11. Mach’s Principle, gravitation & matter distribution – 2010 (revised and reduced 2013)

These are three separate but related papers containing conjectures of Cosmology.

  1. Mach’s Principle and its correlation with gravitation & inertia.
  2. Why the universe appears homogeneous & isotropic, and the manner in which the speed of light might be variable, and its resulting  relation with the passage of time, and some similarities of these proposals to the Absorber theory.
  3. A further conjecture by the inversion of paper 1 to demonstrate negative gravitation and other resulting implications.

Synopsis Paper One:

This conjectures how it appears possible to reconcile gravitation and inertia with Mach’s Principle. Some assumptions have to be made. The first  is that the universe is closed and finite, expanding out equally in all directions, and that the distribution of mass is not uniform therein but that there is a large preponderance moving near light velocity at the outer edges with much smaller quantities of matter closer to the centre point moving out far less rapidly. The effect of large amounts of mass near the outside edge moving out at near light velocity enhances the gravitational effect relativistically to strongly affect the motion of all matter further within. This is the universal effect demonstrated by Mach’s Principle and Foucault’s pendulum, and which also suggests a simple rationalisation of inertia.

This paper is based on the results of others summarised in general terms rather than mathematical formulae, which I then adapt with the results of my own observation to come to some radical conclusions. I use no maths not being adept in that admirable skill, but should any reader well versed in physics with such ability be intrigued by a vestige of possibility in my conjectures, then perhaps they might be tempted to see if at least some of them held water mathematically.

In my mid teems I saw the action of the large Foucault’s pendulum that used to hang in the entrance of the Science Museum in Kensington, and its majestic slow sweep was enough to encourage me to read and be astounded by the explanation that the pendulum swings not in the same line with the earth as it rotates which one might intuitively expect, but with the rest of the universe. I found this intriguing but then forgot about it until I came across the problem again a decade or more later, through reading as much of Mach’s work I could find translated from the original German. I tried to assimilate this with all that I had learned about gravitation by that time, and failed. I also sought for any such explanation of this principle that the physicists and cosmologists might have come up with, but found none that I could understand. I was struck that such a physical state of affairs which was so obviously observable seemed to be ignored by the scientific community. As a result, I now go into Mach’s work at some length in this respect.  

It seems that Mach never defined in specific sentences his principle, although its most graphic verbal form attributed to him was “When the subway jerks, it’s the fixed stars that throw you down.”  Or, as a perceptive friend of mine remarked: “I pick up a cup of coffee in the kitchen and turn with it to walk to my desk. Once again the pattern on the surface stays unturned relative too …er … the universe and once again the mystery of inertia is slap in front of our eyes. For most, too close to see, to understand?”

One of the closest references to it is in his ‘Science of Mechanics’, commenting on Newton’s bucket experiment:

“Newton’s experiment with the rotating vessel of water simply informs us that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the earth and the other celestial bodies.  No one is competent to say how the experiment would turn out if the sides of the vessel increase in thickness and mass till ultimately they were several leagues thick.  The one experiment only lies before us, and our business is to bring it into accord with the other facts known to us and not with the arbitrary fictions of our imaginations…”

Mach shied away from defining any principle implied by his thought experiment, due to his tight discipline of refusing to believe or take into account any effect which could not be observed.  However, the implication of the principle is there, and later he continues.

“The comportment of terrestrial bodies with respect to the earth is reducible to the comportment of the earth with respect to the remote heavenly bodies………..   For me, only relative motions exist, and I can see, in this regard, no distinction between rotation and translation. When a body moves relatively to the fixed stars, centrifugal forces are produced; when it moves relatively to some different body, and not relatively to the fixed stars, no centrifugal forces are produced…….. Can we fix Newton’s bucket of water, rotate the fixed stars, and then prove the absence of centrifugal forces?  The experiment is impossible; the idea is meaningless, for the two cases are not, in sense perception, distinguishable from each other.  I accordingly regard these two cases as the same cases, and Newton’s distinction as an illusion ……..”

The point was discussed again in Mach’s ‘Conservation of Energy’, and for further clarification of the way in which he was thinking an extract is quoted below.  Apparently Einstein owed a great deal to Mach’s work in the former’s development of his theories of relativity, and a premonition of Einstein’s thought experiment for demonstration of the principle of equivalence by consideration of the motion of a windowless lift, might be perceived in the following passages.

“Obviously it does not matter whether we think of the earth as turning round on its axis, or at rest while the celestial bodies revolve round it.  Geometrically these are exactly the same case of a relative rotation of the earth and of the celestial bodies with respect to one another. Only the first representation is astronomically the more convenient and simpler. But if we think of the earth at rest and the other celestial bodies revolving round it, there is no flattening of the earth, no Foucault’s experiment, and so on – at least according to our usual conception of the law of inertia. Now, one can solve the problem in two ways: either all motion is absolute, or our law of motion is wrongly expressed. Neumann preferred the first supposition, I, the second……..

But, if we wish to apply the law of inertia in an earthquake, the terrestrial points of reference would leave us in the lurch, and, convinced of their uselessness, we would grope after the celestial ones.  But, with these better ones, the same thing would happen as soon as the stars showed movements which were very noticeable….. We ask for the first time which star we are to choose, and in this case easily see that the stars cannot be treated indifferently, but that because we can give preference to none, the influence of all must be taken into consideration.”

This last paragraph summarised for me his perspicacity and ability to demonstrate in a few simple words the pointlessness of thinking in absolute terms.  His principle can be defined in simple terms as follows: ‘Every particle of matter in the universe, and its motion, has an effect on every other particle elsewhere in the universe.’ Foucault’s pendulum in the front hall of the Science Museum in Kensington was the example of the principle in operation. I have often tried to resolve the question how is this principle, undeniable through observation, has been reconciled with gravitation. It seems to me that its implications have been if not ignored, at least left hanging unresolved by 21st century science. If so then the current understanding of inertia must also be in question and well overdue, and which has perhaps been emphasised by this recent confusion on the nature of matter, both dark and observable.

