12. Dark matter: A gravitational effect, mediated by the observable and closed universe – 2022

(Revised  Feb 2022)

This paper is an off shoot from my principal interest and various papers on the operation of mind and memory under the general title of Duplication Theory. It is drafted in terms of the first person singular rather than the more usual objective and impersonal approach customary to most scientific papers, it being highly conjectural. My proposals on Dark Matter and gravitation date back to a paper from 2010  that has since been amended and improved in presentation, but at that time was derived to reinforce the concept of the universe being finite and bounded. This was an implication as part of my rationale for  memory’s operation, that there was be a connection between the latter and the shape and structure of the universe. It is the latter that is relevant to the first part of this essay which then later deals with dark matter, on which subject there have been recent astronomical findings indicating possible progress on the connection between dark matter and gravitation.

The Shape of the Universe and the Lorentz Transformation on mass in Rapid Motion

A synopsis of the 2010 paper (25 pages) on Inertia, Gravitation and the Absorber theory, is briefly as follows.  According to the generally accepted FLRW metric (Friedmann, Lemaitre, Robertson & Walker) the shape of the universe is either flat and infinite, or hyperbolic, or closed and spherical in structure.  If the version of the closed and spherical universe is assumed as the most likely, being the easiest to visualise mentally, then we are also aware that in terms of the observable universe, the latter is expanding out at light speed with a currently estimated radius of about 46.5 billion light years. This assumption led to a possible scenario which could be split into two alternative versions to explain how and why gravitation acts, as opposed to quantifying the force with which it operates, defined by Newton’s inverse square law. These two alternatives are as follows.

An observer on a star system not that far distant from the centre of such a sphere expanding out from the origin point of big bang, would be traveling out a velocity far less than that of the star systems of galaxies of matter close to the singular periphery of the spherical universe, which would  travelling at near light speed.

Due to the effect of the Lorentz transformation, the mass energy equivalence of these far-flung bodies on their slower moving galaxies further within, would be relativistically vast. If so, then the resulting gravitational effect of these outer galaxies at near light speed on these interior star systems would be enormously augmented. This assumption led to two alternative possible proposals for a mechanism behind gravitation, which also then leads to an explanation for dark matter.

The first alternative assumes that attractive gravitation effect of the almost infinite relativistic mass of the outer galaxies on those at inner levels from all directions from the containing sphere, would create inertia in the form of resistance to an omnidirectional increase of acceleration. This would appear to be in accord with Mach’s principle, which to my knowledge has never been satisfactorily explained. The problem here, very briefly, is why does a suspended Foucault’s pendulum oscillate with reference to the stars and not the Earth’s rotation. Mach allegedly described his principle as “When the subway jerks, it’s the fixed stars that throw you down”. This can be more formally be described as ‘Every particle of matter in the universe, and its motion, has an effect on every other particle elsewhere.’ From when I first made this observation a number of decades ago, I have maintained a persistent intimation that there must be a strong  connection between gravitation and Mach’s principle.

Thus,  the very substantial quantities of matter near the periphery moving outwards at near light speed would exercise a huge attractive effect on all matter further within. If, for instance, the attractive force of just one nearby section of the expanding universe on, say the Earth, were considered, and if the inverse square law were invoked, this would be exactly countered by the much larger opposing section at the opposite end of the universe, albeit so much further distant.  In short, there would be equilibrium of all such forces of attraction, assuming that matter was moving at constant velocity rather than accelerating.

Then, if a further assumption was made, that that this rim of the expanding universe would be travelling at light speed, then as such, it would be the largest singularity state conceivable. Beyond the limits of the expanding spherical universe, there would be another continuum, which we could never register or experience.

