Scale Dependent Gravity, Black Holes and Large Scale Structure
Gravity will weaken from the source proportional to the inverse radius squared which is measured as two interacting mass charges weighted by their distances from each other
F = GMm/r²
Since the force is inverse to the radius, we know that as the force increases the distance must decrease and vice versa. If the force is large enough however, it should appear to take longer for gravity to weaken over larger distances, or the larger the gravitational field the more reaching its effects are since this depends on the field strengths themselves.
This means that while a force can be read from the equation as small, the equation could be taken large because to maintain a force action over large distances must imply a large interaction or binding energy. In order to make sense of such a thing gravity would have to become scale dependent and requiring explicitly a particle and a cosmic scale force.
The force equation will only make sense so long as M and m are always interacting regardless of how far they are from each other (which remains a hypothesis of the Newtonian model), for instance, Newton did not assume some critical distance in which the interacting over a distance is pretty much negligible in a realistic general model, or that local gravitational effects are strong enough that anything outside of it has negligible effect.
The interaction of two point masses will drop off more rapidly than that for two planets moving away from each other. This again has to do with their field strengths, but the fact it takes longer for larger gravitating bodies tells us something about gravity which seems natural. Gravity is only as long range as its mass content will allow them to be.
At least, this has been strengthened in my opinion weighted by the evidence over the last number of years on close studies of large scale cosmic structure. This hasn't broken physics, it's just that people hadn't understood the force problem properly when relaying the model for varying masses. The basic premise here, is that 1/r^2 drops off proportional to the field strength - which depends on the gravitational mass - this is such that we do not end up making silly statements that would lead to gravity dropping off at the same rate no matter what the field strength or systems in question. Of course, it shouldn't and not only this but the local gravity should at a critical distance, simply have negligible effect on the distant particle; this all boils down to what the cosmic scale gravity is, it's a binding energy phenomenon.
An excellent example is a typical spiral galaxy like our own, harbours a supermassive black hole with trillions of solar masses that has been suggested in literature to be approximately the same amount of binding energy required to help keep a galaxy like our own together. The larger the black hole, by no exception or surprise, usually end up in galaxies even larger than our own, it seems proof positive that the larger the black hole, the larger the galaxy. And so for many years, it perplexed me why we did not properly seek for the answer of dark matter in such a model.
Many will know from my previous rants that I dislike dark matter, with good reasons. I am not happy the effects of dark matter are absent for the first four billion years of the universes evolution. A number of galaxies further in present day show no apparent dark matter effects. I argued that, coupled with scientific research that showed in mainstream a direct mathematical link between black hole bulge size and rotation curves was strong enough evidence to reconsider the role of the SMBH as being at least partly responsible for the rotation curves - the other contributors I expect will be other black holes in the galaxy and with additional spin dynamics of the supermassive lack hole, there may also be a polarisation of space itself.
I demonstrated different galaxies that had lost their black holes and showed how the evolution of the galaxy would be affected by it, becoming more loose and less structural over time. It seems that this was due to the centrifugal force pushing the galaxies internal dynamics away because of an intrinsic loss of binding energy required to hold the system together. It seemed with cosmic spectacles we could have seen earlier, evidence that black holes played some of the most essential parts in not only binding the galaxy together, but was also capable of spinning the galaxy in the direction of its own angular momentum.
In fact, there is no typical galaxy in the Universe which spins opposite to the supermassive black hole it harboured and this to me was not a case of chance. Nor was I be willing to accept the alternative explanation that black holes only rotate that way because "they formed from the spinning dust of matter at the centre of primordial adolescent galaxies that where only beginning to form," because even then this did not answer why we cannot detect it for the first four billion years or how a recent large study analysis showed a preference for galaxies to spin in a particular direction to boot... Yet it was perfectly understandable that black holes where perhaps not large enough during this period which seemed to answer this missing dark matter problem sufficiently without any additional physics. And while no theory can adequately explain in mainstream why most galaxies rotate in a particular direction it can be understood if black holes had always been there under a unification approach.
The ability to be blind to many of the problems the dynamics of the long range effects of gravity could really be, makes us re-evaluate what we meant by Newton's force equation. It seems that like any general force equation F=ma, the force depends on the mass content and as a consequence the quantity 1/r^2 thins out differently over distance. This depends on the acceleration the two systems feel in response to each other - this is a relative problem, so it depends on the frame of reference. For instance, the acceleration experienced by a human on Earth is almost a set constant... At least on terra firma. On others planets, the strength of gravity depends on the mass, resulting in the acceleration experienced "there. "
F = GMm/r²
If m is the small mass of an infalling body to a large mass M then it experiences an acceleration depending on the mass of the measured system
g = GM/r²
So acceleration and the force thus experienced, depends on the mass of the system but additionally, it affects how the force law will drop off. A large mass indicates a slow drop (in any ideal graph) allowing the force to be experienced over larger distances. When talking about how black holes binded a galaxy together, often ran into people saying "then gravity must be working in a new way" and I never agreed with this statement. Gravity has been working exactly how experimentation has told us to describe it as. It seemed strange to me that dark matter could be anything except this... Boiling down to a misunderstanding of the force law and binding energies required as associated to those distances. In many ways "gravitational locking" has to be related to the binding energy of the system. Its these kinds of phenomenon I expect to give rise to things like frame dragging, which brings us to a related subject. Further, when spin of a black hole is included with trillions of solar masses, a polarization of Spacetime itself is in fact a real possibility.
Think then how excited I was to find polarization models attempting to explain dark matter. A simple search on the internet will provide many results.
On, How We Misunderstand Newton's Force Equation
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