A simple way to provide another way of looking at Gravitation and inertia that would satisfy Mach’s Principle is to consider the universe as bounded and finite. Whether the universe is infinite and unbounded, finite and unbounded, or finite and bounded is a question which has vexed the experts since Alexander Friedmann first considered it in 1922, and is still very much unresolved, but it seems that the closed and finite option is just as plausible as any other, and in my mind much more so since it can be visualised easily enough. I was going to add an appendix or footnote to enlarge on the various forms of likely possible universe but have decided against it since those at whom this paper is principally directed will be very familiar with them. The assumption is therefore that the universe can be visualized in simple terms as a sphere expanding outwards from its centre point of initial big bang. If so and if the Big Bang certainly took place then initially the radiation must have spread out from the centre, presumably at light speed to occupy space where there was nothing formerly, so that there might be a ring of singularity between this space filled with energy in outward motion and beyond it where there no such continua of time and space. Whether there is such a singular rim is not crucial to this paper but it is considered in the follow up second paper, and further reinforcement for this view point exists in the work of Arthur Milne, Rouse Ball Professor of Mathematics at Oxford who died aged 54 in 1950 and this will be enlarged on in the second section below.

After a while matter started to precipitate out as energy was dissipated and the universe cooled down. The way in which this is thought to have occurred is covered in numbers of well written books for the layman written by expert physicists into which I will not delve here, but what is interesting for me is that presumably this precipitation of matter starts initially furthest out from the hot centre as it spreads out and away from the centre and start to cool. I also assume that this matter near the edge is traveling very fast and arguably at close to light velocity. It seems not too unreasonable to assume that the initial hot plasma of the big bang near the rim might have cooled and converted to solid mass before that closer to the centre. Thus there would be larger amounts of matter distributed nearer the rim than further within, on top of the relativistic effect to increasing its mass with respect to an observer close to the big bang point of origin. (See Diagram 1).  This assumption is contrary to the current evidence from the cosmic microwave background that the universe is probably homogeneous and isotropic, and my response to that is answered more specifically in the second paper and also possibly that our observable universe is a far smaller percentage of the universe’s actual dimensions than we anticipate.


If the universe were finite and bounded with a great deal of its mass  close to the outside edge and traveling outwards at near light velocity as described above, then this would have an interesting effect on slower moving galaxies well within the universe. The mass of the outer edge galaxies would be relativistically huge if they were traveling at near light velocity. The attractive force of gravitation exercised by this vast mass moving out would be experienced by all lesser matter within, and indeed if there were to be some force tending to accelerate the motion of the latter away from their motion in a straight line, they would experience a pressure against this: inertia. Such a scenario appears at first sight to satisfy Mach’s principle.

To rehearse the hypothesis thus far, on the assumption that gravitation is a force of attraction then the very substantial quantities of matter near the periphery moving very rapidly outward and certainly well beyond the limits of visibility from Earth, would exercise a huge attractive effect on all matter further within the universe. If for instance the attractive  effect of just one nearby section of the universe on, say the Earth, were considered, and if the inverse square law were invoked, this would be exactly countered by the much large section at the opposite end of the universe, albeit it so much further distant. In Diagram 2 the forces from opposing sides of the universe are shown to balance out on a stellar mass two thirds of the distance from the centre. Three examples are shown to emphasise the position but one should be self explanatory enough. In short there would be equilibrium of all such forces of attraction assuming the matter were moving at a constant velocity rather than accelerating, although it seems intuitively possible to me that there might be some inertial effect on this interior matter if it were to start to accelerate for whatever reason. Perhaps a mathematician could present some justification for this in algebraic terms.

Obviously if two stars (or planets) were to approach each other then the increased gravitational force between them would start to push them together so that they would start to curve towards each other and when they reached distances close enough that they could not escape, they would fall into an elliptical orbit, an effect with which we are very familiar. As already stated such a scenario would be the basis for a revised definition for Mach’s Principle, and it would also deliver a basis for the concept of inertia to be redefined. The force of attraction of the vast masses near the periphery would be equal in all directions (inverse square law), and would act on all matter within the universe so that  their initial motion expanding outwards would be unaffected whilst at constant velocity, but which would resist any acceleration, as if, very simply speaking, they were immersed in treacle. In short the effect of inertia would be inextricably intertwined with the attractive force of gravitation, which I understand that current science holds they are not. In Einstein’s famous thought experiment, if an enclosed and windowless elevator cabin in outer space were suddenly accelerated upwards, its occupiers could not tell whether this was due to a force of gravitation from some other massive nearby object or just due to inertia of mass resisting the effect of the accelerating force acting on the elevator. Although per this dictum, gravitation is equivalent to inertia, one can exist without the other, but according to this new scenario, not so. There would be no effect of inertia without the existence of the huge hidden mass of the universe expanding out near its periphery.


My whole conjecture of gravitation and inertia defined in this manner is based on the assumption that the universe is finite, bounded and expanding outwards, and that matter is certainly not evenly distributed within: quite the opposite. For many years I had assumed that that this was just too simplistic an example for most astrophysicists to take seriously, but from what I have read over the years I now surmise that it is just as likely an outcome as any of the other possible alternatives, all the more so as it has become clear over the couple of decades, how little is known about the true nature of matter as disturbing observations from astronomy arrive indicating that visible mass is a very small proportion of matter in the universe, about 4.6% observable matter with 23% being dark matter and the rest 72.4% as dark energy. Given that such observations if correct, are likely to cause our understanding of cosmology to have to be radically revised, my conjecture as set out above might not now seem too radical, and it has the advantage of satisfying Occam’s razor: simplicity. In which case I am encouraged that there might be something in the hypothesis of gravitation which incorporates Mach’s Principle.

