Galactic M-Sigma Relation and the Anomalous Stellar Velocity Dispersion

Galactic M-Sigma Relation and the Anomalous Stellar Velocity Dispersion

Inverse gravitational decline versus inverse square decline


Analyzing the implications of a black hole singularity with near infinitely tight curvature close to the center and what this means to the mathematical form of the gravitational field, one concludes that a postulated singularity requires that black hole gravity declines as 1/r, not as 1/r^2. This effective “infinitely” deep gravitational “point-mass” geometrically implies a hyperbolic gravitational field profile. So, the concept has some bizarre twists.

But, general relativity does not permit a 1/r gravitational field in 3-D + t spacetime. However it does allow a hyperbolic field in 2-D + t spacetime. By GR, gravitational force must decline as 1/r^(n-1), where n = spacial dimensionality. If n = 2, gravity declines as 1/r. So, it is also posited (postulated) that there exists a 2-D, sub-event horizon, hyper-spinning, centripetally induced, infinitely broad disk singularity in all central galactic SBHs. Having mass probably concentrated nearer to the singularity center but being of spacetime in nature, the entirety of the disk singularity is immune to the event horizon of the black hole. It can therefore extend outward to far beyond the galactic rim even to nearby galaxies within a cluster or supercluster.

This 2-D gravitational field is also quantum renormalizable. It is well known that items in a 3-D space can be projected perfectly onto a 2-D surface – the holographic principle. Might this be a simple route toward validatable, falsifiable quantum gravity?

This postulated set of logical statements is immune to criticism. If otherwise logical, it cannot be argued against. It must be experimentally tested. Observation is the only choice to conclusively validate or falsify such an argument. See the definition of “postulate” given below.

Postulate

Definition of a Postulate

• A Postulate is assumed to be a true statement, which does not require to be proved.

More about a Postulate

• Postulates are used to derive other logical statements to solve a
 problem. If a problem is thereby solved, especially if proven by
 other data, the postulate must also be true.

• Postulates are also likened to axioms.

In other words, postulates are to be accepted at face value “for the sake argument” for whatever they may be worth as if they were indisputable axioms. THEN, if a whole argument containing such postulates actually works, there may be much joy. If not, it is back to the drawing board.

Newton’s law of gravity and Kepler’s laws are all easily adjusted to accommodate the hyperbolic 1/r G-field in two dimensions plus time. Kepler’s 3rd law in 2-D is derived from 2-D Newton analogously to the 3-D derivation. It is NOT the same result as if orbiting 3-D objects were limited to an Euclidean plane.

The G-field diagram is hyperbolic when its equal gravitational force contour lines are drawn with spacing in such a way that a 1/r relation is followed to the origin where spacing approaches zero. If the contour lines are then plotted having a z axis, Flamm’s hyperboloid is the result. This is a spacetime diagram, not a gravitational potential diagram.

No inner galactic bulge stellar orbits need be fitted to raw Kepler. Kepler does not define these orbits. Kepler’s laws are used merely to analyze them. The orbits are what they are. Kepler’s 2nd law applies no matter what the form of the central force. The “adjusted” Kepler’s 3rd law follows exactly from Newton’s law of gravity with reduced dimensionality according to GR. It is "adjusted" Kepler that should be used to compute central galactic supermassive black hole mass. See the Gary Kent post on WordPress.com.

There is nothing more to prove. What there is still to be done is to compare with observation.

Mathematically, the constant velocity distribution observed in spiral galaxies is explicitly derived. This means that the M Sigma relation is explained because peripheral stellar v = (GM/r*)^½. Also, Milgrom’s MOND constant, "a[o]", is derived, where a[o] = GM/r*r[∞] = v^2/r*r[∞]. This implies that the universe must have a finite or maximum r because a[o] is an observed finite non-zero quantity. And, M, the black hole mass, may include the masses of many tens of thousands or more of very large stellar mass black holes that are thought to be embedded in every galaxy. The unit vector of r, r*, is used to maintain dimensional integrity.

No modification of Newton’s law is required. But, Newton must be regarded in the context of a 2-D hyperbolically curved spacetime. So, gravity for black holes declines as 1/r and is not an inverse square relation.