About 40 years ago it first occurred to me that all the electromagnetic  (EM) waves emitted from any such source of an oscillating charged particle might possibly be drawn out to duplicate the action of this huge singular rim. In other words, the EM radiation (photons if conceived as particles) would to be  drawn out at the same velocity to duplicate the direction and action exactly of this very singular edge of the universe. At that time, I had failed to become aware of the of the limitations produced by the fact of the observable universe, and which only occurred to me in this context in early 2021, inexcusably late as ever (further comment on the consequences of the observable universe is described towards the end of this paper). Such a scenario also would provide a remarkably simple explanation for the action and behaviour of electromagnetic radiation.

Thus, if this further assumption is made that this singular rim travelling out at light speed, supported by the existence of the observable universe, here would effectively be a resonance or duplication effect, mediating the motion and action of all EM radiation within. This should in turn  enable a number of existing unknowns to be resolved as to the way in which action is transmitted across space at light speed to be presented with some seemingly simple answers.

An Alternative Interpretation of Gravitation’s action

This assumption led to a second possible alternative explanation for gravity’s action if it was assumed that it acted as a repulsive tendency rather than attractive. Inevitably this was very counter intuitive, but it leads to a possible solution of great simplicity and efficacy allied to the assumption of an expanding spherical  universe. 

Such a gravitational force would act inwardly on all matter within, due to the multiple peripheral star systems traveling outwards at near light speed. The relativistic energy mass of these would act overwhelmingly inwards  to centre of such a contained universe. But if so, planets would not spin around stars and life would not be held down to the surfaces of the planets. However, there is a relevant analogy here which seems to give a not impossible answer, and which as far as I know, has never occurred to anybody else yet.

The effect of transmission of EM radiation across space is very much reduced if conducting material is placed between the transmitting source and a receiver. In short there is a very palpable blanketing and reduction effect in the transmission of electromagnetic energy across space, in which case why should not the same apply to gravitation?

If it did then the result would be an apparent attraction effect within the universe due to one large stellar mass blanketing off this total inwards repulsive force, from the mass of a smaller planet in close proximity. This would result in the smaller mass being apparently pushed (seemingly attracted) towards the larger mass. So simple really, almost suspiciously convenient but it ought to be worthy of serious consideration, there being so little existing understanding of how and why gravitation appears to act attractively, other than we have always assumed that it just does.

It has also occurred to me that the old saw of ‘like repels like and opposites attract’ certainly applies generally to electromagnetism for no known reason other than it just does. In which case it would seems suitably parsimonious if the same rule applied to this other all too pervasive tendency of gravity.

In summary my conjectures on gravitation are  contrary to the current favoured assumption that the universe is flat and probably infinite, although neither version, together with some others, have yet been proved with any certainty on the question of the shape of the universe. However, it seems possible that the recent launch of the Webb telescope might provide more concrete information about the structure and composition of the universe. The Hubble and other recently launched telescopes have shown us how many of our recent assumptions of the latter have been not only misleading but possibly even crashingly  wrong. I have assumed  that NASA are not inclined to spend $10 billion without good reason, bearing  in mind that apparently the cost of construction of the HCL by CERN on completion in 2010 was also about $10 billion.

Spinning Spiral Galaxies and Dark Matter

Reverting  to dark matter, in 2013 I added an afterthought to my 2010 paper. This demonstrated how my rationale indicated that dark matter was a misnomer, it being nothing to do with particles, but instead it could result from increased gravitational effects in the plane of a spiral galaxy which would  not be observed in spherical globular cluster galaxies. There would be, ex hypothesi, no such augmented gravitational effect in a spherical galaxy with equal external gravitational force of attraction in all directions, as opposed to the external effects created in the plane of spiral or elliptical galaxies. At that time there had been a few observations of spherical cluster galaxies indicating no dark matter. This led me later to draft a more definite rationale on dark matter in another paper later in mid-2020, shortly after I had read about two recent astronomical studies on dark matter, one from Durham university, (Oman 2019) and another slightly earlier study from a large team of Chinese astronomers (Qi Guo, Zheng  et al 2020).

