Amendments and updates to Sections D & E with effect from January 2011
An early version of this website was put out first in spring 2007 and since then I have read more cosmology and as a result, section D on the isotropy of light and the Absorber Theory, together with section E on Cosmological implications, need to be updated and amended. In January 2010 a Dutch physicist, Erik Verlinde, published a paper on the origin of gravity and the laws of Newton which encouraged me to consider that some conjectures on this subject that I had entertained some years ago might be worth revisiting and setting into print. I also read about the cosmological work of Edward Arthur Milne, Rouse Ball professor of Mathematics at Oxford who died young in 1950. Towards the end of 2010 I completed a paper on this subject in three sections and this is set out below. Although the conclusions derived therein are as a result of my earlier work on Duplication Theory, it will be noted that there is no reference to this in the paper below. This is because theories on the mind’s operation are notoriously difficult to verify prove by repeatable experiments, whereas my cosmological conjectures if anywhere near constructive, should be more easily verifiable by astronomical observations or arithmetical proofs by the astrophysicists.
Mach’s PRINCIPLE, GRAVITATION & MATTER DISTRIBUTION
These are three separate but related papers containing conjectures of Cosmology.
- Mach’s Principle and its correlation with gravitation & inertia.
- 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.
- A further conjecture by the inversion of paper 1 to demonstrate negative gravitation and other resulting implications.
Synopsis paper 1
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.
Having been surprised in my teens at the explanation of the way in which the Foucault’s pendulum swung in the entrance to the Science Museum in South Kensington, and its implication that it bears out Mach’s Principle, some years later I read everything that Mach had written translated into English, to see if I could work out a connection between gravitation, inertia and this apparently inexplicable principle. 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.”
I give just one quote from his Book ‘Conservation of energy’
“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.”
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. My attempt to rationalise gravitation and Mach’s principle with inertia was as follows. I had to make a few assumptions, the first being to consider the universe as bounded and finite, which is one of the possible alternatives from the those developed by Alexander Friedman in 1922 and then later by LeMaitre, Robinson and Walker) and which is still very much unresolved. 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 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 would be no such continua of time and space. Reinforcement for this scenario was provided by 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 the initial explosion matter starts to precipitate out from the hot plasma as energy spreads out and the universe cooled down. When first considering the problem it occurred to me that this precipitation of matter starts initially furthest out from the hot centre as it spreads out and starts to cool, in which case there would be a higher concentration of matter further out towards the edge of the universe which is the position as shown in Diagram 1. However it seems more acceptable to assume in accordance that the distribution of matter in space is homogeneous as per Friedman’s solutions for an expanding universe and we know from Hubble’s law that it is expanding and that this even distribution has been confirmed as (far as can be observed which I conjecture is probably minimal relative to the actual full dimensions of the universe) by the sky maps produce by the WMAP and Planck satellites.
In this scenario the matter near the edge will be traveling at close to light velocity, so whichever alternative is correct, there would be far larger concentrations of matter distributed nearer the rim as far as an observer within, much closer to the big bang centre, due to the effects of the special theory of relativity. (See Diagram 1).
To repeat a crucial point: the mass of the outer edge galaxies would be relativistically huge if they were traveling at near light velocity in relation to galaxies further in moving out at much lower velocities, regardless of whether the matter distribution was homogeneous or not. The attractive force of gravitation exercised by this vast mass moving out would be experienced by all lesser matter within. 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.
Thus 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. In short there would be equilibrium of all such forces of attraction assuming the matter were moving at a constant velocity rather than accelerating.
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 so that the effect of inertia would be inextricably intertwined with the attractive force of gravitation. There would be no effect of inertia without the existence of the huge hidden mass of the universe expanding out near its periphery.
My 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 not evenly distributed within. Observations from astronomy have indicated since the 1970s that 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. 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
C.Brans & R.Dicke. Mach’s Principle and a Relativistic Theory of Gravitation. Physical Review , November 1961
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 homogeneous 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 neighbourhood 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 two further are made, then the behaviour of Electromagnetic radiation can be qualified in a manner in many respects similar to the results of the Absorber Theory by Wheeler and Feynman in 1945. 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 other words a huge singularity. The big bang has created a universe of time and space the outer edge of which is EM radiation which I call the singular rim for convenience, and which is expanding out at light velocity. The second 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. There is a rationale for this assumption which is not included in this paper for reasons of brevity (see www.mindandmemory.net) but the results clarify the isotropy of light in a manner easy to understand.
