to reproduce the observed shift of the Mercury's perihelion. I want to emphasise that I didn't formulate this interaction from some first principles, and then found that the calculated perihelion precession agrees with measurements. Not at all. That would be a really great accomplishment, and I don't claim that.

What I have done in this paper is, simply, a proof of principle. I wanted to show that one can, in principle, find an instantaneous gravitational potential, which satisfies all requirements that I formulated in the beginning of the paper (relativistic invariance, unitarity, agreement with experiment, etc.). In fact, I believe, that one can write many different potentials that would satisfy all these requirements. Currently, I have no idea what additional fundamental principles are needed, which would select just one true potential.

My primary objective was to break the monopoly of GR on explanation of experimental facts. I wanted to show that there is a much wider class of acceptable theories, which agree with existing observations. It is even more important that some of these theories are perfectly compatible with quantum mechanics, which is not true for GR.

I guess my only suggestion would be to de-emphasize the action at distance premise since you have alternatives.
This is something that I wouldn't like to do, because all interactions in my approach are true action-at-a-distance interactions. As I said earler, I don't exclude the possibility of radiation of free gravitons. But this possibility doesn't change a bit the instantaneous (non-retarded) character of interactions between massive bodies. In other words, gravitons can exist as free particles in my approach, but there is no place for them as "virtual interaction carriers".

But you raise a good point in that, while there is slowing of binary systems, - it doesn't mean necessarily that it takes the form of gravitational radiation - for all we know it the energy may be absorbed in some form of dark matter
I remain agnostic regarding the physical nature of radiation emitted by binary pulsars. My first choice would be the usual electromagnetic radiation. If this is true, then there should be an unexplained bump somewhere in the EM emission spectrum of the binary system, and the integrated radiation power under this bump should match the energy loss calculated from the orbital decay. That's all I can speculate about regarding this possibility. The second choice would be the emission of gravitons, but this choice is less attractive due to the speculative nature of these particles.

My own view is consistent with GR in part - in that masses condition space - they do not act directly upon one another. As you probably know, there are several authors including Sciama, that have developed theories to explain inertia in terms of Mach's principle - all such theories require instant action at a distance - so you might want to read some of these if you have not already done so. I will send you a link to one of Selleri's articles. Selleri is not accepted by main stream, nor as you know, is Van Flanderen. Selleri however, has a list of accomplishments a mile long, so he can't be ignored summarily
I would appreciate your sending me references to Sciama and Selleri.

Thank you.
Eugene.

Eugene - try this link oldserver.ba.infn.it/~selleri/ - 10k

Articles R39 and R27 should be of some interest. If That Link doesn't work, you can google Franco Selleri and get a lot of his papers

Would be interested in your opinion on the inertial transforms -

Yogi

Just checking - looks like that link is incomplete - i will try to get it right

Eugene - try this link http://oldserver.ba.infn.it/~selleri/ [Broken] - 10k

Articles R39 and R27 should be of some interest. If That Link doesn't work, you can google Franco Selleri and get a lot of his papers

Would be interested in your opinion on the inertial transforms -

Yogi
Hi Yogi,

thank you for the link to Selleri's papers. I read the paper R39

F. Selleri, "Recovering the Lorentz Ether", Apeiron 11 (2004), 246

where he proposes "inertial transformations" that are supposed to replace "Lorentz transformations" of special relativity. I have quite a few objections to different statements in this paper. I'll mention just two objections, which look the most obvious to me:

1. His "inertial transformations" imply that the velocity of light should depend on the velocity of the light source. I remember seeing experimental works in which this dependence was investigated directly. If I remember correctly, they measured the velocity of gamma quanta emitted by fast moving particles. In agreement with special relativity, no dependence on the particles' velocity was found. I don't have exact references to these papers. I'll try to find them tomorrow.

2. Selleri is right that it is difficult to measure Lorentz transformations for the time and position of events in direct experiments. However, it is much easier to measure their cousins - Lorentz transformations for the momentum-energy of relativistic particles. These transformations have been observed in numerous particle experiments, and they form a foundation for relativistic particle kinematics established with great precision. I haven't noticed any discussion of "inertial transformations" for momentum-energy in the Selleri's paper. However, I suspect, that his version of such transformations would be also different from the special-relativistic experimentally established version.

Regards.
Eugene.

ADDED: Reading his other paper R27: "Bell's spaceships and special relativity" didn't change my opinion.

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I remember seeing experimental works in which this dependence was investigated directly. If I remember correctly, they measured the velocity of gamma quanta emitted by fast moving particles. In agreement with special relativity, no dependence on the particles' velocity was found. I don't have exact references to these papers. I'll try to find them tomorrow.
Here is the reference:

T. Alvager, F. J. M. Farley, J. Kjellman, I. Wallin, "Test of the second postulate of special relativity in the GeV region", Phys. Lett. 12 (1964), 260.

They directly measured (using the "time of flight" method) the velocity of gamma quanta emitted in decays of relativistic $\pi_0$ particles.

I can also recommend a good website with lots of references to experimental tests of special relativity

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

Eugene.

Hi Yogi,

thank you for the link to Selleri's papers. I read the paper R39

F. Selleri, "Recovering the Lorentz Ether", Apeiron 11 (2004), 246

where he proposes "inertial transformations" that are supposed to replace "Lorentz transformations" of special relativity. I have quite a few objections to different statements in this paper. I'll mention just two objections, which look the most obvious to me:

1. His "inertial transformations" imply that the velocity of light should depend on the velocity of the light source. I remember seeing experimental works in which this dependence was investigated directly. If I remember correctly, they measured the velocity of gamma quanta emitted by fast moving particles. In agreement with special relativity, no dependence on the particles' velocity was found. I don't have exact references to these papers. I'll try to find them tomorrow.

Regards.
Eugene.

ADDED: Reading his other paper R27: "Bell's spaceships and special relativity" didn't change my opinion.
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?

Regards

Yogi

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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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.

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

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?

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.

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 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.

" 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?

" 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 [Broken]. 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.

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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.

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,

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.

Eugene.

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.

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

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.

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).

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... 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.