Both teams had observed that spiral galaxies are spinning faster than they should be according to Newton’s inverse square law of gravitation. Astronomer Vera Rubin made this observation about our galaxy in the 1970s which was disgracefully ignored for nearly a decade,  rather than an award of  the Nobel. This observed effect was then, and is still now, thought by a large majority of expert academic opinion, to be due to the presence of large amounts of heavy matter within their spiral structures, which is now called ‘dark’ being otherwise undetectable.

Telescopic techniques are now so advanced that they can measure spin for very distant galaxies, and their many recent observations have also recently established that smaller globular cluster galaxies which are effectively spherical, do not show any increased rate of rotation, delivering the conclusion  there is no dark matter surrounding them.

By 1980 it was shown most galaxies must contain about six times as much dark as visible mass. Thus, there appears to be a possible answer in terms of gravitation rather than the prolixity of various exotic particles proposed to date. 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 a spiral galaxy, such as our own. In which case the gravitational effect on a star in the midst thereof might be greatly increased by the attractive effect of the relatively close proximity of the other star systems in that flat plane of the spiral, or indeed elliptical galaxies, but not at right angles to the plane of the spiral, where the gravitational attraction would remain much the same.

The forces of attraction in the flat plane of the spiral would be over and above the gravitational effect of the singular rim of the spherical universe expanding outwards spherically in all directions. The result would presumably be that a majority of stars in the midst thereof, would each exhibit similar higher velocities of rotation than those which would otherwise be indicated by the inverse square law. If so, there would be no need for a halo of dark matter to encircle the galaxy. Since globular cluster galaxies are spherical rather than flat and spiral, and thus less densely distributed in any one plane, then ex hypothesi, this is what might be expected and which would be consistent with my explanation of the nature of gravitation mediated by the relativistically immense mass energy of galaxies near the peripheries expanding near light speed. Hence there is no need for dark matter but just a revised version of the gravitational effect experienced along the flat plane of a spiral galaxy.

Dark Energy

However, this does not explain why the universe should not only be expanding but that its rate of expansion is also increasing, and which has posed an apparently insoluble problem to date for the cosmologists. Soon after the  counter intuitive conjecture occurred to me that gravitation might possibly act repulsively via a blanketing effect of matter on adjacent matter within the universe, as opposed to the apparent attraction effect described above, I realised that such a repulsive effect would also conveniently account for the expansion of the universe. Since the success of Saul Perlmutter’s astronomical observations in 1997, resulting in a Nobel in 2011 we now know the universe is not expanding at a constant velocity, as formerly believed, but instead is instead accelerating out at increasing rates of velocity.

Such a scenario for repulsive gravitation would also provide a very simple answer to the problem of dark energy which has been an insoluble problem for cosmology and astrophysics over the last couple of decades, in attempts to account for the observed increasing outward expansion of the universe.

If the explanation for dark matter is not connected with a redefinition of gravitation, then so be it, but the search for dark matter particles has been continuing with negligible indication of success for decades. Moreover, given the recent successful launch of the Webb space telescope on 25/12/21, there appears to be a reasonable chance that observations for the latter will be very informative about the composition and structure of the universe, which is one of the main intended functions of the project.

The Correlation between the Passage of Time and Expansion of the Universe

There is a further fascinating consideration about the expansion of the universe. In 2019 I attended a lecture by physicist Carlo Rovelli, in which his description of his recent book ‘The order of Time’, made a crucial point that had not previously occurred to me. He stipulated that in an isolated process of increasing disorder, known as entropy, the latter could be measured, and that it could increase or remain the same but that it could never decrease. In other words, heat passes only from hot bodies to cold, and never the other way round. He then explained that this is the only equation of fundamental physics that knows any difference between past and future, which is crucial for any discussion on the nature of time.