All the other effects that have been observed that have been traced to Dark Matter are also explained in this way. These include the anomalous velocity dispersion in spiral galaxies and in clusters, the weak gravitational lensing, the Sunyaev-Zel’dovich, the Sachs-Wolfe and the Bullet Cluster effects.

The hyperbolic G-field parsimoniously explains these phenomena without appeal to any unfalsifiable hypotheses of exotic dark matter. Weakly interacting massive particles and other alien perpetrators of Dark Matter effects have been researched avidly for a very long time. They must be regarded now as unfalsifiable hypotheses because it has become clear that there is no way to prove or disprove their existence or it would have been done by now.

The hyperbolic SBH singular ultra-spin disk G-field might have mass, perhaps like Alan Guth’s inflaton field in the false vacuum. Its mass, but not its hyperbolic gravitational spacetime configuration, could be confined to below the event horizon. The horizon itself could be greatly distorted - including any surrounding plasma or photon sphere. So, a photon passing through the expansive hyper-spin singular spacetime disk would experience therein an enhanced gravitational field, just as if it had passed through a Dark Matter “halo”.

The open cell foam, network or spiderweb structure of the large scale universe is also explained by the extensiveness of the hyperbolic field and its form as a 2-D saddle shape “hyperboloid of one sheet” embedded in 3-D space. Galaxies and galactic clusters will be expected to align so that the hyperbolic surfaces of their 2-D fields tend to coincide. So, even the initial structure of the nascent universe would be influenced by supermassive BHs therein which could have formed very quickly at that time.

They might have been there from t = 0 + an instant, for all we know. After all, if the inflaton particle was like an unstable subatomic particle, it may have decayed into smaller particles including many SBHs. Some have said that the inflaton particle must have decayed all at once. Under these extreme initial conditions, what experimentally validated physical law or fundamental principle is quoted thereby? So, it decays all at once. To what?

In short, the hyperbolic 1/r SBH galactic G-Field explains all the phenomena that have ever been traced to Dark Matter. The hyperbolic G-field IS Dark Matter. Its potential energy profile is generally higher than the profile of an equivalent inverse square G-field. Since m = E/c^2, it accounts for the unseen and unseeable missing mass of Dark Matter. The HBHG field is mathematically derived rigorously and satisfies the mathematical requirements of all observations.

I have written a paper on gravitational decline with distance, but I need a reviewer to help check my mathematics. kentgen1@aol.com

The Hyperbolic Hyper-Massive Black-Hole Universe

The Hyperbolic Hyper-Massive

Black-Hole Universe

Hawking did not buy his own pronouncements regarding the disappearance of information into black holes. Instead, he and some others invented a whole new theory of black-hole thermodynamics. So in a sense, the black-hole event horizon is a real surface. It is sometimes called a "quasi-surface". The center of a black-hole is a physically real singularity. It is constrained only by the Heisenberg Uncertainty Principle. There is no such thing as quantum gravity (QG). How many papers are published in ArXiv on unicorns? By their standards, there should be dozens! So, any appeal to QG to put the Kibosh on black-hole singularities is therefore bogus.

See The Hyperbolic Hyper-Massive Black-Hole Universe and Galactic Gravitational Field (HHBF), which is a paper written for the blog http://garyakent.wordpress.com that describes the e-Model for inflationary expansion of the universe. The hyperbolic hyper-massive black-hole gravitational field is a phenomenological postulate, that is, it is a tentative premise that should be confirmed by experiment or observation and need not wait for theoretical justification. In the case of galaxies and galactic clusters, there is already enough observational support for the galactic hyperbolic super-massive black-hole gravitational field (HSBF).

The point is emphasized that Birkhoff's Theorem and other interpretive principles derived from general relativity cannot apply to any real black-holes. These rules presume that the massive bodies that are considered are always "unperturbed" and are perfectly "spherically symmetric". No real black hole meets these criteria. The rules are good only for approximate calculation, not for"precision cosmology".

