Newtonian Unified Field Theory?


No Unified Field Theory

Modern physics is supposedly based on Einstein’s general theory of relativity for gravitation, Maxwell’s electromagnetics  and quantum mechanics, but there is no unified field theory including both gravitation and electro/quantum mechanics.

Einstein spent the later half of his life in lonely fruitless search of a unified theory, while the physics community came to accept the perceived incompatibility of general relativity and electro/quantum mechanics as an unsolvable problem, and marched on.

But an incompatible theory is like a body with cancer which slowly takes life away and the lack of a unified field theory has led modern physics into strange directions away from rationality, towards multidimensional string theories and multiverses way beyond any human comprehension.

The position is locked with deep trench lines: gravitation is to be described by general relativity and general relativity is incompatible with electro/quantum mechanics. General relativity is a geometric theory describing gravitational forces as effects of “curved space-time”, but there is no geometric theory for electro/quantum mechanics, which is basically a field theory in Euclidean “flat” space-time.

It is thus natural to ask why gravitation has to be described by a geometric theory of relativity instead of Newton’s theory, and there does not seem to be any good answer, but dogmatics.

Of course a physicist would say that the (anomalous precession of the) perihelion of Mercury can be explained by general relativity but not by Newtonian gravitation and so Newtonian gravity has to be abandoned. But claims of impossibility seek support from inability or ignorance, and may easily be incorrect, as indicated below.  As concerns the urgent problem of dark matter/energy general relativity offers nothing better than Newtonian theory.

Newtonian Field Theory

Let us then scrutinize Newtonian gravitation before we dismiss it,  remembering Einstein’s “Newton, forgive me”, and recalling from the previous post on God’s Equation \rho =\Delta\varphi, that Newton’s theory follows from two basic postulates:

  1. The gravitational force field F (per unit mass) is given as  F=-\nabla\cdot\varphi, where \varphi is a gravitational potential. 
  2. Matter density \rho satisfies \rho = -\nabla\cdot F, and thus \rho =\Delta\varphi (with normalization).

1. is the same as saying that the gravitational energy of a body only depends on its location (e.g. altitude) and not on the path to be brought there, that is that the gravitational force field is conservative.

We take 2. as a definition of gravitational mass density, noting that 2. is the same as saying that the flow of the gravitational force field F into any volume is equal to the amount of gravitational mass in the volume.

Newton’s 2nd Law for gravitational acceleration takes the form:

  • \rho F = \rho\frac{Du}{Dt} that is F = \frac{Du}{Dt},
which expresses that gravitational  acceleration \frac{Du}{Dt} is the same for all bodies, with u material velocity, as an expression of conservation of momentum or balance of kinetic and potential gravitational energy.

Newtonian mechanics now results if we define inertial mass to be equal to gravitational mass, expressing the equivalence principle, and postulate Newton’s 2nd Law for all forces, thus defining force in terms of mass and acceleration. Doing so we  thus refer all forces to gravitational forces and all mass to gravitational mass.

We thus find that Newtonian mechanics including

  • Newton’s theory of gravitation
  • Newton’s 2nd law
  • the equivalence principle,

can be viewed to be “created” from

  1. a given conservative gravitational force F
  2. assuming gravitational acceleration is the same for all bodies.

We thus find that Newtonian mechanics is so general that there is no reason to seek a generalization in the form of Einstein’s general relativity.

Instead of dismissing Newtonian mechanics we are thus led to seek a generalization including dark matter/energy, possibly by allowing \Delta\varphi to take on negative values, as explored in Newtonian Gravitation of Matter and Antimatter.

Altogether, Newtonian mechanics is compatible with electro/quantum mechanics and it is possible that  it may be generalized into a unified field theory combining gravitation with electro/quantum mechanics in some form of selfgravitating MHD.

