R. P. Singh: A Constructive Model of Gravitation

Posted: May 2, 2012 by Rog Tallbloke in Astronomy, Astrophysics, Energy, Gravity, methodology, solar system dynamics

UPDATE: Raghu has now reworked his theoretical model, now under discussion here.

My Thanks to Raghu Singh for presenting this paper to the Talkshop. We have been in touch for a while now, and I have had some behind the scenes appraisal going on with a quantum physicist, who has now sent a copy to a personal friend who works with the LHC team at CERN. This is a serious and demanding paper, and I would ask interested parties to download and read the pdf document, since formatting all the equations is too difficult for wordpress’ limited capabilities, and so THE MATHS AND RELATED COMMENTARY IS NOT SHOWN IN THIS POST.

A Constructive Model of Gravitation

Raghubansh P. Singh
1534 Malvern Hill Place; Herndon, VA 20170; USA

Abstract for the conference
May 1, 2012
This paper proposes a physical model in which gravitational interaction between masses is mediated by their mass-momentum fields. A mass in the mass-momentum field of another mass experiences two types of gravitational forces: repulsion due to separation; and attraction due to motions but under specific conditions.

The model addresses: gravitational interaction between matter and matter and between matter and energy; gravity’s effect on spectral lines, clock time periods, and the length of an object; and gravitational radiation from an accelerating mass. It explains Mercury’s orbital precession rate. It estimates the speed of gravitational radiation; revisits inertia and pseudogravity; and makes new predictions. It compares the predictions of the model with those of general relativity.

It rediscovers that gravity bends a light ray, increases the wavelength of emitted light, dilates the time period of an atomic clock, and elongates a material rod. An experiment similar to the Pound-Rebka’s is suggested to test the lengthening of rods. The model rediscovers that at a black hole: time run virtually stops; light virtually turns flat in waveform but still propagates; light passing nearby might go around it and return toward its source; and rod flattens to the point where it disintegrates. It finds that time is physically meaningless in the absence of mass. The model, despite lacking observed values of its three ‘constants,’ agrees on the older predictions well within an order of magnitude.

The model makes new predictions: gravitational interaction is also repulsive; the classical gravitational constant is not constant; an accelerating mass emits gravitational radiation, which in turn accelerates masses at 45 degrees to the direction of propagation; and gravitational radiation propagates at about 18.5% of the speed of light and has four degrees of polarization.

The model introduces for gravity mass-momentum field, which, being of the type almost similar to electric-magnetic field, could help decipher gravity further, possibly as a fundamental interaction.

For the life cycle of the universe, the model does not seem to favor a steady or an expansion-for-ever state.

1. Introduction
Newton (c. 1686) discovers the law that gravitational attraction between two bodies is proportional directly to the product of their masses and inversely to the square of their separation distance.
Einstein1 (c. 1915) publishes the general theory of relativity, according to which gravitation is due to the curvature which matter creates in the field of space-time geometry. The field of space-time geometry is the gravitational field. Astronomic collisions and interactions among celestial bodies notwithstanding, so far there is no evidence of gravitons or waves in the field of space-time geometry. Why and how matter warps space and time are left unexplained!

Milne 2 (c. 1935) holds that “geometry can be selected primarily by the nature of underlying phenomenon and the convenience of representing and analyzing that phenomenon; and transformations of coordinates alone are but translations of language and have not necessarily much to do with phenomena.” Coordinate systems are not a part of the laws of nature.
A few recent theories 3, 4 (c. 1994 – 2012) explain the initial predictions of general relativity in flat space-time geometry.

The strong, the weak, and electromagnetic interactions are mediated respectively by the strong, the weak, and electromagnetic fields associated respectively with the color, the weak, and electrical charges of matter and antimatter. These ‘charges’ and associated ‘currents’ (that is, charges in motion) are respectively static and dynamic properties of matter and antimatter. The strong and the weak interactions are mediated at only microscopic levels; electromagnetic interactions occur at both microscopic and macroscopic levels; and gravitational interactions are known to be effective at only macroscopic levels. (At microscopic levels, fields are quantized; at macroscopic levels, fields are continuous with values at each space-time point.)

The model will be developed in three parts:
- In this first, classical part, gravitational interaction between entities will be similarly reformulated in terms of their pertinent properties and associated fields at the macroscopic level without coordinate systems and observers. Special relativity will be postponed. Quantum theory will be invoked elementarily.
- In the second, still classical part, Lorentz covariant gravitational interaction and field equations will be formulated.
- In the third part, quantum gravitational field theory will be formulated.
For quick referencing, the salient symbols and representative concepts are listed in an Appendix.

2. Assumptions:
We begin the model with two assumptions:

(a) Matter has an envelope of intrinsic mass field.

(b) Motion creates an envelope of momentum field.

Mass is a static property of matter. The range of mass field is infinity. (The origins of matter and mass are not important at the macroscopic level.)
Momentum is a dynamic property of mass-in-motion. Momentum field is effective within a momentum field range, which is proportional to the momentum.


13.3 Centrifugal force
A force normal to a body’s uniform velocity keeps the body in a circular orbit; that force is called centripetal force.
A satellite around the earth is under the centripetal force of the earth’s gravity. The centripetal force is being ‘used up’ in keeping the satellite in orbit; a body in it gets no reaction force and feels weightlessness.
A body on a merry-go-round must have three reaction ‘agents’ to keep it in balance: a seat to push it up against the downward gravity; a backrest to accelerate it to the needed uniform tangential velocity; and a side rest to push it toward the center providing centripetal force to keep it along the circle. When the centripetal force is turned off, the body moves along the tangent with the current velocity.
It is convenient but not necessary to invent pseudogravity (centrifugal force) to cancel the centripetal force in order to avoid radial motion. Centripetal force is real; centrifugal force is fictitious.