Besides, GR should not prohibit a gravitational field that declines as 1/r if a metric is found, similar to the Schwarzschild metric, using assumptions and boundary conditions wherein a singular black-hole is presumed at the outset. If such a gravitational field can be confirmed, the e-Model will serve as more evidence for the existence of our universe as part of a multiverse in meta-time. I appeal for collaborators to help find such a metric.

Hugh Everett may one day be seen as a thinker on a par with A. Einstein. And, John Archibald Wheeler's suggestion concerning the quantum self-interference of probability density waves may be taken more seriously while Everett's declaration of the"reality of probability" as a sort of substance gains credence.

Self-interference can explain the virtual absence of antimatter (AM) in our universe. AM would be confined to our virtual twin, which must exist according to the logical extension of Alan Guth's inflation hypothesis wherein a virtual particle came into existence from a hyper-excited false vacuum which came to exist precisely because of its ultra-high energy level. It would be seen as the deeper mechanism behind apparent "symmetry breaking" and unbalanced annihilation of fundamental sub-nuclear particles and antiparticles to give our universe with matter as the dominant form.

The existence of an interference twin could also be helpful in explaining the hyperbolic field as the resultant of a superposition of states. As the real (to us) expression of a statistical process within the multiverse, we experience only the total sum, the superposed probability density form from which emerges has probability, P = 1. There are ways that such a superposition might affect the shape of a gravitational potential well. Gravity itself may be viewed as a probability vortex or wave in the Einstein Aether. There is much that has not been considered.

Dark Matter is an unnecessary ad hoc fix

Dark Matter is an unnecessary ad hoc fix to fill in the blanks in the Friedmann model under the FLRW metric. Galactic supermassive black-holes exist as true physical singularities according to the Kretschmann invariant and Schwartzchild's analysis. Therefore, as point masses, they must possess a hyperbolic (1/kr) gravitational field, NOT a field that falls off as 1/r². Now, k = constant = 1m, S.I., for dimensional integrity. It is not true that GR cannot tolerate hyperbolic spacetime geometries. "The universe is hyperbolic." said Albert Einstein in his classic paper of 1915.

An hyperbolic field will give constant orbital acceleration to orbiting bodies as far from the center of a black-hole as we might like to measure. This means that bodies near the periphery of a galaxy should seem to move at constant velocity because rotational acceleration does not drop to near zero there as with a 1/r² inverse square law. This constant velocity distribution effect has actually been measured and has given rise to the notion of Dark Matter.

Gravitation does not fall nearest to zero between galaxies in a cluster either. So they too can bend light and affect redshifts in ways that mimic Dark Matter. The rotation of galaxies in clusters is also influenced by the black-holes that they contain with their 1/kr gravitational potential profiles. The not quite counterbalanced redshift effects in the Sunyaev-Zeldovich phenomenon are influence by the hyperbolic galactic and galactic cluster gravitational fields that exist as light falls out of such clusters and super-clusters into a large void and as it climbs out of it again after the universe has expanded by another billion light years or more.

Scientists are mapping, not Dark Matter, but the huge extent of the network of hyperbolic galactic and super-galactic gravitational fields that behave like Dark Matter because of the mathematical properties of the hyperbolic gravitational field are similar to That expected for Dark Matter.

Primordial massive and supermassive black-holes with their 1/kr galactic gravitational fields can also mimic the “halos” of dark Matter that are postulated to have existed just after the big bang and before the emission of the cosmic microwave background. There is nothing that Dark Matter explains that cannot be accounted for just as well or better by the hyperbolic black hole gravitational field.

The hyperbolic 1/kr supermassive black-hole galactic gravitational field explains “the Dark Matter Effect” without Dark Matter and it is more parsimonious and is a falsifiable hypothesis, unlike Dark Matter

The conditions for validity of Birkhoff’s Theorem are not met for real black-holes. Therefore, Birkhoff’s Theorem does not apply. It sometimes may be used as a first approximation, but it cannot be depended upon as a rigid rule for precise calculations. “The physics near the extreme curvature of a black-hole singularity is not well defined”. This covers Birkhoff’s too.