Generalized Newtonian Field Theory

The mass-potential equation (Poisson’s equation) \rho =\Delta\varphi may be generalized into the wave equation:

  • \rho\equiv \Delta\varphi -\frac{1}{c^2}\frac{\partial^2\varphi}{\partial t^2},

with t Euclidean time and c a finite speed of propagation, corresponding to using a retarded potential, which  reduces to the previous case as c tends to infinity.

The anomalous precession of Mercury can be explained with such a retarded Newtonian gravitational potential as shown in On the Origin of the Anomalous Precession of Mercury’s Perihelion by J Gine,which gives the same Gerber’s potential as obtained by Einstein by general relativity.

Regularization with instead a parabolic equation (heat equation) of the form

  • \rho\equiv \Delta\varphi -\frac{1}{c}\frac{\partial\varphi}{\partial t}

is also thinkable.

Newton’s Absurdity

Newton was well aware of the fact that gravitation by action at distance may not be the right approach:

  • That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.
One way out is to turn the question around and view matter as somehow being created locally from the gravitational potential, rather than the potential being created globally from matter.


Comments RSS
  1. Richard T. Fowler

    “Altogether, Newtonian mechanics [. . .] may be general enough to allow a unified field theory.”

    Of course! That’s part of what I’ve been trying to say the last few days.

    But Claes, why won’t you even consider what I’ve written?

    You write, “It appears more reasonable to seek a generalization opening to dark matter/energy by allowing to take on negative values [. . . .]”

    You are saying ‘more reasonable than Einstein’s general relativity’. But why do you disregard my hypothesis, which does not depend on GR, but rather builds on and depends on some of your work?

    In assuming a priori all the assumptions that you mention, Newtonian mechanics becomes a special case of whatever UFT is really true. (I would argue mine, of course!)

    Isn’t “dark energy”, of which nothing is known, postulated to be a source of energy for gravitation, which must have a source because it causes motion and, therefore, heat? But how can dark energy operate to supply gravitational energy for positive matter, in the amounts that are needed? Surely, that would be impossible if the dark energy is being generated far away from the positive matter?

    Besides, I thought you said that this whole concept requires that “dark energy” be antigravity. How can antigravity, alone, supply a continuous power source for all positive gravity? Is this explained by your new model?

    Also, you never answered my question about what is the physical difference between a local operation of differentiation and a global one in your model. Or if you did in the above post, I haven’t recognized it.

    Thank you.


    • Richard T. Fowler

      Sorry, but when I quoted you the second time, I copied and pasted the quote, and my clipboard left out the Δφ.

      The quote should read, in relevant part:

      “allowing Δφ to take on negative values”

      – Richard

  2. Richard T. Fowler

    I would also like to clarify something which I thought was perfectly clear already in my words … before I experience people starting to rip it off and claim I never even thought of it. (Even though it is obviously and unequivocally implied by what I have already written and posted on this website.)

    When Claes writes that his approach is the one that seems the most reasonable, he implies that while his has problems, mine has worse problems … none of which he has yet been willing to discuss in the slightest detail.

    Perhaps what is in his mind is that his approach explains excess measured energy, while perhaps he thinks mine doesn’t even begin to do that.

    Mine SO TOTALLY does that!!!

    Actually, it is his (and Laplace’s) that doesn’t even begin to.

    Why doesn’t his and Laplace’s even begin to?

    Because it assumes that a particle and its antiparticle are created out of nothing, while rejecting the idea that energy is continuously created of nothing in order to support gravitation!

    In fact, their approach assumes that it is IMPOSSIBLE for energy to be created out of nothing at the present time … and, in an incredible irony, that assumption is apparently Claes’ basis for preferring that approach over mine — i.e. because he apparently doesn’t find such creation believable.)

    Only one problem. You have new gravitation constantly appearing from out of each particle! And the new gravitation is constantly causing new motion. This motion can be understood to create and dissipate heat — not just through EM friction, but through subatomic-force pressure or “subatomic friction” as well. So it’s gravitation –> kinetic energy –> heat. Because the heat is spread through space via turbulent dissipation in addition to radiation, my model can explain the existence of the heretofore-unexplained extra energy.