16. Critique
We address the primary criticisms of the model. With all due respect to General Relativity and its rich mathematical structure, this model is simply meant to add to the literature, to the need for more theories and experimentation to help decipher gravity further as a force (fundamental or other), and to use it even beyond the solar system.

1. The model contradicts special relativity.
This new model begins in classical physics, as any brand new theory should. The model not being Lorentz covariant implies approximation. Inclusion of special relativity will enrich the model and improve accuracy with experiments but will turn the equations unnecessarily mathematically complex in this first part at the cost of physical insight. Moreover, as the present-day u/c = 0.4, special relativity may be postponed for now. Special relativity will be considered in later parts.
[We note that covariance with respect to transformations in (x, y, z, ibt) coordinate systems may have to be explored.]

2. The model contradicts general relativity.
The model makes no predictions directionally contradictory to general relativity. Besides, the issue is moot, because the model and general relativity are mutually independent.
A new theory should not be judged by an older theory. A new theory is initially judged by whether: it is internally, physically consistent; it re-discovers older predictions; and it discovers at least one new prediction. The model meets these criteria. Only observations and experiments may falsify a theory. A theory confirmed yesterday could be falsified tomorrow.
[Physics must wait for the experimental evidences on the structure, speed, polarization, and quantum of gravitational radiation to reveal as to which theory (this model, general relativity, hidden dimensions, supersymmetry, or other) nature has been hiding.]

3. The theory does not predict Mercury’s orbital precession rate.
This just appears to be the case. This classical model simply repeats the classical steps of Price and Rush 9 and arrives at the 572 arc-secs/century orbital precession rate. The rest 43 arc-secs/century rate can be obtained by special-relativistic correction to the classical part in flat space-time geometry. 4 (There are additional, albeit infinitesimal, hard-to-detect contributions to the precession rate.)

4. The primordial point violates the principle: “Absolute position and absolute time are never essential initial conditions.”
The universe is said to have begun as a Big Bang at a physical space-point, where the universe’s internal time began as well. The model names that point Primordial Point. The Primordial Point is the sole space-time reference point in the universe. (It is not clear as to whether the universe itself is in motion relative to an external point.) The said principle holds within the universe as a closed system, whose total internal energy, momentum, and angular momentum remain conserved.

5. There are too many adjustable parameters!
The model has only three constants: b, σ, and Gd . The first two are Nature’s (non-adjustable) constants. All other parameters and ‘constants’ are derivable from b, σ, and Gd .



1. A. Einstein, The Meaning of Relativity, Princeton, 1955.

2. E. A. Milne, Relativity Gravitation and World-Structure, Oxford, 1935.

3. T. Biswas, Special Relativistic Newtonian Gravity, Foundations of Physics, v24n4, 1994.

4. D. Barwacz, Orbital Precession without GR [General Relativity], General Science Journal, 2012.

5. E. Freundlich, H. v. Klüber, and A. v. Brunn; Zs. f. Astrophys., 3, 171, 1931.

6. A. Isaacs, Oxford Dictionary of Physics, Oxford, 2003.

7. C. L. Poor, The deflection of light as observed at Total Solar Eclipses, JOSA, v20n4, 1930.

8. R. Adler, M. Bazin and M. Schiffer, Introduction to General Relativity (129, 193), McGraw-Hill, Inc., 1965.

9. M. P. Price and W. F. Rush, Nonrelativistic contribution to Mercury’s perihelion precession, Am. J. Phys., v47n6, 1979.

10. R. V. Pound and G. A. Rebka, Jr., Apparent Weight of Photons, Phys. Rev. Letts., 4 (337), 1960.

11. M. S. Longair, High Energy Astrophysics, Cambridge, 1981.

12. R. P. Singh, Inertia, General Science Journal, 2011.

13. P. G. Bergmann, The Riddle of Gravitation (136), Dover Publications, 1992.

© Raghubansh P. Singh; April 24, 2012.


  1. Brian H says:

    Does the theory cope with the necessity, in doing “orbital mechanics”, of attributing gravitational interactions between moving bodies to the real (non-transmission-displaced) positions and motions, not to the lagged ones?

  2. Roger Longstaff says:

    Does the model explain the “Pioneer effect”? Also, does it explain the anomalous rotation of the galaxies?

  3. Roger Clague says:

    ” An accelerating mass emits gravitational radiation”.

    This seems to be similar to the LeSage’s push theory of gravity. Gravity is the result of masses being in the radiation shadow of each other.

  4. Wayne Job says:

    The fundamentals of physics have failed to tell us what many things are, such as what matter is, tho we use many of its manifestations such as magnetism and electricity as the basis of our modern society. Trying to explain the intricacies of gravity without the basic knowledge of the other forces is only a mind game.

    After the failure at Cern to find the god particle physics needs to go back to square one and start again. 1880 to 1920 was the turning point and the fork in the road confused many and a consensus settled for a century, and, but for practical engineers this period would have been a dark age for science.

    Gravity whether it be an attractive force or a shade effect of repulsion will be self explanitory when science comes to terms with matter and its manifestations. I await with bated breathe.