By the way, any entity that possesses mass by virtue of its motion will be influenced by the gravitational fields that it encounters. It is not so much that a gas mimicking Dark Matter may be very much colder than other gases that such an entity might encounter, but whether such a gas may be much denser. But absolute zero is absolute. Only ground state vibration modes are allowed for gases at absolute zero, translational motion does not exist at K = 0 because it implies a temperature, T > 0 K. So, gases must not exist either. They must be solid crystals. Also, such ground state vibrational modes are only for multi-atom molecules. Intergalactic gas is almost non-existent, is not denser and is not a factor, so it cannot mimic Dark Matter.

No Trouble with Tribbles

NO TROUBLE WITH TRIBBLES

There is no trouble with Birkhoff’s Theorem which says: All gravity fields (including BHs’) act like normal Newtonian fields because all gravity fields drop out of GR naturally and so must be “asymptotically flat”, that is, they must vanish at large distances, i.e. they must follow an inverse square law.

BUT, Birkhoff is based on the particulars of the massive bodies that are treated, like stars; such particulars as the metric are used as premises. The theorem says any unperturbed spherically symmetric field must be asymptotically flat because any mass already behaves as if all its mass was concentrated at the center. It already behaves like a point mass. So, Birkhoff should rule out the hyperbolic (1/kr) supermassive Black-Hole singular galactic gravitational field.

Yet, none of the BH scenarios that are theoretically covered can be considered real. All real BHs are perturbed beyond recognition by their rapid rotation and by their immense quantities of environmental matter and energy, including enormous external gravity fields. Such fields emanate from huge galactic disks or from other whole galaxies with their own embedded supermassive BHs. The direct superposition of such axially coincident and rotationally concurrent mass concentrations with their enormous gravitational fields may well augment the black-hole field in such a way as to force it into compliance with the hyperbolic field "law" for black-holes. Relativistic frame dragging alone could effect this process.

Real conditions should invalidate the theorem.

Also, one critical consideration is that black-holes are NOT mere point masses. They have been shown by Kretschmann and Schwartzchild to be physically real as infinitely dense point particles (within Heisenberg limits) with an infinitely deep gravitational potential well. They are NOT like a planet or a star. This is not properly reflected in the metrics with their singularities necessarily excluded, and is not adequately treated by Birkhoff, or else it represents an exception. Cosmologists say that the laws of physics break down at the intense spacetime curvatures present near the singularity of a black-hole. What else might this means except that even Birkhoff's Theorem cannot be depended upon. These observations may indicate a flaw or shortcoming in the way that Birkhoff's theorem and general relativity are interpreted for spacetimes in the vicinity of black-holes, particularly near the singularity at r = 0.

Birkhoff used the Schwartzchild Metric. But, he could not rightly use the existence of an infinitely deep gravitational well or an infinitely dense point particle because these singular infinities cannot be handled normally. “The physics at a singularity is not well defined.”

It is far easier to accept the possibility of a flaw or exception than to accept the idea of some sort of unfalsifiable Dark Matter comprised of, say, undetectable WIMPs (weakly interacting massive particles). By their very nature WIMPs are supposed to be so “weakly interacting” that they cannot even show up in particle accelerator experiments. The WIMP hypothesis is formulated to be as unfalsifiable as any of the other Dark Matter proposals. As such, it does not merit the label “science”. It is more like science fiction.

So, an hyperbolic (F = GMm/kr) supermassive BH galactic gravity field is possible after all: k = constant = 1m (S.I.), for dimensional integrity. Einstein referred to his equations as being hyperbolic/elliptical in nature. That is, hyperbolic geometry is not outside the realm of GR.

Kretschmann’s invariance and Schwartzchild’s analysis mean that the singularity at the core of a BH is physically real. From our external frame of reference, the exact location of a BH singularity cannot be found because of the Heisenberg limit. So, from our external perspective, a BH core density and central gravity strength cannot be directly “measured” to be “infinite”. But, mathematically, it is so.

And, elementary analytic geometry says that an infinitely deep graphical gravity potential growing from an hugely heavy infinitely dense point mass MUST be asymptotic in nature (NOT asymptotically flat). By symmetry, the other arm of the graphical curve must be asymptotic too, the definition of a hyperbola.

