The Rouke-MacKay model raise a number of speculative ideas that challenge, not only the galactic rotation model, but the very framework of the current cosmological model. While many aspects of this speculation will not be addressed directly, given that they can be reviewed via the published papers, now might be an appropriate point to provide some reflective background to this type of speculation. As such, it might be worth injecting a note of caution at this point; for while the Big Bang model appears to have its own set of issues, it is also predicated on some extremely compelling arguments, e.g.
- Big-Bang Nucleosynthesis
- Baryon Acoustic Oscillations
As indicated, the big bang model is a composite of two expanding density models, i.e. the inflation model followed by the ΛCDM model. Although the very early inflation model is still highly speculative, the two topics listed above appear to provide some compelling arguments for the follow-on ΛCDM model. However, as these topics are not really the focus of this section of discussions, they will only be outlined by way of reference:
This theory relates to the relative abundance of, and the process by which the light elements, i.e. deuterium, helium, and lithium, were produced in the early universe.
In an expanding model, the early Universe is assumed to have been very hot, such that matter would only have existed as ionized particles, i.e. protons, neutrons and electrons. Note, the stability of electrons within an atomic structure is dependent on photon energy, which may be linked to another process called ‘decoupling’ such that nucleosynthesis is really only considering the formation of atomic nuclei, i.e. protons and neutrons. In this context, free neutrons only have a stability of ~10 minutes before they will decay into a proton, electron and neutrino. Therefore, without the process described as nucleosynthesis, it is argued that the universe would have ended up consisting of only protons and electrons, which on cooling pass the photon ‘decoupling’ point would have resulted in a hydrogen universe. However, as the temperature fell, due to expansion, the process of nucleosynthesis started to produce the nuclei of lighter elements in which protons and neutrons began to combine to produce deuterium, i.e. 1 proton + 1 neutron. This is then followed by the collision of deuterium with other protons and neutrons to produce helium and a small amount of tritium, i.e. 1 proton + 2 neutrons. Lithium was formed as a combination of tritium and 2 deuterium nuclei. The net result of this process is that the protons and neutrons in the universe end up in a 6:1 ratio, which eventually explains the basic composition of the observable universe being 73.9% hydrogen to 23% helium with all other elements being accounted for within the remaining 2.1%.
While the strength of the argument above is anchored in accepted particle physics, it is also highlighted that the same expansion model leads to the idea of the critical density of the universe in which baryon matter only accounts of 4.6% of the ‘substance’ of the universe. The remaining 95.4% of the universe is then explained in terms of 72.4% dark energy and 23.0% dark matter, which have no accepted explanation within the current particle model. It is also quite difficult to find any authoritative information on how the decimal point accuracy of these figures was determined or verified against observation.
Baryon Acoustic Oscillations(BAO):
The explanation of BAO is quite technical and so the following note is simply an outline linked to the previous description of nucleosynthesis. Based on this description, the early universe consisted of a hot, dense plasma of electrons and baryons, i.e. protons and neutrons, where high energy photons underwent continuous collisions with baryon particles prior to ‘decoupling’
However, analysis of the Cosmic Microwave Background (CMB) radiation suggests that the primordial plasma was subject to density fluctuations. Within these density fluctuations, matter is subject to greater gravitational attraction that then produces heat due to photon-matter interactions plus an outward pressure. As a result of the counteracting mechanisms of gravity and pressure, oscillations in the density occurred, which might be described in an ‘analogous’ way to sound waves created by air pressure differences, hence the term ‘acoustic’. Such mechanisms suggest that a spherical ‘acoustic’ wave of both baryons and photons would move out from the centre of the density fluctuation at a speed estimated to be over half the speed of light [c]. Before the decoupling event, the photons and baryons were essentially constrained to move outwards together, but after decoupling, the photons are no longer constrain to the lower aggregate velocity of baryon matter and so diffuse outwards at a faster rate. This reduced the pressure within the system and left a ‘shell’ of baryonic matter at a fixed radius, sometimes referred to as the sound or acoustic horizon. However, the fluctuations in the baryon density continued to attract matter, which eventually leads to the formation of galaxies. As such, theory suggests that a greater number of galaxies should be separated by the sound horizon and, if so, the universe would not support one acoustic oscillation, but many overlapping oscillations. While it is not possible to observe this preferred separation of galaxies on the sound horizon scale by eye, the pattern can be measured statistically by looking at the separations of large numbers of galaxies. Of course, there are a lot of technicalities and assumptions buried in the details of the underlying, but supportive evidence, which extends way beyond the ability of this discussion to assess.