  5. Roger Longstaff says:

    “After the failure at Cern to find the god particle physics needs to go back to square one and start again”

    Wayne – is this now agreed? Cern seems to have gone very quiet, both about this and the incredible stuff about superluminal neutrinos.

    All of this stuff about dark matter and dark energy always seemed like a “cop out” to me. Intuition leads me toward some type of modification to the laws of gravity (based upon MOND?). But it must explain the rotation of galaxies and the Pioneer effect (if it is real – I would love to see an experiment to confirm it).

  6. tchannon says:

    Nothing later than the following has appeared in the feed here

    “However, a definitive statement on the existence or non-existence of the Higgs will require more data, and is not likely until later in 2012″ — http://www.interactions.org/cms/?pid=1031301

    “Update: Higgs search papers submitted for publication”


  7. tallbloke says:

    “But it must explain the rotation of galaxies”

    Not necessarily. Let’s not forget Anthony Perratt’s simulation using plasma cosmology principles which successfully evolved a spiral arm galaxy. E/M forces are substantially stronger than gravitational forces in principle.

  8. Roger Longstaff says:

    Thanks TB – I was unaware of that. It sounds more believable, as no new physics is required.

  9. Gerry says:

    Regarding Mercury’s advance of perihelion, in
    the late Tom Van Flandern wrote the following discerning paragraph:

    “While relativists have always been partial to the curved space-time explanation of gravity, it is not an essential feature of GR. Eddington (1920, p. 109) was already aware of the mostly equivalent �refracting medium� explanation for GR features, which retains Euclidean space and time in the same mathematical formalism. In essence, the bending of light, gravitational redshift, Mercury perihelion advance, and radar time delay can all be consequences of electromagnetic wave motion through an underlying refracting medium that is made denser in proportion to the nearness of a source of gravity. (Van Flandern, 1993, pp. 62-67 and Van Flandern, 1994) And it is now known that even ordinary matter has certain electromagnetic-wave-like characteristics. The principal objection to this conceptually simpler refraction interpretation of GR is that a faster-than-light propagation speed for gravity itself is required. In the context of this paper, that cannot be considered as a fatal objection.”

    I might add that gravitons with zero rest mass would not be constrained to subluminal velocities in a flat space-time universe.

    G. E. Pease

  10. Martin Cohen says:

    Time Magazine carried this piece on Dec 14, 1936
    H/T Joe Olson.

    Shift on Shift

    The brilliant, whimsical popularizing of Sir Arthur Stanley Eddington has made ”the expanding Universe” almost a household word. But the telescopic observations of a universe which seems to be blowing up like the fragments of an explosive shell have come mainly from Mount Wilson Observatory’s brilliant Astronomer Edwin Powell Hubble. Beginning in 1928, Hubble and his coworker, Milton LaSalle Humason, showed that the light from the most distant nebulae (clouds of stars) which he could photograph in Mount Wilson’s giant telescope was shifted far toward the red end of the spectrum. Such a redshift is observed in the light of a star known to be retreating from Earth, so it was assumed that the distant nebulae were retreating in all directions. On these observations, and on the theoretical expanding universes formulated by de Sitter and Lemaitre before any observations were made, the case for the expanding universe rested.

    Sir Arthur has never lost his enthusiasm for this cosmic soap bubble. But the speeds indicated by the amount of redshift, some of which now equal 25,000 miles per second, have made many astronomers doubt. Other causes for the redshift were suggested, such as cosmic dust or a change in the nature of light over great stretches of space. Two years ago Dr. Hubble admitted that the expanding universe might be an illusion, but implied that this was a cautious and colorless view. Last week it was apparent that he had shifted his position even further away from a literal interpretation of the redshift, that he now regards the expanding universe as more improbable than a non-expanding one.

    To the National Academy of Sciences Dr. Hubble communicated the results of his most recent survey of the distant nebulae. The distribution of these bodies in space forced him to conclude that a non-expanding universe theory “is more economical and less vulnerable.” If the red-shifts do not really indicate velocity, he wrote, one has a “rather simple and thoroughly consistent picture of a universe in which . . . the large-scale distribution of nebulae is uniform throughout the sample available for inspection.” On the other hand, to assume that the shifts really indicate receding velocity forces one to adopt a very curious model of the universe. “The model is closed and very small—a large fraction can be observed with existing telescopes—and is packed with matter to the very threshold of perception—. The rate of expansion has been slowing down so that the past time scale is remarkably limited. In short, the necessary adjustments and compensations suggest that the model may be a forced interpretation of the data.” In plainer language, this meant that Astronomer Hubble is now willing to abandon the expanding universe to mathematical cosmologists and philosophers, pending a further development of theory, or the erection in 1940 of Caltech’s 200-inch super telescope, which may finally settle the question.

    [Quote ends] —docmartin

  11. Thank you for your comments. I read the comments and admit I don’t have all the answers. This paper is the first in a three part series. I will prepare responses and post them here.

  12. Michael Hart says:

    It’s a bit ironic that the BBC has just now reported that the LISA gravitational waves detection project failed to get funded:

    Seems like a shame. I’d be interested to know what people here think about it.

  13. Roger Longstaff says:

    I knew people involved in LISA, and had a very minor part in it at one stage. I am very sad that it has been cancelled. It was a groundbreaking effort to detect gravity waves in space, as all terrestrial attempts have so far failed.