    Ironically, it is Claes’ and Laplace’s model which apparently fails to explain the extra energy, because in order to work, the model requires ALL of that energy, AND THEN SOME MORE which as far as I can tell, it doesn’t even bother to guess at where it comes from) just to provide for observed “positive” gravitation. So not only is there nothing left over to account the extra unseen energetic mass … there’s not even enough to drain away from the antimatter to power all of the positive gravitation!

    So, Claes, it seems that your model, which you’ve adapted from Laplace, actually has the exact flaw that you are seemingly attributing to mine … and then, after adopting that flaw, you are turning around and suggesting that your model is more believable than mine, apparently because you believe mine has the flaw that you’ve tried to attach to it, which it doesn’t have!

    My mind reels at how much denial of reality there is in the world today.

    It’s time to start addressing the actual physical issues of forces and energies — in the serious manner of an accountant keeping track of money — rather than just appealing to prior assumptions and declaring, “case closed, and the exact quantities don’t matter”.


  3. claesjohnson

    Hi Richard, you seem to have many things to say. Please send me links to your material and I will try to respond.

  4. cementafriend

    Claes, there are some Unified theories around. Here is a site . Do not know anything about it but I note he has commented at this post . I have not read it but there have been lots of comments. Another interesting site with some theories is I do not agree with everything there but some of his thoughts raise doubts about some classical physics. You might like his thoughts here (Why the Transforms of Special Relativity are not Symmetrical)

  5. Richard T. Fowler

    Hi Claes!

    Thanks for the offer. Honestly, I don’t have anything written other than what I have already posted as comments on these last four posts.

    Could I write some more? Yes, I suppose I could. But I wanted to give you a chance to continue it. I think that frankly you could do it a lot faster than I could. If you prefer to e-mail me your response, you may. I will also write up a post summarizing what we’ve discussed here and put it on my blog, and if you like you may respond there.

    CaF, good to see you again!

    Both of you,

    Please remember that my concept was not fully developed until I really started to understand the novelty of Claes’ finite precision computation, which was this December that has just passed. The concept treats gravitation in a manner very similar to the way that Claes’ energy theory treats heat. So I am doubtful that these others can really treat energy as thoroughly as my concept does.

    Also, because my concept gravity the way that Claes’ theory treats heat, my concept implies that the appearance of a direct relationship between mass and gravitational potential is an artifact of imprecise measurement. But the very close relationship would follow from these two items, in combination:

    1) a statistical averaging-out of gravitational flux over all directions within a dense body (much like we end up with the appearance of a “Planck constant” in thermodynamics, even though that is not really a constant but just a statistical average); and also from

    2) the supposition that a particle can hold relatively litle gravitational energy over and above the amount that it receives from the void every instant.

    Have to eat breakfast and then will post on my blog. Thanks Claes for your patience in considering what I have written already.


  6. Richard T. Fowler


    I have waited for approximately six days, and have had no reply from anyone.

    I am going to offer you a hint that I hope will help you understand my hypothesis better.

    I would very much appreciate any feedback (including from readers) as to whether this helps you understand and/or provide a reply to my comments on the last four posts, including this one.

    The hint is this….

    In a continuously expanding universe, the pressure on the stars is always being let up (i.e., lowered) — never raised.


  7. Roger Anderton

    Newtonian Unified Field theory is Boscovich’s theory. Boscovich’s theory was the next step in the Newtonian paradigm. But that gets overshadowed (ignored) because of too much attention on Einstein; leading to teaching physics students – Newton and Einstein, but miss out the bit in the middle of Boscovich.

    At Boscovich Conference 2011 it was explained that Quantum physics derived from Boscovich’s theory etc.

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