If you can collaborate on a paper, let us prove that an hyperbolic spacetime geometry around a realistic supermassive black-hole can be genuine and that the postulated hyperbolic (1/kr) field can, indeed, account for all effects currently ascribed to so-called “Dark Matter”. As a partner, of course, I shall do a yeoman’s share of work, including the scut-work of referencing & literature search. I am in an ideal position to do this!

garyakent@aol.com

"It is far easier and demonstrates much less intelligence to shoot down an idea than to show how to make it work."

What Imbues the Higgs with Mass?

What Imbues the Higgs Boson with its Mass?


Speculation or fringe theory is really what we are all about here on this forum, no? In some way or another, this is true. If we were all in the business of writing texts, we would be paid. OR, we would pay journals to publish our junk if we wanted to propound fully qualified articles or developed papers. I understand Brian Greene's, Alan Guth's and other astrophysicists’ descriptions perfectly well. But, I am not about to duplicate their formulations and recount their descriptions just to make a point. There is not enough space in the forum server for me to do this anyway.

Take my whistling in the wind for whatever it may NOT be worth. My MAIN POINT, these days, is always that the hyperbolic (1/kr) black-hole singular galactic gravitational field is acknowledged to be for real and is being studiously ignored...

Now, if that other big unfalsifiable massive particle we call the Higgs Boson is the particle that imbues all other particles with their mass, what imbues the Higgs Boson with its mass?

Higgs theorists are pulling their "pud". The Higgs is an ad hoc addendum that is a poor band-aid for the kink it was supposed to fix. Just what was that, anyway? Oh yeah, no explanation of "mass" in the standard model.

Higgs is not really part of the standard model (yet). If the Higgs is not found, they will simply add in another ad hoc splint. The standard model will not collapse. Eventually, they'll get it right, though, I'll bet.

Funny, there is no explanation of the origin of gravity in GR either, only that it exists mathematically associated with mass. Why cannot we be satisfied with two sides to the same coin? Yin and Yang? If mass and gravity are two ways of looking at the same thing, is it not futile to try to merge them into one - when they are NOT one? OR, if they are already merged as best they can be?

This implies quantum and GR are just "so" - two facets of the same reality. If we try to merge the two, we shall go blind. The GUT or TOE is a fantasy. What if I am right? Millions, perhaps billions more will be spent pursuing Harvey down his rabbit hole. We will get just a mouthful of mud

Much less than mass, there is no implicit validated account of gravity in the standard model of particle physics either. If there is a Higgs boson and Higgs field, it should be possible to derive the existence of the full fledged macroscopic gravitational field from them by means of the "correspondence principle". Then we shall have quantum gravity. Nah! Too easy. On the other hand ...

Part 2 Try Alan Guth's "inflaton" particle

But, as far as other unfalsifiable new hypothetical heavy bosons are concerned - try Alan Guth's "inflaton" particle: A hyper-massive excited particle in a humongously excited "inflaton field" that cannot be distinguished from gravity itself, except by its degree of excitation.

Suddenly, it decays. It decays into daughter particles and these then decay. Some of this decay debris has a long half-life. And enormous mass. The rest decays into matter and energy as we know it. But, the long half life particles remain as ultra-massive black holes. These decay, not via Hawking radiation, but by virtue of their intense infinitely deep singular gravitational fields that cause them to erupt into this same universe (somewhere "else").

They spew out smaller black holes and matter/energy detritus like a Roman candle, (The Big Barf). Because of dependence on random processes and/or temperature, the daughter black holes they generate this way should follow a "normal" or "Poisson" distribution, perhaps. Statistically, this might be verified. Yet, it would take time for these BHs to start gathering in more matter to form full fledged galaxies. Some additional BHs may then form by accretion in the expected way.

Perhaps this process would indeed result in very ancient super-massive BH masses following a Poisson distribution. If I was a mathematical physicist, I am sure I could derive it. But, I am just a modeler.

Note that this process will result in sufficient inhomogeneity without invoking acoustic anomalies, quantum instabilities or other forms of additional turbulence to give the energy/mass distribution we see today, especially in the CMB.