The growth of entropy is nothing more than the familiar and natural increase of disorder over time. Thus, the entropy of increasing disorder is the only way we can know that there is a past and a future time, and it can only flow in that direction at a fundamental level. We know that the entropy of the universe is increasing as it expands, and on that basis, if the not unreasonable assumption is made that the passage of time was to be directly proportional to and governed by the rate of expansion of the universe, the resulting possible implications are fascinating.

Since 1997 we know from observations of supernovae, that not only is the universe expanding, but also that the rate of expansion is accelerating.  On the assumptions described above, that the universe is closed, bounded and finite, expanding out at light speed, it occurred to me in the late 1970s that it might be no mere coincidence that in such a scenario, the rate, direction and velocity of this singular rim would appear seemingly to be duplicated by the motion of all EM radiation within the universe. If this were the case then if the rate of expansion were to vary, up or down, then light speed might mimic that action, although it would be presumably hard to decipher as an observer on such a planet, unless of course time might actually start to reverse.

Asymmetry of EM Radiation and Passage of Time

 On this conjectured basis, not only would the passage of time be directly linked to the rate of expansion of the universe, but also the way in which EM radiation would be acting to mimic the latter. Not only would the velocity of EM radiation be duplicated by the velocity of the rim of universe in all directions, but also its particular structure. This would not be a perfect sphere, but rather an ellipsoidal shape depending on its location within the universe. However, to an observer within on a particular planet, EM radiation created from an oscillating charged source would appear relativistically to be radiating action out as a perfect sphere at light speed in all directions. But for a mythical observer outside the universe, the structure of the radiation waves would appear to be ellipsoid, and varying with the distance from the initial point of the big bang location.

One implication of this model is that time would be standing still at the singular rim of the singular universe expanding out at light speed, and if for whatever reason the expansion were to reverse into contraction, time within the interior would have to reverse. Such a conclusion might be pleasing to all physicists who defer to the fundamental rule that all effects in nature ought to be symmetrical, whereas currently EM radiation, being outwards only, offends this tendency as it is currently experienced.

The Absorber Theory of Feynman and Wheeler

One of the reasons that such a scenario occurred to me decades ago was that such a hypothesis is not dissimilar to some elements of the ingenious Absorber theory of Feynman and Wheeler (1945). This is well known enough to most physicists but not considered that relevant today. The two of them produced it together to demonstrate EM transmission of photons could be considered as a symmetrical effect which is currently not experienced, being retarded or travelling only one way outward, never apparently to return.

The Absorber theory showed how EM radiation could be considered symmetrical via a rationale of possible time reversal with advanced or incoming EM waves in compensation. It was also based on the assumption that such transference of EM action could be transmitted as a non-local force at a distance. This apparently also resolved anomalies of the difficulty of one particle going through two slits at the same time to produce an interference pattern on a screen. I use this scenario to support that part of duplication theory which involves a quantum entanglement effect for the transfer of similar structures of firing synapses in the form of memory across time.  A crucial factor for the operation of the Absorber theory to operate, is that is has to be assumed that the whole system is enclosed within an opaque box.

But that was exactly how my conjectured universe within the singular rim also has to be arranged to explain gravitation, although I do not know whether Wheeler or Feynman considered that such an opaque universe exactly matches one which is bounded and finite. However, I now have a vested interest in such a belief, and it is encouraging to read that two of the last century’s finest physicists produced a theory which appears to support my proposals as  to the shape of the universe. Duplication theory describes the operation of mind and memory which also explains the transmission of EM action as a nonlocal effect, as does the absorber theory, and both are based on the assumption of a closed and finite universe.

Unless we have more accurate information about the nature of such major unknowns of why and how, for instance, gravitation operates, and for how and why Mach’s principle operates, it seems unlikely that we might ever be able to obtain more than a superficial grasp of existence. Another such major but little queried unknown is why light speed should be at one particular constant value rather than variable. I anticipate that a number of our existing belief structures will have to be radically amended or possibly discarded in due course, in which case the sooner such fundamental questions are recognised as crucial, rather than just assumed as unquestioned givens, the greater will be the rate of increase in our understanding of existence.