Since this conjecture relies on the fundamental assumption that the universe if closed and finite I will conclude by a quote from Einstein in an address to the Berlin Academy of Sciences in 1921:

I must not fail to mention that a theoretical argument can be adduced in favor of the hypothesis of a finite universe.  The general theory of relativity teaches that the inertia of a given body is greater as there are more ponderable masses in proximity to it; thus it seems very natural to reduce the total effect of inertia of a body to action and reaction between it and the other bodies in the universe…  From the general theory of relativity it can be deduced that this total reduction of inertia to reciprocal action between masses – as required by E. Mach, for example – is possible only if the universe is spatially finite.  On many physicists and astronomers this argument makes no impression… 


Mach E. The Science of Mechanics

Mach E. The Conservation of Energy

Einstein. Berlin Academy of sciences, 1921

Milne E.A. Relativity, Gravitation & World Structure,  1935


Why the universe appears homogeneous & isotropic, and the manner in which the speed of light might be made variable, and its resulting  relation with the passage of time, and some similarities of these proposals to the Absorber theory.

Synopsis Paper Two

Further to the assumptions made in paper 1, another  is made that there is an  edge to the bounded universe expanding out at light velocity from the original burst of radiation energy, beyond which is singularity without dimensions of time or space. A further assumption is made that the velocity of any source of EM radiation will be drawn out in all directions to exactly duplicate the outward action of this large singular rim. This renders the universe to appear isotropic and homogenous to an observer based within the universe on any planet system moving out, whereas viewed externally this would not be the case which reinforces the argument set out in part one, this being contrary to current evidence suggested by the cosmic microwave background. An implication of such a scenario is that were the rate of expansion of the universe to alter so would then light velocity. The Absorber Theory is then briefly explained which requires for its operation that the universe be enclosed in an opaque container, which would be a result of a finite and closed universe. Similarities of the Absorber Theory with the current subject proposals are discussed along with some crucial differences. The variation and possible reversal of the expansion of the universe with the implications for passage of time and the retention of symmetry are proposed.

Arthur Milne was an eminent mathematician at Oxford, and controversially at the time he argued that under Einstein’s special relativity it was impossible for an expanding universe to have homogeneous matter distribution.  He also proposed the universe does have an outside edge, and that the whole universe was created at a single point in flat space-time, and thereafter occupies the interior of a bubble that expands at the speed of light into previously empty space. This Milne model is also isotropic so that there was no difference between the fast moving galaxies near the rim and galaxies at rest near the centre of the bubble, since any galaxy and its neighborhood will subjectively appear to the occupants to be at the centre by the Lorentz transformation. This is remarkably similar to the assumptions made in the first section above. An implication is that if this outside edge is moving out at light speed its time will not have changed since the moment of big bang.

Together with the assumptions made in the first paper, if a further modest one is made together with an accompanying larger one, then the behaviour of Electromagnetic radiation can be qualified in a manner in some respects similar to that of the Absorber Theory first set out by Wheeler and Feynman in 1945, along with some resulting implications on the nature of the passage of time in fairly simple terms. The first assumption is that there is an outside edge to the finite universe formed of radiation that was first emitted at the initial moment of the big bang. Within this volume the universe has the continua of space and time with which we are familiar, but beyond there is nothing of which we have knowledge: no time no space: in short singularity. It is as if the fact of the big bang creating EM radiation has created a universe of time and space and other associated phenomena but that beyond its outer edge which I shall call the singular rim for convenience, there is nothing, not even a void. This singular rim is expanding out at light velocity, which does not seem to be too great an assumption if it is first accepted that the universe is finite, closed and bounded. The accompanying larger assumption is that the EM radiation generated by every source or oscillation of charged particles within the universe is drawn out to exactly duplicate the action of this outer rim of expansion from the first moment in time. This might appear radical enough and no solid grounds are given for it in this paper and at this stage all I can suggest is that the results and implications are aesthetically satisfying to such a degree that they should perhaps not be summarily dismissed.

Consider an oscillating charge generating electromagnetic waves, (or a light source from a fluorescent tube) near the centre of the universe. If we assume that the outer edge is expanding out at light velocity, the motion of the generating source close to the centre will be minimal compared to that of the periphery, although it will be expanding slightly outwards.  The EM waves will duplicate the action of the singular boundary (the singular rim) exactly in all directions, and will radiate out in the form of a slightly squashed sphere, flattened along the line of motion, as far as an observer outside the universe were concerned, assuming for the moment that were possible. 

This is represented by position A1, in diagram 3. At position A2, halfway between the centre and the rim, the generating source will be moving outwards at about 1/2 C, half the velocity of the singular rim, C, and as a result, the wave front of EM radiation will not be so spherical, but more ellipsoidal, or squashed and lengthened along the line of motion.  At position A3, very close indeed to the singular rim, the source is traveling at, say nine tenths C, the EM waves in the line of motion between the source and the nearest point of the singular rim, will be traveling at a velocity only slightly greater than that of the source.  This will result in a compression of wave fronts, and a large extension on the other side of source towards the furthest point of the singular rim.

The above observations are all made by an external observer outside the system, and stationary with respect to the centre of the universe, which of course is presumably not  possible, but easy enough to visualise. To an observer inside the system, things appear differently, due to the law of relativity. If a particle is traveling at .95 the speed of light, very close to the singular rim, then to an observer in the immediate vicinity, also close to the singular rim, the wave fronts would not appear squashed, but rather perfectly spherical (B on Diagram 3). This is due to the Lorenz contraction and the time dilation effect.  Put simply, it is nothing more than an application of the familiar Doppler Effect.  As far as the hypothetical external observer outside the universe is concerned, the wave front in between the source and the nearest point on the singular rim are only moving at 5% faster than the source, whereas the corresponding wave front diametrically opposite furthest from the source, is moving away from the source at 1.95 times light velocity. 