Now for Black-Hole existence: the singularity case of a mass with radius r = 0 is different, however. If one asks that the solution set to the simultaneous homogeneous nonlinear partial differential equations in GR be valid for all r, one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant (which says) at r = 0 the curvature blows up (becomes infinite) indicating the presence of a singularity. At this point, the metric, and space-time itself, is no longer well-defined, but not undefined.

For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the GR theory and not just an exotic special case. Such solutions are now believed to exist and are termed black-holes. Because they certainly are gravitational singularities, they must have a unique gravitational potential field profile. By simple geometry, they must be distinguished by a hyperbolic (1/r) fall off in the gravitational field strength. This fact is currently being ignored.

F = GMm/kr, k = 1m (S.I., for dimensional integrity) means black-hole gravity falls off hyperbolically, not parabolically as according to Newton. This F equation is fully Newtonian, however. It just focuses on black-holes as being unique, and, of course, they are. Note that k = 1m is an explicit reminder that we deal with a gravitational singularity here.

Part 3 ... Mordechai Milgrom is a reputable careful worker

Mordechai Milgrom is a reputable careful worker. His data are used to support the idea of Dark Matter, not MOND. Not by him, though, he still teaches MOND. Where do we get Dark Matter from GR or from the standard theory of particle physics? Where?

WIMPS are even more hypothetical and unfalsifiable. DM itself is just a patch used to fill in the blanks in Friedmann. If one can derive Newton from GR, then one can derive the hyperbolic (1/kr) black-hole galactic gravitational field using the right assumptions. These would be interesting in themselves...

Unfalsifiable hypotheses cannot be used to refute facts. TeVeS theory is such an hypothesis like such quantum/GR hybrids all are. They have never predicted one single unique item and no such prediction has ever been verified. A theory that does not predict competently is not a theory and does not deserve the attention of mathematicians nor scientists.

All math, all science, is metaphor. All language is ultimately just metaphor including, and especially, Scripture. It is impossible to fully capture reality with any kind of human language. Prodessionals' neglect of this principle is what many people mean when they claim that scientists are insufferably arrogant and grossly naive. These critics go too far, though. Then they claim science is Myth. They create this Myth. Let us endeavor NOT to do so ourselves.


Gak

No cynic is happy.

Dark Energy & Dark Matter As Pseudoscience

If one carefully reads the papers submitted to ArXiv astrophysics, one sees that Saul Perlmutter's and Adam Riess's supernova research groups were not independent and that they were in deep collusion. Perlmutter and Riess actually wrote a paper together.

The data that the two groups got regarding the distances to supernovae and other bright extremely distant objects was not concordant at first. In order to make the two data sets conform, together, they had to apply an "adjustment". This fudge factor was used to bring the data of one set into alignment with the other so that a smooth plot could be made that included all the data points. The sense of this fudge factor alone is the sole "evidence" that they cite for an accelerating rate of expansion of the universe. The adjustment could have been made in the other sense. Then, the universe expansion rate would have been seen as decelerating. But this is unexciting, uninteresting and unmarketable. So acceleration was "in".

Furthermore, Mordehai Milgrom's discovery of the MOND (modified Newtonian dynamics) effect does not recognize that spiral galaxies almost always contain supermassive black holes in their nuclei. Black holes are enormous relativistic point masses with infinite density. Such "singularities" must have singular gravitational fields also. Such fields decline as 1/r - hyperbolically (not as 1/r^2 or parabolically, as assumed by Newton's Law of gravity).

The difference between the hyperbolic gravitational potential and the Newtonian parabolic one accounts for Milgrom's residual centripetal acceleration constant that he found for stars near the peripheries of spiral galaxies. So, the invention of supernatural "Dark Matter" to acount for the MOND effect is as unnecessary as the concoction of spiritual Dark Energy to account for non-existent "acceleration".

So, what do we do about the "missing mass" necessary to account for the flatness apparent in the anisotropy shown by the cosmic microwave background radiation? The easiest way is to postulate that the universe is about 22 times as massive as our little telescopes can discern.