While the density fluctuations of the universe appear to underpin many important mechanisms within the expansion model, the ΛCDM model itself is still anchored in the large scale assumptions of a homogeneous and isotropic universe. Within this model, the critical density is uniformly distributed throughout the universe, although its value and component make-up vary as a function of time due to the ‘equations of state’ of each density-pressure component. However, while thermodynamics appears to play an important role in some of the processes being outlined, the accepted large-scale model of the universe appears to be dominated by gravitational ‘forces’. While those appreciating the complexity introduced by special and general relativity might question the retention of Newtonian terminology, it is a requirement that relativistic theories converge towards the Newtonian approximation, when the relativistic effects of velocity and gravity are not a major consideration. In the context of the large-scale model of the universe, space appears to be geometrically flat [k=0], such that any implied gravitational curvature around even super massive galactic black holes equates to only a microscopic pin-pricks in the total spacetime of the homogeneous universe. If so, we might return to the idea outlined in an earlier discussion of Newton’s shell, which led to two variants of Newton’s law of gravitational force. The first variant shown below is the classical solution of a gravitational force between 2 masses, i.e. [M,m] separated by a distance [r]; see diagram below for reference:
This is the external solution of Newton’s shell theorem, which he used to prove that the gravitational force is a function of the distance between the centre of the mass linked to [M,m]. In this context, if we assume the energy-mass density within a black hole horizon is also homogeneous, then the external gravitational force does not demand that it has to collapse to a point singularity: see later table related to the idea of matter degeneracy. However, the current focus is orientated towards the internal solution, which has the following form:
In , the radius of the shell is defined as [a], which is a constant and suggests that a mass [m] within the shell of mass [M] feels no gravitational force anywhere within the volume of the shell. This result would appear to hold true irrespective of the thickness of the shell, provided it was uniform in density. Therefore, while Newton’s theorem was based on a shell of a given thickness, there appears to be nothing in the theorem that restricts the thickness of the shell. As such, there would appear to be nothing to stop the theorem from being extended to a homogeneous volume of space of a given density, where the density might be reduced to that of homogenous intergalactic space. While we might wish to draw some parallels with the Newton shell model and the ΛCDM homogeneous model, there are a number of variants that need to be considered:
Let us start by assuming that the radius [a] is finite, which means that we can define the contained mass, e.g. [M2], plus assume that there must be some gravitational centre of this mass. As such, if we now place a smaller mass [m] at any arbitrary position within the larger homogeneous volume, it will be attracted to the gravitational centre defined by [M2], although the effective mass [M1] will now be defined by the positional radius [r] of mass [m]. So by the rules of  and , mass [m] is not affected by the implied mass in the external region, where r<a, only by the internal region, where r>a. Of course, if we were to assume that the size of the red dot in the diagram above, linked to mass [m], was actually the size of our visible universe and the energy-mass it contains, we would have to consider the implication of the free-fall acceleration under the gravitational pull of mass [M1] related to the radius [r] position of our visible universe within some larger, but spatially finite universe. While the gravitational acceleration might be enormous, it might also be argued that its effects might be similar to free-falling within an enclosed elevator. In this context, the elevator would define the frame of reference for all observations, where the motion of everything within our visible universe could only be measured relative to this local frame of reference.
But what implications would follow from a spatially infinite universe?
In terms of the ΛCDM model, the ‘physical’ universe already extends beyond the ‘visible’ universe, as defined by [R=c/H], as linked to the description of the ’particle horizon’. However, most cosmologists now seem to accept that the physical universe could extend so far beyond the particle horizon that many may describe the universe as being infinite for all practical purposes; although in truth, nobody really has any idea just how big the universe might really be. In this respect, it may not be so unreasonable to consider the implications of extending the simple Newton shell model to an infinite radius. If so, one implication of an infinite universe is that it would make the definition of a centre of gravitational mass ambiguous, such that mass [m] would not necessarily be subject to any net gravitational effect from the rest of the universe. As such, gravitation would be limited to a description of localised fluctuation in density within a generally homogeneous universe; although this model might in-turn be problematic to Mach’s principle, i.e. as the possible cause of inertial mass. Within the context of the Rouke galactic model being used as a framework for discussion, there appears to be no obvious description of how Mach’s principle might actually link the local inertial frame to the mass in the rest of the universe, e.g.