Hence the external observer, stationary with respect to the centre of the universe, would see the wave fronts traveling at .95C very much flattened and distended (C Diagram 3).   However, as far as an observer based on the moving source is concerned, the position does not appear distended like this at all. This no more than the Doppler effect: the whistle of an approaching train is constant in pitch (frequency) to the train driver, but higher in pitch to the external observer when approaching and lower when retreating. This would appear to account for the fact that the universe currently appears to be isotropic and homogeneous  as illustrated by results of the cosmic microwave back ground observations and the conclusion that the universe is expanding outwards evenly in all directions, but which is incorrect if this assumption were proved valid. This reinforces the argument in the first paper since otherwise the current cosmic microwave background (CMB) observations of the universe appear to indicate it is homogeneous and isotropic which is an argument against the viability of the reasoning set out in paper 1. 


There is an experiment being carried out in Holland and the UK with huge radio telescopes (LOFAR or low frequency array) part of whose purpose is to investigate the large scale structure of the universe and its evolution and to ascertain whether or not matter is randomly distributed in the universe, which if successful, might in future be more extensively done by erecting such arrays far apart in space.  It seems that some of the astrophysicists involved in the project are hopeful that the result might be that matter distribution is not random, which an enticing prospect for the conjectures made in this paper.

If the singular rim of radiation on the edge of the universe is traveling at light velocity then time will have stood still for this edge from the moment of the big bang. If it were to slow down, and with it, ex hypothesi, that of light velocity within, then the passage of time will presumably change and slow down pro rata within the universe. If the expansion were to reverse into contraction then by this supposition time the passage of time would also reverse, as would also all EM radiation to perfectly duplicate its earlier actions. Such a scenario would produce an exact reversal of all activity in the universe to ultimately dissolve back into the big crunch of a singularity or perhaps nothing at all. This would bring about the satisfactory conclusion of symmetry having been perfectly maintained, both in time and space. Our current observation and understanding of the way in which EM radiation acts does not easily allow for such a symmetry to be established, even though Maxwell’s basic equations indicate it should be. This lack of symmetrical behaviour was one of the reasons why Feynman and Wheeler sought to produce their Absorber Theory to reconcile this difficulty, as discussed later below.

The velocity of light is known to be a constant of huge significance and I have often questioned why it should be at this specific velocity. In this respect I understand that measurements are being undertaken to enquire whether it is constant or variable and that there is quite a body of papers and books on the subject of VSL or the variable speed of light, especially notable being those by Physicist Lee Smolin. If I am queried as to why every radiation source within the universe is drawn out to emulate the action of the singular rim, apart from demonstrating above the simple and satisfactory results it gives, I will go so far at this stage to suggest the following.

The singular edge of the universe is a singularity of the largest sort imaginable, bigger for example than that of the black holes that are speculated might be at the centre of most galaxies. This being so it might not seem so unlikely that it would have a pervasive effect on every other smaller and similar effect within the universe. Every source of electromagnetic radiation within the universe will involve repetition of the action of a charged particle of some sort (or identical particles electrons- usually in huge numbers) and I propose that this causes a ripple in the framework of space time which will duplicate or resonate exactly with that outwards motion of the singular rim, and this would be equivalent with the mechanism proposed in paper 1 for the way in which Mach’s principle operates: that every particle of mass works on all others, with everything be interconnected in a holistic universe. What is more, the greater the number of such duplicated actions, or the greater the frequency, the stronger the effect of the radiation.

This may seem just too much a simplistic interpretation of cosmology to be considered acceptable without a more detailed and comprehensive rationale but the results of such assumptions produce a fairly clear explanation of what we observe to occur in nature. It provides a very simple explanation for the isotropic way in which light behaves, which otherwise can cause non physicists some bafflement, and then it would also dispose of the problem of renormalisation that the physicist Dirac so disliked.  This resulted from the fact that electrodynamics based on Maxwell’s theory requires that EM waves should be symmetrical through time. However, as we currently observe and understand them, waves of radiation are only spreading out one way in time, and this lack of symmetry is the cause of mathematical difficulties which have yet to be resolved.

The Absorber Theory of Wheeler and Feynman first published in the Review of Physics 1945 attempted to deal with this problem. When I first read about it the mathematical content seemed too technical for me to bother to absorb its detail and anyway, it was held out to be not much more than an elegant mathematical exercise in cosmology with little or no implications for the real world. I came across it later and was struck that one of the conditions required for its operation was that the universe be enclosed in an opaque container. This might have seemed somewhat obscure to many, but I saw at once that my notion of universe bounded by a rim of singularity fitted other considerations I had about cosmology, and I considered the subject further. It occurred to me that the theory might not have been taken that seriously in the 1940s simply because nobody had animadverted the serious possibility that the universe might be closed and finite which would effectively meet the theory’s requirements in this respect.

The theory expounds a novel manner in which the universe might operate and which did not depend on the notion of causality that is required by exchange particles or photons in physics today. I found the theory to be best explained in a book by P.C.W.Davies, ‘Space and Time in the Modern Universe’ by P.C.W.Davies, who was then Lecturer in Applied Mathematics at Kings College London. I have borrowed abridged and paraphrased some paragraphs from his book rather than attempt my own new and inevitably more inexpert version. Davies explains that radio or EM waves travel forward only in time, whereas electrodynamics based on Maxwell’s theory requires that EM waves should be symmetrical through time. However this lack of symmetry causes formidable mathematical difficulties which have always plagued the descriptions of the interaction of charged particles with the EM field. Wheeler and Feynman sought to resolve these problems not by changing the basic form of Maxwell’s theory, but instead speculating on a deeper reason for why only future directed radiation occurs, rather than the dismissal that the universe is simply ‘made that way’.  This they did by analysing what would happen if an accelerating charged particle emitted radiation equally onto the past and future.  Clearly this type of behaviour is in straight contradiction with experience, but they found the following remarkable result.  Suppose a single, charged particle in empty space, when set into motion, radiates symmetrically one half advanced waves into the past, and one half retarded waves into the future (the latter being ordinary radio waves with which we are familiar).  Then that same particle, when placed into an opaque box, will only fully radiate fully retarded waves into the future.  Open the box and the advanced waves will reappear.