  14. It is unfortunate that the funding of gravitational wave detection has been set aside. There have been and there will be theories explaining various galactic, solar, and planetary motions, but only the structure, speed, and polarization of gravitational waves will help us decipher gravity. I hope as economy comes back, the funding is restored.

  15. The constructive model is basically a modified Newtonian model, except that the classical gravitational constant is not constant across universal space and time. There are a few “classical” theories (independent of general relativity) which explain anomalous rotations of galaxies, the MOND, the Pioneer effect, and the initial three predictions of general relativity. These theories have not been published. I will have to get authors’ permissions to cite them here. When they permit, I will cite them here.
    Some physicists are trying to demonstrate that general relativity is not necessary. These theories, if correct, might simplify gravity.

  16. Roger Longstaff says:

    Mr. Singh, I look forward to anything that you might add. I do not think that GR needs to be disproved, but rather that it is not the final word, and needs refinement.

    BTW – my miniscule contribution to LISA was to (hopefully) persuade ESA to try to measure the gravitational constant in space, and to try to determine whether it is a scalar, a scalar field, a tensor …….. When I left it a few years ago they reckoned they could take meaningful measurements with the LISA Pathfinder spacecraft – but I assume that is now cancelled as well.

  17. Dr. Longstaff, I never meant to imply that GR needs to be disproved. Just that is GR necessary to explain gravity. It never hurts to look for other models. There are several reasons for doing so in the case of gravity, as you well know.
    The constructive model cites a few references which show that a flat space-time geometry can be as useful in rediscovering the three initial predictions of GR. On the other hand, the space-time curvature by the sun could be flat enough.
    The controversy over G would not be easy to resolve. As I said before, I believe that a clear physics of gravitational radiation will go a long way in pointing us in the correct direction. I hope LISA would come back.
    May I ask you to look at the Predictions, Remarks, and Critique sections of the paper one more time?
    (I am still waiting for the authors’ permissions..)

  18. wayne says:

    One of the most interesting aspects of any gravitation theory is how they are going to treat an absolute frame of reference. Many think everything is relative but that doesn’t seem to be so and it’s core is in the Mach principle.

    I you spin about your arms want to rise. The rotation imparts a force. Now imagine yourself in a spacesuit in void space, so void you are prevented from seeing stars, how do you ever know if you are spinning on some axis and could you possibly invent an instrument to measure whether you are rotating or not and relative to what?

    I can envision such an instrument and by its very existence it tends to prove that there is an absolute frame of reference, not an absolute zero point but an absolute still non-rotating frame.

    Anyone have thoughts on that and whether this new theory handles it sufficiently with it’s mass and momentum fields?

    I also noticed multiple references to “the rotation of galaxies”, ie. dark matter, I do have a possible explanation that I have not told anyone, but on e close friend, and it is that science has ignored gravity’s influence on virtual particles in their fleeting existence at every point in space and this causes an anomalous stress-energy-mass to any gravity well. Around 1×10^-35 g/cm3 I figure. Gravity is a one direction field and if virtual particles do in fact exist, ruled by Heisenberg uncertainty principle, their acceleration due to gravity centers cannot be ignored. You heard it here on Tallbloke’s TalkShop. ;-)

  19. Roger Longstaff says:

    Dr. Singh, Thank you for your reply – I take your point about GR. I will read your paper again and await further ones with interest! (BTW, I am not a “Dr”, just an amateur).

    Wayne, I had vauguely wondered about a “virtual gravitational field”, but more or less discounted it as it would require a stronger field strength inside galaxies than outside, otherwise it would have no net effect on matter. Could the presence of matter amplify such a field? Also, does it not imply an absolute frame of reference, with all of the problems that that could bring?

    It is good to see people “thinking outside of the box”.

  20. Roger Longstaff says:

    Sorry Wayne, I should have thought more carefully about what you said – I take your point about Mach’s Principle.

    Does your “anomalous stress-energy-mass effect inside a gravity well” hypothesis relate to the known principle of burning propellant as deep as possible in a gravity well during a planetary fly-by? Or have I completely misunderstood?

  21. wayne says:

    Roger Longstaff, I’ve held that thought for a number of years up in my head and it wasn’t until I sat through a six hour lecture on dark matter and dark energy from CERN the I brought back up that old suspicion and really started to give it some serious thought. I spent some time way back on the Pioneer anomaly and each of these just reinforced my curiosity further. First, I’m not sure if it is even possible but I’m getting older and I knew if I never opened my mouth on the subject it just might leave with me, unsaid and unknown forever. So don’t take me lightly please.

    It first hinges on the actual existence of virtual particles, the seething fleeting moments of particle pairs jumping into and out of reality, the time of existence ruled by the uncertainty principle or that is what I have read. The lighter particles can exist longer that heavier particle pairs before they rejoin and disappear. They exist on borrowed energy from the void of space itself. But during their fleeting ‘existence’ would they not both, the real matter and anti matter particles of the pair be accelerated a very, very tiny amount toward any gravity center, depending on how close they are as any matter. I’m thinking big scale here, mainly galaxies but something as tiny as the ~8e-08 cm/s2 sensed by the Pioneer pair might possibly be related. It seems the effect would be linear.

    Seems to me that would continuously move these infinitesimal packets of internal energy toward the center creating a certain sense of ‘pressure’ inward. Don’t know. It would take some very good minds on physics to answer the question for even I know a lot in the area of astrophysics I am no expert by any means. It’s a call out to see if anyone so qualified might read this and give it a moments thought.