The Observable Universe and its physical limits

When I first drafted an initial version of this paper in 2010, there seemed little concrete evidence existing to support such a closed system, until last year in 2021 when I belatedly realised that the concept of the observable universe acted to confirm that we can never be aware of anything beyond  this radius of this circumference. This latter fact in itself suggests that the universe has to be considered closed and bounded, although such a conclusion does not seem to have been taken seriously by many others assuming they have even considered the possibility in the first place. However, the launch of the James Webb space telescope on 25/12/21 might change things here. One of its functions is to see back far closer in time to the big bang via the red shift, than has been managed in the past. It seems there might be a reasonable chance that we might thus be able to establish by observation a far better understanding of the composition and structure of the universe.

In the last few decades, the Hubble and other newer telescopes have already ascertained that our current understanding of the latter has to be much amended to explain the filamentary structure of the galaxies, and other inexplicable phenomena such as the Sloan great wall, not to mention the embarrassing possible existence of Dark matter.  I wait to stand corrected and amazed if the latter transpires to be anything connected with particles.

But, if my prediction of the nature of dark matter as gravitational, transpires to be along the lines described above, or other variations thereon, such a result would be a huge paradigm change for our understanding of the laws of nature and physics. There have been a number of theories proposed   by others on a gravitational basis, (Brans, Dicke 1921; and Sciama 1953)  most of them now discarded, but some fresh versions have been put up recently. In late 2021 Sabine Hossenfelder revoked her earlier belief in particles, to assume it must be some new gravitational effect. The recent few gravitational theories I have come across, involve radical revisions making assumptions that the law of gravitation is not constant but variable across the universe, depending on location and other factors yet to be ascertained. Mathematical arguments supporting such theses are complex and beyond my competence. It is possible that observations from the Webb telescope might provide indicative information about the structure and composition of earlier times not that long after time of the big Bang, and if so, the conundrum of dark matter might be resolved together with clarifying evidence about the mechanism and action of gravitation, still sadly lacking.

Gravitation and Mach’s Principle

Inevitably my preference is for parsimony of circumstance and explanation, and the explanation above also supports my description of the significance of Mach’s principle. This conjectures that there is a direct connection between Mach’s principle and inertia, and thence with Gravitation, which I described earlier in an earlier paper:Mach’s principle, inertia, gravitation and dark matter (revised February 2021), but which this paper now updates and further revises.

My interpretation of gravitation, in its connection with the shape and structure of the universe. as described above, also has a fundamental connection with the operation of mind and memory, in connection with the shape, structure and composition of the universe as briefly intimated with reference to the Absorber theory above. The latter is my first interest and on which subject I have a number of relevant papers under the general description of Duplication theory, dealt with elsewhere ( and ResearchGate).

Nick Greaves
16/01/22 Revised 21/02/22


Rovelli, C. Order of Time,   2018

Friedmann, A. Zeitschrift fur  Physik, Vol2 21,  1924

Mach, E. The Science of mechanics, The Open Court Publishing Company 1893

Mach. E. History and the root of the Conservation of Energy, Open Court, 1910.

Wheeler, J & Feynman, R. Interaction with the Absorber, Rev Modern Physics 17, 157-161  1945.

Brans C. & Dicke R. Mach’s Principle and a Relativistic Theory of Gravitation, Physical Review, 1921

Sciama, D. On the Origin of Inertia, Royal astronomical Society Notices, 1953

Oman K. 19 newly discovered Dwarf Galaxies, Astrophysical journal letters 25/09/19

Qi Guo, Zheng  et al. Further evidence for a population of dark matter deficient dwarf galaxies, letter published 25/11/19, Nature Astronomy, 25th November 2020

Greaves, N.G. Correlation of information across space and time to explain memory via Quantum Entanglement,,  2018

Greaves N.G. Passage of Time,  2019

Hossenfelder- S.  Is dark matter real? 07/10/21