The waves from the accelerating particle move outwards until they strike the inside surface of the box, where they set into motion the charged electrons from the box atoms.  The retarded wave strikes the box a little after it leaves the vicinity of the particle, but the advanced wave strikes the box before the particle has even been moved.  So, paradoxically, the electrons in the box vibrate in anticipation of the subsequent motion of the charged particle. The prospect of causing a response in the walls of the box at an earlier time may appear a little bizarre, nevertheless, in physics it is quite permissible either to interchange cause and effect or else to have cause following effect in time, provided that everything is self-consistent.

The salient feature of Wheeler and Feynman’s work was to demonstrate by a simple calculation that, provided the box is fully opaque (so that no waves whatever can penetrate to the exterior) then the advanced waves from the box just cancel the advanced waves from the source particle. The effect of the response waves from the box on all the charged particles is to cancel all the anticipatory motions occurring before the source particle is moved, and to produce exactly the right radiative damping force on the source particle to account for the transfer of the energy from the particle to the walls of the box.  To an inhabitant inside the box, the electrodynamic behaviour of the system is thus entirely in accordance with our everyday experience.  If, however, the box is not entirely opaque, paradoxical advanced effects still occur.

A development of this argument showed that electromagnetic waves could be considered as perfectly symmetrical in time, and it also showed that, instead of the concept of the electromagnetic field, this would have to be replaced by the concept of direct action-at-a-distance between the charged particles.  This latter would probably not be instantaneous type, which characterises Newton’s theory of gravitation, but a delayed action, propagated at light speed.  This action would operate both forwards and backwards in time. An implication of this Absorber Theory can also be shown to be that the universe will collapse back to a point, which is what one might reasonably expect, if the behaviour of the universe is to be symmetrical, and it is currently expanding outwards from a point of the big bang.

The above five paragraphs give a brief description of the Absorber theory which caught my attention some time ago. I had great difficulty in attempting to visualise the way in which it operates, although I found its conclusions about the nature of photons and the lack of necessity for an exchange particle very attractive. The assumption given above on the way in which light velocity is mediated presents a different hypothesis to that put up by Wheeler & Feynman, but there are still some similarities, and my version is much easier to visualise. This is why I have spent a little time on the latters’ work, both leading physicists of the 20th century and whose conjectures are not to be ignored. 

The closed universe as I have describe may not appear to be an opaque box as required by the Absorber Theory, since the outward edge of the radiation singular rim is never reached by any other EM radiation from within, but this would be different if the universe started for whatever reason to contract. Then it would be an opaque box since suddenly all EM radiation within would also reverse and presumably run backwards through its original course of actions. Effectively time would be reversed except for that of the outside rim of the universe, which with its motion at and mediating light speed, would never have progressed from the first moment of big bang:  the outside edge would never display any passage through time. If the universe eventually contracted back to nothing then the action of EM radiation would have been perfectly symmetrical as required by electrodynamics and Maxwell, which I assume was one of the anomalies Wheeler & Feynman set out to resolve in their Absorber Theory, and which my alternative also brings about albeit from different assumptions. Such a scenario is far easier to visualise and understand which seems an advantage and reinforces for me the viability of the content of the first paper, and my version does not employ the force at a distance of the Absorber Theory to replace the photon unless my notion of a shiver of potential for duplicated action spreading, or rather drawn out in the fabric of space time at light speed from every charged particle source of EM radiation could be considered as that.

One final quotation on the subject of constants, variable or not, which is relevant to the above and is worth quoting from Paul Dirac is as follows:

“One field of work in which there has been too much speculation is cosmology. There are very few hard facts to go on, but theoretical workers have been busy constructing various models for the universe based on any assumptions that they fancy. These models are probably all wrong. It is usually assumed that the laws of nature have always been the same as they are now. There is no justification for this. The laws may be changing, and in particular quantities which are considered to be constants of nature may be varying with cosmological time. Such variations would completely upset the model makers.”


E.A. Milne. Relativity, gravitation and world-structure, Oxford: Clarendon Press 1932

Davies, PCW.  Space and Time in the Modern University Cambridge, Univ Press 1977.

Wheeler, J & Feynman, R.  “Interaction with the Absorber as the Mechanism of Radiation,” Reviews of Modern Physics, 17, 157–161 (1945).                        

Paul Dirac. “On methods in theoretical physics”, June 1968, Trieste.

Lee Smolin. The Life of the Cosmos, Oxford University Press 1997

Nick Greaves,
Lesignac Durand, Charente

3. An inversion of paper 1 to account for Dark Energy and the expansion of the universe

Synopsis Paper Three:

This section is similar to the first but that instead of gravitation being a force of attraction, it is reversed to one of repulsion. All the same assumptions have to be made together with some further conjectures. The first is that since two separate particles of mass cannot occupy the same space at the same time: matter repels matter being part of  the driving force for the outward expansion of the big bang, with such an effect possibly being related to the phenomenon of dark energy and its connection with anti gravity. The fact that gravitation is experienced as an attractive force is rationalised as follows. The  effect that the respective masses of two stellar objects (stars, galaxies or whatever) will have on each other locally will act to blanket off the repulsive effect of the outer edges of the universe in all directions other than that between the two masses.