|“…the Kerr metric fails to be Machian precisely because the chosen boundary conditions (a central rotating mass with no mass at infinity) are incompatible with Mach’s principle, which requires the concept of rotation to be related to other static matter.”|
However, it may be possible that the implied conflict between an infinite universe with Mach’s principle is just a question of whether the scope of all matter interactions within an infinite universe can still have some form of finite limit or boundary condition. While we shall refrain from getting too carried away with all this additional speculation, it might be worth considering whether there could be some mechanism that could link the matter within some arbitrary local frame of reference, e.g. a rotating galaxy, to the distant stars. For Mach’s reference to ‘distant stars’ seems to suggest some form of interaction between a local system of particles and all the other particles in the ‘visible’ universe. The use of the word ‘visible’ is used in the sense that this interaction mechanism might have some finite limit due to a form of ‘opaqueness’ within the matter universe. For example, based on the particle density of inter-galactic space, there must come a point, where the direct ‘line of interaction’ to other more distant particles in the physical universe becomes blocked by intermediate particles. If so, then any interactive mechanism between matter particles may be limited by this form of opaqueness and give some tangible credence to Mach’s principle, as well as defining a finite boundary condition for any metric of spacetime, as being researched by Rouke. We might consider the implications of merging the infinite Newton shell model with the idea of some finite boundary condition.
In the diagram above, a spiral galaxy is placed at the centre of its own arbitrary ‘visible’ universe, where the distant stars are analogous to an extremely thick shell of mass [M], such that there is not net force on any mass, i.e. [m1] or [m2].
|Note: There would appear to be a caveat to the zero net force statement above in an expanding universe. As described, gravity might be seen as a force [FG] that binds all particles to each other, which based on the Newton’s shell argument might cancel out. However, this status-quo would appear only to hold true in a static universe. For in an expanding universe, there has to be some other force [FX] that over-powers this status-quo that drives the expansion. So while we might assume that the force of gravity [FG] would tend to slow this expansion, the actual expansion force [FX] need not have any obvious relationship to [FG], such that [FX-FG] is not necessarily proportional to [FG].|
However, if every point in the physical universe can define a finite boundary, e.g. radius [R], where the ‘opaqueness’ blocks all further direct matter interaction, we might proceed to consider the implications of Mach’s principle within this model. As such, the distant stars within radius [R] are simply part of the homogeneous density of a finite ‘visible’ universe, which Mach’s principle suggests is the root cause of the inertia of all mass objects, when subjected to an acceleration. However, with respect to the diagram above, let us first consider mass [m2], which is not subject to any acceleration force, i.e. [F=ma=0], but is travelling with constant velocity [v]. Now the Newton shell model suggests that mass [m2] is subject to a force from every particle mass in the universe, now constrained by the radius [R], which within the internal space of the conceptual infinite shell complies with , i.e. all forces cancel out. As such, we might formulate the situation as follows:
In , the suggestion is that the mass [MS] of the universe is defined by a finite radius [R] and the density [ρ], which we might assume remains constant over any reasonable time period, i.e. all of human history! Although mass [m2] is moving with a velocity [v], the geometry of Newton’s internal shell solution does not really change in each snapshot in time. As such, there is no local perception of any force [F=ma=0] on mass [m2] and we might begin to see a possible correlation between the gravitation mass and the inertial mass. However, if we extend the logic in  by assuming that mass [m2] is subject to an accelerating force, i.e. [F=m2a>0], then:
Based on , the inertial force associated with [m2] has also be linked to the gravitational force, which links the inertial and gravitational definition of mass. If we now consider mass [m1] rotating with constant velocity within a spiral galaxy, it might initially appear that there is no obvious acceleration within the local reference frame. However, the rotation of [m1] causes the distance between itself and every star in the visible universe to change at a variable rate that could be interpreted as a cyclic acceleration with respect to the distant stars. If so, then  might now be interpreted in the following form:
If so, Mach’s principle would interpret the dynamics of a rotation, even with constant velocity [v], differently as there would appear to be a cyclic force on mass [m1]. Of course, at this stage, this idea is only speculation, although it is a speculation that will be reviewed in more detail under the heading of the ‘Wave Structure of Matter’, which considers the suggestion as to why the matter interaction is limited as outlined.
So do such speculations have any conclusions?
In a word, no. However, it is not clear that any real certainty exists within the scope of cosmology, as it stands today, although some might reasonably argue for a specific model on the grounds of probability. In this respect, the generally accepted cosmological model is considered to have the highest probability, presumably based on the consensus of those with enough understanding of all the in-depth issues. However, others might still argue that history can provide many examples of where the accepted knowledge and consensus of the majority, and the knowledgeable, had to be eventually overturned.