    As to rocket propellant, well, yes that is way off the topic. That just maximizes the fuel use and has nothing to do with what I was writing as far as I can see.

  22. wayne says:

    “Also, does it not imply an absolute frame of reference, with all of the problems that that could bring?”

    Don’t think so. It’s real to Dr. Feynman too and that is good enought for me, for i see the same thing. Think deep on that. If the entire universe were also rotating would we when rotating with it feel zero acceleration then? That thought is what brings in the other questions. It’s a great thought to think of, don’t you agree? Isn’t that action at a distance that phyics left behind a long time ago? Just threw that out for some to think about while we were on the subject of gravity theories for it does have to be covered by any theory.

  23. Roger Longstaff says:

    Wayne, Many thanks for your reply. Please understand that I do NOT take you lightly!

    You say “It first hinges on the actual existence of virtual particles, the seething fleeting moments of particle pairs jumping into and out of reality, the time of existence ruled by the uncertainty principle”. Does not the Casimir effect lead you to belive that this is correct? It does it for me.

    Also, Mach’s Principle is impossible to ignore.

    It seems you were not referring to momentum exchange within a gravitational well, as I originally thought. If I now understand it correctly, you see a galactic gravitational field distorting the otherwise uniform vaccum field that exists in “empty space”, thus producing an addittional attractive force, such as can be observed in ionic matter, from the virtual particles while they are in existence (and possibly prolonging their existence, beyond the Heisenberg limit)?

    The above may be pure nonsense, and nothing at all to do with what you are proposing. However, I think that we are much the same – still searching for one more clue after many, many years of questions….

    Best regards, Roger

  24. wayne says:

    Roger, your reading that very correct it seems and I have experienced the Casimir in a plant on a perfectly flat machined surfaces, I just put that in for I’m not sure if, other than the Casimir effect, it is now well accepted fact. And you used the word i couldn’t seem to find as I wrote above, vacuum energy field, that’s it. Basically could that be it? The matter not visible, undetable, but in a sense real though hugely diffuse. I’ve never heard that raised or I wouldn’t have said it here, but it keeps stuck in my head and raised ever time I hear someone say ‘dark matter’ or ‘galaxy rotation’.

  25. wayne says:

    This is one complicated theory, on first sight it looks too complicated to seem natural, not saying it isn’t, just a feeling. I guess I have just read too many thousand papers like this one that you cannot spend enough time with just mostly verbal description of it’s confirmation calculations to judge anything about the content in detail. Sound interesting, but they always do.

    But hinged on the big-bang “primordial point”? Now there’s a real absolute frame of reference.

  26. tallbloke says:

    Would it be better if we treated the centre of the galaxy as a ‘primordial point’ and didn’t concern ourselves too greatly about a ‘big bang’ ‘primordial point’? After all, given the various conflicting evidences regarding cosmological distances, we can’t get too categorical about intergalactic gravitation, can we?

  27. wayne says:

    TB, could be. I tried carefully not to pass any judgement on this theory not having the math expertise to test it one way or the other, just can’t get the gist of it yet. Why is 45 degrees necessary and correct. Why the 18.5% s.o.l. propogation, is it a scaling? Since I have never seen anyone layout the solution to Mercury’s 43 arc-second correction I’m alsways left just reading words with no math substance. And I would like to know if this theory decomposes back to the Newtonian form as an approximation, I have seen that performed on general relativity though that the math in doing so went just a bit over my head.

  28. Roger Longstaff says:

    Wayne – could we imply a “London Force” between virtual pairs, if they exist within the same Plank time? See:


    If we then assume that the matter within galaxies affects the rate of virtual pair production, in comparison with “empty” space, can this lead to a MOND effect?

    Through a glass, darkly…………..

  29. So many questions! Thanks. Answers might improve the model.

    1. The Pioneer effect. My former GR classmate thinks it could be due to an infinitesimal change in the classical gravitational constant. Perturbations do keep us busy. The model predicts that G is not constant. Dirac said that many years ago as well. Variable G will perturb.

    2. Mercury’s orbital precession. Please see Ref. 9 for 572 arc-secs/cent and Ref. 4 for the rest anomalous 43 arc-secs/cent. This precession is now clearly explained in flat space-time geometry. Please also see Ref. 4.

    3. Other GR’s initial predictions are explained in the model.

    4. Mathematics. All mathematics are basic in the model. Of course, you will agree that the mathematics in the model is way simple compared to GR’s tensors. It took me one week to go through Schwarzschild’s algebra when I was a student.

    5. In physics, we handle equations of motion by isolating the main source and innumerable smaller perturbative sources. It is not easy to account for all perturbative sources; even if do, it is difficult to solve many of them. Theoretically addressing normal and anomalous rotations of galaxies are quite difficult. We can’t figure out all the motions of our sun.

    6. Absolute position and time. There is not enough room here to discuss it. But I urge you all to look at Eugene Wigner, Symmetries and Reflections. The essays in there made me a humble physicist.

    7. We can devise all the equations to explain motions. But the one thing that Nature has will show us the light at the end of tunnel. That is emitted radiation. We know so much about em radiation. We know nothing about gravitational radiation; we can’t even find it. The main purpose of the model is to present another take on gravitational radiation. Unless we explain observed gravitational radiation, we will never decipher gravity as a fundamental force. Two of my former classmates think that no gravitational radiation exists. GR has quadrupole-moment gravitational radiation. This model has this radiation as described in there. The 45 degree emission and 4 degrees polarization come out from the theory. Only experiments can falsify it.