This third paper is far more speculative, and apparently outrageous, but so closely allied to the two preceding, and the possibilities of which I find so intriguing that I cannot forbear to set it out. Put briefly, it is based on the fundamental assumption that like repels like, and in the same way that opposite electric charges repel, so units of mass repel each other, for the same reason at a fundamental level that two separate particles of mass at whatever microscopic scale cannot occupy the same space at the same time. Everybody is aware that gravitation is a force of attraction, but on the assumption that the universe is closed and finite, then due to a blanketing effect, gravitation could be operating repulsively on the macro astro-scale despite our contrary experience in the local small scale dimensions of our observable universe. Such assumptions would appear to allow the quandary of Mach’s principle to be rationalised with gravitation, and for inertia to be presented in an altered perspective, similarly to that demonstrated above in paper 1. Before the mechanism of repulsive gravitation is explained I will first attempt to identify a few other circumstances which might render such a notion less instantly unacceptable. Since the awareness in the last couple of decades that the composition of the universe is only about 4.6% observable matter with 23% being dark matter and the rest 72.4% as dark energy, it is arguable that there needs to be a radical new approach to cosmology. I would prefer it not to be so complex that only highly qualified mathematicians can grasp its essentials, which is one reason this paper is couched subjectively in simple terms.

I have read with fascination about the possibility that the dark energy might need to be represented generally in the form of negative gravitation since the universe appears to be expanding faster than anticipated. More recently I have read about the work of Dutch physicist Erik Verlinde who came up with a proof in January 2010 indicating that gravitation is not a fundamental force but rather an emergent phenomenon that arises from the statistical behaviour of microscopic degrees of freedom encoded on a holographic screen. This encouraged me to reconsider some conjectures that occurred to me on the subject of Mach’s Principle in the middle nineties, but dismissed as too fanciful at the time. Given this more recent information coming in from the observations of the astro physicists, and again I have been able rationalise a new framework to present a simple explanation of how Mach’s principle and gravitation interact, as before. Diagram 1 (see below) still holds good, showing the universe with most of the matter near the outside edge expanding out at close to light velocity

DIAGRAM 1 (repeat)

We know from experience that similar electrical charges repel each other, and I now make the large assumption that similarly two units of mass will also produce a repulsive force, contrary to the gravitational attractive force that we are all aware holds us on to the surface of the Earth and in turn revolves the Earth about the sun. Why this should be so, I cannot justify other than to say that on the atomic scale we know that two nuclei or any other two very small particles (fermions of Pauli’s exclusion principle) cannot occupy the same space at the same time, (unless perhaps converted to radiation energy) in which case they must be repelling each other, albeit as the distance apart increases so does the repulsive tendency.  Such a scenario would give a rationale of sorts to entropy in general and  for the outward expansion of the universe and also perhaps to its possible rate of increase, but leaving that possibility aside for perhaps another occasion, how can such a contrary to experience statement be justified?

If the universe is finite and bounded and most of its mass is close to the outside edge and traveling outwards at near light velocity as described above in paper 1, then this would have an interesting effect on slower moving galaxies well within the universe. As before the mass of the outer edge galaxies would be relativistically huge if they were traveling at near light velocity. If there was this repulsive effect between separate masses (or galaxies, or clumps of galaxies), the repulsive force thus exercised on the interior galaxies would presumably be balanced out in accordance with the inverse square law (mathematicians to confirm), so their velocity would not be affected. However if there were to be some force tending to accelerate them away from their motion in a straight line, they would experience a pressure against this: inertia. As before, Mach’s principle would be endorsed.

But this has not yet got round the fact that a dropped weight falls to Earth rather than shoots up into the heavens which perhaps one might expect if there were such a repulsive force. When I first speculated on this scenario in the middle nineties, I gave up at this point, since I could see no way round it, and there was no other encouragement of which I was aware at the time to persevere: no hint that negative gravitation might be an offshoot of dark energy which there now apparently is. However a simple possibility has recently occurred to me which does not seem too unreasonable, and that can perhaps best be described as a blanketing effect. Whilst pondering on this apparent cul de sac, I happened to recall the reported occasion that a householder living close to the Crystal Palace TV transmitter in London had run thick cables round his roof and managed to power his domestic electrical needs for free by induction. He was caught eventually because the TV users immediately behind him in the area complained of very poor reception and the BBC triangulated the complaints down to his house.

This was a very clear example of the blanketing of EM radiation and when this obscure recollection arose for no particular reason some months ago it suddenly occurred to me that here was an explicit example of EM blanketing that had a direct correlation with my consideration of repulsive gravitation. If my assumption were valid that gravitation was to act in much the same way as EM radiation, like repelling like, then there should indeed be such a blanketing effect. EM waves from an oscillating charged source will be absorbed by a conductor placed in their path and effectively blanketed from traveling any further in the direction beyond that conductor. There can be little doubt about that. But why should not the same apply to gravitation if it could be the case that gravitation was either similar in its fundamental operation to electromagnetism, or indeed possibly a derivative of it?

To rehearse my hypothesis, if gravitation were repulsive then the very substantial quantities of matter near the periphery moving very rapidly outward and certainly well beyond the limits of visibility from Earth, would exercise a huge repulsive effect on all matter further within the universe. Now if the repulsive effect of just one nearby section of the universe on, say the Earth, were considered, and if the inverse square law were invoked, this would be exactly countered by the much larger section at the opposite end of the universe, albeit it so much further distant. In diagram 2B the forces from opposing sides of the universe are shown to balance out on a stellar mass two thirds of the distance from the centre. This is very similar to diagram 2, except that the forces are outgoing instead the reverse, and again three examples are shown to emphasise the position but one should be self explanatory enough.  In short there would be equilibrium of all such repulsive forces assuming the matter were moving at a constant velocity rather than accelerating. Again it seems intuitively possible to me that there might be some inertial effect on this interior matter if it were to start to accelerate for whatever reason.