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 rim exactly in all directions, and will radiate out in the form of a slightly squashed sphere (an ellipse?), flattened along the line of motion, as far as a notional observer outside the universe was concerned. 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 a hypothetical external observer outside the system, and stationary with respect to the centre of the universe. 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, or 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 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.
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. This would bring about the satisfactory conclusion of symmetry being achieved, 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 and also Joao Magueijo of Imperial University, London.
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, 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 this elegant and short paper I 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.
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 ‘Space and Time in the Modern Universe’ by P.C.W.Davies, who was then Lecturer in Applied Mathematics at Kings College London. 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 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 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 for reasons which are ably explained Davies’s book.
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, reversing the big bang.
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. The closed universe as I have described it is effectively an opaque box as required by the Absorber Theory, all the more so if for whatever reason the universe started to contract rather than expand: all EM radiation within would also reversed 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 the mediating speed of light, would never have progressed from the first moment of big bang. 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.
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
Joao Magueijo. New Varying Speed of Light Theories, Astro-physics, Oct 2003
Nick Greaves. Lesignac Durand, Charente 29/08/10
3. An inversion of paper 1 to account for Dark Energy and the expansion of the universe
Synopsis Paper Three:
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 in sections 1 & 2 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. 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 lesser masses) 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. Some implications of this scenario are given for Dark matter and energy.
This third paper is very speculative indeed. 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, and such a scenario would also give a rationale of sorts to entropy in general and for the outward expansion of the universe.
There has been some theorising that dark energy might need to be represented generally in the form of negative gravitation since the universe appears to be expanding faster than anticipated. 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. the position on the relativistically vast mass close to the rim is as described in section 1 above still holds good, showing the universe with most of the matter near the outside edge expanding out at close to light velocity
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 (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, 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.
This conjecture is confounded by the fact that a dropped weight falls to Earth rather than shooting upwards. However a simple possibility recently occurred to me which did not seem too unreasonable, and which can best be described as the possible existence of a blanketing effect. Such an effect certainly exists when a mass of conducting material is placed in the way of EM radiation. 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.
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. 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 above, except that the forces are outgoing instead of the reverse. In short there would be equilibrium of all such repulsive forces assuming the matter were moving at a constant velocity rather than accelerating so that there would be an inertial effect on this interior matter if it were to be made to accelerate.
However if two stellar bodies 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. It appears that here is some sort of alternative scenario for the explanation of gravitation as a repulsive force. In order to rationalise the extreme case of the attractive gravitational forces of neutron stars, it has to be assumed that the repulsive force created by the prolixity of stars and galaxies at the outer edges is vast and all pervasive which it will be if every object with rest mass is subject to inertia. It also has to be assumed that the blanketing effect is incremental, rather than just on or off. 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 for instance, a neutron star.
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.
If gravitation were a repulsive force which could be blanketed by intervening mass then a basic rationale for dark energy and indeed the big bang at once suggests itself. A section on the problem of dark energy in Paul Davies book ‘The Goldilocks Enigma’ seems relevant.
“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 https://staff.science.uva.nl/~erikv/page20/page18/page18.html ) came up with a theory which has caused some interest and comment from the physics fraternity. 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. The abstract reads as follows: “Starting from first principles and general assumptions Newton’s law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies.
A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton’s law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.”
My proposal of repulsive gravitation agrees with Verlinde’s statement that Gravity is not a fundamental force but an emergent phenomenon. 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
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 were observed to be travelling at much the same velocities as those further in which conflicted with the inverse square law. 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.
It occurred to me recently 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 their 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 so then here was a 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. I understand that dark matter has to be cold, which would also fit very well with my proposals. Such an explanation for dark matter would hold good for both attractive and repulsive gravitation.