    8. I ask you all to look at the theory and tell me whether: it is physically logical; it is self-consistent; it has adequately explained older GR predictions; and its new predictions are sensible. Please remember this first part is classical.

    9. I urge you all to look at the Predictions, Remarks, and Critique sections one more time.

  30. wayne says:

    Roger, London dispersion force was new to me, I haven’t tried to keep up for the last few years. Since it is an effect between already existing matter seems that would already in the field we experience here on Earth (the GMs). Five years ago there were multiple MOND theories and now I’m sure there are just more so maybe this effect is just what they were looking for to explain the modifications in the theory. But who knows, maybe. I’m leaving it wide open.

  31. Response to Mr Tallbloke’s comments of May 4th:

    Yes, a reference frame with origin at the center of the Milky Way would not alter the model’s local predictions at all. I favored the Big-Bang point for inter-galactic gravity in case future physicists may want to take a look at it. But I don’t trust much data and theories on inter-galactic forces. I have a physicist friend who derived MOND force (for the fringes of galaxies) using just special relativity and without dark matter!

    What I am implying here and in my previous responses is that more than one theory can explain several gravitational phenomena, but one and only theory can explain gravitational radiation’s structure, speed, polarization, and quantum. The radiation, be it electromagnetic or gravitational, is the litmus test for any theory — pass it and be part of the history or fail it and be a footnote. We are greatly indebted to Faraday and Maxwell. We don’t have any satisfactory experimental data on gravitational radiation.

    Superstrings, hidden dimensions, supersymmentry, and quantum gravity have not addressed gravitational radiation. We have so far two models: GR and this constructive model. Since I don’t have a phone line to Faraday or Maxwell or God, only experiments and observations have to tell us which one or neither is correct.

    Please keep sending me comments. They are helping me.


  32. frankdejongnl says:

    Mr. Singh, a very interesting article. Could you explain how you come from Eq. 4 to Eq. 6? I filled in the vector identity Ax(BxC) = (A.C)B – (A.B)C for Eq. 4, and ended up with Eq. 6 for the first term (p1 // p2 => p1.p2 = p1 p2), but the second term, (p1.r) p2, seems to introduce a force component that changes in magnitude. It is zero when r is perpendicular to u1~u2~u, but actually equal, but opposite in sign to the first term if r // u.

    I’m sorry if I wasted anyone’s time with faulty geometry.

  33. Mr. de Jongnl, you are right! We get those terms and more. But as the masses are too far away from the Primordial Point, vectors u1 and u2 are parallel. Thus Eq. (6) from (4). The para above Eq. (6) explains it. Do you think we can improve that para?
    Other left out terms may explain some other effects. But these days I am working on the gravitational fields equations.

  34. frankdejongnl says:

    Mr. Singh, I redid my math again, rewriting p1 = m1 (u+du) and p2 = m2 (u-du), with du a small difference with respect to the bisector u of u1 and u2 through O. I get for the force between moving masses:

    k4/r^3 m1 m2 [ (u.u + du.u - u.du - du.du) r - ( u.r + du.r )( u - du ) ].

    My problem is the following: if r is parallel to u, the term within brackets reduces to:

    [ -(du.du) r + ( |u| |r| ) du - ( du.r ) u + ( du.r ) du ].

    Note how the only term in the direction r (between the masses) is vanishingly small. In effect, there is no attractive force between the masses.

    Another way of looking at it is seeing that if p1, p2 and r are exactly parallel, the product of p1 x r x p2 must be zero by the properties of the vector product; in other words, there is no attractive force in the direction towards O?

  35. Mr. de Jognl,

    Please look at Fig.1. As masses m1 and m2 get farther away from O, angle alpha (a) gets smaller. Thus velocities u1 and u2 get more parallel and vector r is almost normal to both u1 and u2. Under these special conditions, you can use either math or physics, and get Eq. (6) or (7). I did not use math unless I have to, but you will get the same result though by expanding the triple vector product. I can see the attraction clearly as a physicist.

    I wish I can paste the diagrams here; they would have shown you how a physicist visualizes things. :
    Draw two parallel vectors u1 and u2. Place m1 and m2 on u1 and u2 respectively. Draw a vector r normal to both u1 to u2 from m1 to m2. Vector r x vector u2 is a vector R (say) out of the paper. Vector R x vector u1 gives you a vector F12 from u1 to u2 on the paper.

    Please read the para above Eq. (6) again. This is true in any sector for r < S12.

  36. Frank de Jong says:

    Dear Mr. Singh,

    I’m sorry for not making my point clear. You appear to assume that r is always perpendicular to u1 and u2, but I think that this is only true if the masses are traveling “side-by-side” away from O. What if the masses are traveling not only in parallel directions (u1 || u2), but also on the same line through m1, m2 and O? Then r || u1 || u2, alpha = 0, and r x u[1,2] = 0.

    In other words, you seem to assume that all masses are on a infinitesimally thin spherical shell surrounding O and moving outward, but that’s far from realistic, isn’t it? Maybe in higher-dimensional spaces involving time this is true…

    Best regards and thanks for your patience,


  37. Dear Mr. de Jong, I will try again.

    Take a circle at the Primordial Point O. Divide it into four quadrants. This is easily extended to a sphere at O. Consider the masses in a given quadrant. They are far away from O. So, some masses are almost parallel (angle alpha acute), some very parallel, some are on the same line. Some on the boundaries have velocities normal; however, such masses are almost parallel, very parallel, or on the same line with respect to the masses in the adjacent quadrant. Attraction is optimal between very parallel ones, less so among nearly parallel ones. Those which are on the same line do not attract, but they attract their side neighbors. In summary, masses in a region of space are attracting to some extent. (Masses in opposite quadrants repel.)