However if two stars (or planets) were to approach each other (Diagram 3B), the proposed blanketing effect would start to push them together so that they would start to curve towards each other and when they reached distances close enough that they could not escape, they would fall into an elliptical orbit. So without having any precise description of whether this would work in mathematical terms, it appears that here is some sort of alternative scenario for the explanation of gravitation, not as a force generated from first principles as a fundamental tendency but rather derived as a result of the more fundamental tendency for like to repel like, which as mentioned above I regard as the mechanism behind entropy.

In order to rationalise the extreme case of the attractive gravitational forces of neutron stars, some further qualifications are required. It has first to be assumed that the repulsive force created by the prolixity of stars and galaxies at the outer edges is vast and all pervasive. But since every object with rest mass is subject to inertia, which will be caused by the action of this repulsive force acting inwards as mentioned above, the latter effect would indeed have to overwhelming. Furthermore Mach’s Principle is satisfied by such a conjecture and along with it, the mystery of inertia is made relatively simple.

These huge forces of repulsion are not only due to concentration of galaxy clusters near the edge but also due to their moving at very near light speed.  It also has to be assumed that the blanketing effect is incremental, rather than just on or off. If, for instance, the constituents of a neutron star are tightly packed together enough to almost completely absorb and cut out the repulsive effect of the opposite end of the universe on a planet in orbit, then the huge repulsive force of the other half of the universe exposed to the planet will force it into the neutron star. This has nothing to do with attraction, and for the conjecture to hold water it has to be assumed that the repulsive force of the universe’s outside edge is far greater than the  repellant force that will also be exerted on the planet by the neutron star. The large mass of the latter is expanding outwards at a steady rate within the universe and will only demonstrate that it has considerable inertia when some other force acts on it to change its velocity.  But according to the conjecture of this paper, this is entirely due to the existence of the massive expanding outer regions, and without which there would be no inertia or gravitation effects.

As already stated such a scenario would be the basis for a revised definition for Mach’s Principle. In summary it would do away with the notion of gravitation as a separate effect but instead allow the repulsive force driving the expansion of the universe to also define inertia. This force  being equal in all directions (inverse square law),  would act on all matter within the universe so that  their initial motion expanding outwards would be unaffected whilst at constant velocity, but which would resist any acceleration. This is all as before in paper 1.



One of the more tenuous implications that suggested such a scenario was that everything could be reduced down to terms of the outward action of the big bang. If this were so, then never mind the attempted unification of the four forces (Gravitation, electromagnetism, and strong & weak nuclear), everything instead might be reduced to an analysis of the kinetic action of the outward spread of the universe (entropy) and possibly a counter tendency provided by an organisational principle that is responsible for the development of complex organisms and life, albeit this latter possibility is well beyond the scope of this paper. Such a scenario was just an embryonic vestige of possibility, no more, but it was attractive. As I have already stated, in the middle nineties I had no idea there was such a thing as dark energy, and I gave up my speculations on repulsive gravitation as just too ridiculous to take seriously, despite it seeming so satisfying aesthetically. Now I have recently read more about the nature of dark energy and speculated on the disruptive effect it is going to have on physics. It seems likely that a whole new paradigm might well have to be produced to qualify and explain this recently discerned phenomenon, so radically different is it from the various standard models that currently hold sway. And to my gratification it occurred to me that a principle of negative gravitation might fit the bill in a number of ways, and quite recently I read more about this subject when I came across a book by physicist Paul Davies, the Goldilocks Enigma in January 2010. The sections on the problem of dark energy were an eye opener for me. I knew that nobody could explain what it was and that it comprised maybe 70% of matter in the universe but I had not realised that it was a negative gravitation effect, and huge one at that. To illustrate the point I quote from Davies’s book: 

“In the mid 1990s two groups of astronomers stunned the scientific community by announcing that the expansion rate of the universe is actually speeding up, as indicated by observations of supernovas in distant galaxies. That is, the universe is now expanding faster than before, and looks to run away with itself if the trend continues. The discovery rocked the foundations of cosmological theory, built as it was on the firm conviction that gravitation acts as a brake on the expansion, serving to slow it down from its explosive start at the big bang to the relatively modest rate observed today. Now the name of the game had changed. A mysterious antigravity force is opposing gravity and has succeeded in transforming deceleration into acceleration…….

It is too soon to predict that the force causing the universe to accelerate is one and the same as Einstein’s original antigravity, although that is certainly the simplest explanation. As I have explained, antigravity can be considered as a consequence of the energy- and the concomitant negative pressure- of empty space itself. Alternatively we can attribute the energy and negative pressure to an invisible field that permeates space. Either way, we don’t see anything of it, so the generic term dark energy is used to denote all these possibilities Astronomers are planning better measurements to find out more. Whatever it is, if you add up the dark energy responsible for making the universe accelerate, you find that it actually represents a total mass that is more than all matter-visible and dark- put together. It seems that dark energy constitutes most of the mass of the universe yet nobody knows what it is……”

In further support although the connection is not immediately obvious due to the technical nature of the paper, in December 2009 year a Dutch physicist, Erik Verlinde  (see )  came up with a theory which has caused a great deal of interest and comment from the physics fraternity, at least it seems to have done so from my limited contact with the latter on the internet. It is a theory that derives Newton’s classical mechanics. This was followed by the publication of  ‘On the Origin of Gravity and the Laws of Newton’ on 6 January 2010. Wikipedia reports as follows:

“In his theory gravity exists because of a difference in concentration of information in the empty space between two masses and its surroundings. He does not consider gravity as fundamental, but as an emergent phenomenon that arises from a deeper microscopic reality. He says that on the smallest level Newton’s laws don’t apply, but they do for apples and planets. You can compare this to pressure of gas. Molecules themselves don’t have any pressure, but a barrel of gas has. Verlinde’s approach to explaining gravity apparently leads naturally to the correct observed strength of dark energy. Previous failures to explain its incredibly small magnitude have been called the greatest embarrassment in the history of theoretical physics. His theory combines the thermodynamic approach to gravity with ‘t Hooft‘s holographic principle. If proven correct, gravity is not a fundamental force, but an emergent phenomenon which arises from the statistical behaviour of microscopic degrees of freedom encoded on a holographic screen. Verlinde’s suggestion of gravity being an entropic phenomenon attracted considerable media and weblog exposure, and led to immediate follow-up work in cosmology, the dark energy hypothesis, cosmological acceleration, cosmological inflation and loop quantum gravity. Also, a specific microscopic model has been proposed that indeed leads to entropic gravity emerging at large scales”.

What Verlinde says himself in the introduction to his paper is as follows:

“In this paper we present a holographic scenario for the emergence of space and address the origins of gravity and inertia, which are connected by the equivalence principle. Starting from first principles, using only space independent concepts like energy, entropy and temperature, it is shown that Newton’s laws appear naturally and practically unavoidably. Gravity is explained as an entropic force caused by a change in the amount of information associated with the positions of bodies of matter.

A crucial ingredient is that only a finite number of degrees of freedom are associated with a given spatial volume, as dictated by the holographic principle. The energy, that is equivalent to the matter, is distributed evenly over the degrees of freedom, and thus leads to a temperature. The product of the temperature and the change in entropy due to the displacement of matter is shown to be equal to the work done by the gravitational force. In this way Newton’s law of gravity emerges in a surprisingly simple fashion.  The holographic principle has not been easy to extract from the laws of Newton

and Einstein, and is deeply hidden within them. Conversely, starting from holography, we find that these well known laws come out directly and unavoidably. By reversing the logic that lead people from the laws of gravity to holography, we will obtain a much sharper and even simpler picture of what gravity is. For instance, it clarifies why gravity allows an action at a distance even when there is no mediating force field. The presented ideas are consistent with our knowledge of string theory, but if correct they should have important implications for this theory as well. In particular, the description of gravity as being due to the exchange of closed strings can no longer be valid. In fact, it appears that strings have to be emergent too.”

I cannot take in the mathematical proofs of the paper but what struck me at once was a number of similarities in his work to proposals. For instance my notion of repulsive gravitation agrees directly with Verlinde’s statement that Gravity is not a fundamental force but an emergent phenomenon, an expression which I had previously not come across. There is also a correspondence in his involvement of the holographic principle with my other work which is not covered at all in these three papers having little apparent relevance to cosmology but the implications of which led  me to the conclusions above.


Davies, P. The Goldilocks Enigma, Allen Lane 2006

Verlinde, E. On the Origin of Gravity and the Laws of Newton, Institute for Theoretical Physics, University Amsterdam, Jan 2010

Nick Greaves,

More recent after thought:

When recently considering the search for dark matter and the nature of WIMPS or MACHOs, I came to a solution of sorts in line with the above proposals as follows. I was aware that one of the reasons for the estimate of dark matter taking up 95% of the universe’s mass was also based on the original observations of Astronomer Vera Ruben from 1980 when she published a paper indicating that the stars on the outer reaches of the galaxy, which should have been circulating around the centre at much slower speeds than those further in, were observed to be travelling at much the same velocities. It was reasoned that the reason for this must that there was a large halo of dark matter stretching out to these outer reaches. No other evidence of this has yet been found, although there have been many experiments searching for  rare massive particles and also theories that the laws of Newton do not prevail at such distances (Milgrom: Modified Newtonian Dynamics). I have to say that my subjective intuition is that such searches will be fruitless.

I was considering the problem recently of why it might be necessary for dark matter to be contained in a halo around galaxies, in order to explain why outer stars were observed to revolve at much the same velocity as the inside stars, something which should not occur according to Newton-Kepler predictions. It suddenly occurred to me that in a spiral galaxy, such as our own, a star in the midst thereof  would be blanketed from the repulsive (or attractive) effect of the outer rim of the universe by all the surrounding stars in that one plane of the spiral on the assumptions made in this paper. When such galaxies are viewed from a distance it is quite possible to see how relatively crowded the stars are placed around the centre of the galaxy. In that plane the usual accepted rules of gravitation and motion might not apply in the midst of that mass of stars due to the repulsive effect of the singular rim of the universe being blanketed off or at least diluted, and they would then each exhibit much the same velocities. I cannot be sure that this would be the result but it seems to me that there would be much less inverse square law involved, and if so then there would be no need for a halo of dark matter to encircle the galaxy in a sphere. Having said that, the stars on the outer edges of the galaxy would presumably tend to rotate at lesser velocities according to Newton-Kepler predictions being seriously blanketed only to one side by the central bulk of the galaxy.

This was speculative enough for me to be interested but not too excited by such a possibility, until I read further from a Wikipedia summary on dark matter that globular clusters of stars within galaxies show little evidence that they contain dark matter. From which I conclude that the inverse square law of gravitation as we understand it acts as we might ordinarily anticipate with the outer stars circulating at appropriately lower velocities. Since globular clusters are spherical rather than spiral, and less densely distributed in one plane, then by the same reasoning as above, this is what might be expected and would not be inconsistent with my explanation of the nature of gravitation. If my reasoning in the development of this hypothesis was not basically flawed, never mind the assumptions on which the whole argument were based, then this was an interesting and simple conclusion to explain why the halo of dark matter around the galaxies was probably a non starter, and reinforce the possibility that gravitation might be regarded as an emergent force. Such an explanation for dark matter would hold good for both attractive and repulsive gravitation.

December 2013