    Cosmological observations suggest that gravity is not uniform in form and strength throughout the Milky Way. MOND at the fringes of the galaxy is an example. There are so many things we do not know. Most of our observations are in the solar system and maybe a little beyond.. We cannot say if Newton’s or Einstein’s gravity is exactly applicable in each galaxy and between galaxies (such as Milky Way and Andromeda). The model says something like that about the uniformity of gravity.
    We humans have to assume something reasonable so as to make sciences possible and useful to help us survive and evolve. We need something workable and cannot wait for the perfect picture and solution. “Perfect is the enemy of good enough.”

    I recommend Nobel Laureate Physicist Eugene Wigner’s Symmetries and Reflections. Good luck.

  38. Wayne Job says:

    Wayne and Roger Longstaff. it is not necessary to invoke imaginary particles coming in and out of existance to try and explain gravity. It has been known for probably one hundred years that electrons appear fully formed and stable in a vacuum tube with no input.

    These little buggers are coming into being and infesting the entire universe, they also tend to have an affinity and get together to make quarks, these little mongrels also like to dance and join hands to make neutrons. Hard to fathom really but these bloody neutrons are like magnets for electrons that just keep appearing. Suddenly we have clouds of hydrogen, I wonder what happens next.

    I am unsure wether these hydrogen molecules are pushed or sucked together but they tend to form clouds and then clumps, these clumps tend to be rather large and hot. They then manufacture all of the stuff that we hold dear.

    Dark matter and dark energy are an invention to make the standard model work, it is also unnecessary to invoke imaginary particles when real ones do the work. The electron once in existance is self sustaining and reinforced by the force that created it. Everything below an electron in physics is created by smashing energy particles into energy particles and reading the entrails. All the spin and charm in the world does not make the findings anything more than debris that exists only for a fleeting moment.

    Most of the energy in the universe is in the vacuum, that is why the standard model does not work, maybe this mysterious force called gravity is hidden also in the vacuum, and it may be a push and not a suck.

  39. I am having a problem understanding this comment from Wayne and Roger. Is it related to my model on gravity? Are you sure? If so, which imaginary particle I suggested. I have not even quantized the mass-momentum field yet, assuming that the field is quantizable.
    The most elementary of all particles are the quarks and leptons. The electron is a lepton. The standard model [of elementary particles] is to a more than great extent a remarkable success for the human mind.
    I consider vacuum as invisible energy, not arithmetical zero.

  40. Roger Longstaff says:

    Wayne Job,

    I have not been here for a few days, but, re. your comment – If the Casimir effect is real (which experiments suggest it is) – is not the question “how does this affect the standard model of gravitation (eg. Newton, modified by SR and GR), if at all?”

    With respect to electrons appearing in vacuum tubes – are these not the “electron cloud” that exists at the surface of the cathode? Surely, if they appear elsewhere it must be as part of an electron/positron pair?

  41. Casimir effect has nothing to do with gravity. I do not understand why this effect is in play in this context.
    We do not have gravity or gravitons, if they exist, included in the standard model of elementary particles — yet. Gravity is still the odd man out.

  42. wayne says:

    Thanks Roger Longstaff and Wayne Job for the comments. Wayne, that’s a very interesting example in vacuum tubes. Are you speaking how vacuum tubes end up, over time, with hydrogen found within? There’s another example, along with Casimir, shows their reality even though you can’t detect anything unless enough local energy pulls the pairs into reality. But then they are actually real and can be detected where they are saying “dark matter”, so far, has yet to be detected in any manner but the anomalous gravitational attraction at large scales.

    I’m keeping a leery eye on dark matter, don’t totally buy it yet, but if it is somehow proven that it does exist then that might be one possible explanation. I found it hard to get that thought out of my mind.

    That example of Casimir was not being tied directly to gravity, just one proof of virtual particles. Do you see a gravitational field affecting them during their brief moment of “existence”? Or are they shielded somehow?

  43. Frank de Jong says:

    Dear Mr. Singh,

    You said:

    Those which are on the same line do not attract, but they attract their side neighbors. In summary, masses in a region of space are attracting to some extent.

    Great, so I think we agree on that point.

    Now, I don’t have a problem assuming that gravity can be variable across the vastness of space, but on and near Earth, it does seem to be directionally uniform to a very high degree. How can that be, if two masses (say, earth and a satellite) on the same line through O do not attract, but when their displacement is perpendicular to that line, they do attract? How can it appear that these forces are the same in magnitude?

    If you want to give up explaining, I understand :-).

    Best regards,


  44. To Wayne (May 14):

    I hope they have a name for that virtual particle you mentioned. In any case, any particle, virtual or other, will “interact” with an energy field, such as gravitational field. (I will revise my antiquated knowledge of Casimir effect. It has been so long.)

    I am taking some risk when I say the following:
    I think mass field is dark matter; momentum field is dark energy. A field is not directly observable. I don’t have any proof but I am working on it. Now their new roles are reversed: dark matter repel; dark energy attract.

  45. wayne says:

    “I hope they have a name for that virtual particle you mentioned.”

    Their names? All of them but the length of the time they exist is inverse to their mass as I have read, electron, positron, the neutrinos (electron, nu and tau) and their anti-particles. That is their names, all particles.

    I got interested in nuclear physics in about the tenth grade. A college graduate next door gave me his nuclear physics book and I followed that branch through the ‘80s. Books from the library had great bubble chamber photographs, lots of them, and they just fascinated me. Looking at Feynman pouring over thousands photographs on a light table looking for ‘x’ particle, seemed the dimensions of the photos were about one square meter and I would play games to try to calculate what magnetic field across that chamber would it take to spiral that positron in the manner as in the photo. My friends though I was rather quirked to be interested in such reality. To them it was not really reality, and I never understood why they could not look at the photos and see that, in fact, all of these particles are there and do exist, sometimes for just a fleeting moment. Some pairs would just jump into existence, fly with trailing bubbles, then disappear in a few inches. Those are the particles I am speaking of.

    [Reply] Leptons, protons, and wheretheygons :)

  46. Tenuc says:

    Wayne Job says:
    May 13, 2012 at 1:27 pm
    Wayne and Roger Longstaff. it is not necessary to invoke imaginary particles coming in and out of existance to try and explain gravity. It has been known for probably one hundred years that electrons appear fully formed and stable in a vacuum tube with no input…

    For more information on link between vacuum tubes, photons, electrons, ions and ‘hot’ fusion, do a web search for Philo T Farnsworth. Back in 1965, he had developed the Mark III Farnsworth Fusor which produced 15.5 G-neutrons/sec. at 150 Kv and 70 mA. Also managed 30sec bursts of sustained sustained fusion reaction. His backer, ITT Corp, pulled the plug plug on his work because of external pressure which threatened to destroy the company.

  47. wayne says:

    Just noticed a typo that might lead someone to discard what I just said… try mu, not nu. Fat fingers.

    Tenuc, of course you can create particles from nothing (virtual particles) with the correct equipment and energy input. But then they have become literally real. I was more speaking of just the virtual aspect, there sometimes, but never really there, but gravity has no opposite field. This is just a toy thought but I thought others might like a puzzle in the realm of gravity.

  48. In response to Wayne and Tenuc:

    It seems the conversation has digressed to quantum physics. When, in the third part of my model, I quantize the mass-momentum field, I would know what kind of “graviton” would show up. This virtual graviton would be exchanged between masses to mediate gravitational interaction (repulsion or attraction) but at the microscopic level. At present, we have a graviton of mass zero and spin 2 as Dirac told us many years ago. So, please let us postpone this discussion at the quantum level until I get to the third part.

    Physicists have been looking for gravitational waves for some years. It is surprising that astronomical collisions and interactions among super-massive galaxies can’t send us even a whisper of such waves So, I thought maybe we have been looking at the inappropriate structure of these waves. So I proposed a different model starting with very basic physics. I have arrived at a very different structure. Maybe this structure could be detected or maybe not. Who knows until we do some experiments? There is one and only one model that can explain the real gravitational wave/pulse. Let us find that model. When we turn lucky we will deal with the quantization.


  49. To Mr. de Jong (May 14):

    Yes, I have not been completely successful in explaining the spherical symmetry of gravitational forces.

    A short history. We six of us took GR in early seventies. Two versions of the paper have been reviewed by all of them. They all voted for Version 2. That’s what you have. Version 1 explains the spherical symmetry and many others. Despite, my former classmates thought that Version 2 with 100% analogy with electrodynamics will be more convincing and acceptable. We will figure out unexplained items later.

    Fortunately, in Version 1 only Table-1 has changes in the two cells in the gravity column. The rest of the paper is completely intact. Surprising!

    In due course of time after I have discussed Version 1 again with my former classmates, I will send the correction. So, please read the paper to the end and send me more comments. I am very much interested in finding out what you think of Section 9 (Gravitational Radiation from accelerating mass). Nothing but this section will make or break this model.

    A word on gravitational radiation speed. I do wonder how come gravitational force which is 10**40 times weaker than electromagnetic force can emit gravitational radiation at the speed of light? If you look at waves on taught strings and sound waves in various media, you will see that speed of waves depend on the underlying interactions. (Taughter the string the higher the speed. Sound travels at 350 m/s in air, 1500 m/s in water, and 5000 m/s in steel.)

    Currently I am working on Part 2 of the model, which is Lorentz covariant gravitational field equations. Here it does not matter at all which version I select.


  50. Brian H says:

    Since you can’t calculate orbital interactions without assuming real-time gravity interactions, saying gravity moves light-speed seems pointless and nonsensical.

    P.S. Taught and taut are not the same word. They have nothing to do with each other.

  51. Brian H says:

    typo: “moves at lightspeed”

  52. To Brian H.:

    Thanks for the kind words. I apologize for the spelling blunder: it is “taut” actually. Nonetheless, the question about the relationship of the intensity of emitted radiation to the underlying interaction strength is valid and alive.

    Gravitational radiation. The model says that no gravitational radiation is given off by a mass in a circular orbit. In an elliptical orbit, no gravitational radiation is given off at apogees and perigees but in between whenever a component of momentum is not normal to centripetal acceleration. Here the maximum intensity is not enough for the earthlings to detect the radiation. So I did not include the calculations in the model. But I suggested a test in the Remarks section. I calculate the magnitude of gravitational radiation due to the sun’s primordial speed. This can be tested as instruments get sensitive enough,

    There is only so much a human being can do at one time.