If the universe is that much bigger and more massive, it would account for the CMB characteristics, the red-shift effects, the gravitational lensing effects and the SZ effects that are being used to give credibility to acceleration and Dark Energy. In other words, Dark Energy and Dark Matter are scams on the scale of Piltdown Man and Cold Fusion. Remember, many reputable scientists fell for these frauds. Clearly, this kind of pseudoscience is still going on today!

Dear American Gypsie

In reply to AmericanGypsie for the comment given several posts ago:

Grey dust has been eliminated by the observation of the magnitude/redshift relation for very distant SNe Ia supernovae. Their spectra, brightness and redshifts are all concordant with calculated great distances.

Interstellar gas will not cause redshifts unless it is ionized, like a plasma. But, the existence of a plasma would eminate from all distances so that the distribution of locations of plasma emmision sources would not match the observed emmision source locations. And, the CMB power law (a type of frequency distribution) across the sky and across the spectrum, would not match the observed CMB (you know, that pretty sky chart showing the red and blue patches got from the WMAP satellite).

The disparity between the radius, radius of curvature or Hubble radius derived from H naught and the the magnitude of the scale factor got from application of the Friedmann equations is very large. This lack of agreement stems from the fact that the Friedmann equations calculate the scale factor of the entire universe, not just the "observable" universe.

The inverse of H naught gives the Hubble radius or the approximate size of the observable universe (U). There are other ways to calculate this dimension depending on the type of observation that is made. But, they are in good agreement. For instance, the size of U is a bit smaller because the value of H naught that is obtained for X-rays by the Chandra X-Ray Observatory is a bit larger (77 km/s/Mpc) than the value for H naught got from ancient SNe Ia (72 km/s/Mpc). Brightness measurements alone indicated the universe is very large and very old.

X-ray redshifts will be very different from microwave redshifts and would occur by different mechanisms if it was caused by interferences and not by virgin emmision from the the time of "recombination" after the Big Bang.

It's funny that you suggest scientists may be Christians in disguise. They are mostly atheists or agnostics.

The Plasma panacea that has been proposed to account for everything is being pushed by Fundamentalist Christians as indicating that U is much younger, say, about 6,000 years old. They want to debunk the Big Bang and all it entails because it indicates age in the billions of years.

They will never succeed and they should give up.

Your comments are very good and I appreciate the thought that you have obviously given to this issue. If only certain scientists would give it the same.

However, I surely would not call general or special relativity mere scientific popularism. The Principles of Relativity are the second best validated pillars of all science.

The first best validated Principles are those regarding quantum mechanics and particle physics' quantum chromodynamics (the God Particle type of a merger between quantum science and relativity).

Because popular books have been written does not mean that they have no serious basis just because they are popular.

Black-Hole Gravitational Field

The Hyperbolic

Black-Hole Field Anomaly

Supermassive black-holes pervade the universe. In the field of our view, within the light cone of our observational limit, there are over 200 billion supermassive black holes residing at the centers of large galaxies. There are probably many more large naked black holes residing in enormous dust clouds or simply standing alone as bald singularities in elliptical galaxies and globular clusters and within galactic clusters and superclusters. These invisible black-holes simply have not had enough time to accumulate a large cloak of glowing matter that emits light by virtue of its in-fall to their event horizons. Therefore, they are truly black.

Black-holes and their hyperbolic gravitational fields fully account for the dark matter necessary to keep galaxies spinning at their observed rates and to bind galactic clusters and superclusters. If there are large enough numbers of such black holes to do this job, then the assumption of the Cosmological Principle is dead wrong by this fact alone.

It is as though the universe is made of Swiss cheese and we have assumed it is made of white cheddar. It is well known that a medium filled with small bubbles or tiny solid particles behaves very differently toward the propagation of any type of energy through it. Numerous small bubbles, for instance, lower the speed of sound and affect the way a medium like water absorbs microwaves. Shock waves propagate so differently that the behavior of the explosion front in the conventional chemical explosive has to be taken into account in the design of nuclear weapons. Bubbles and dispersed solids must be avoided.

When assumptions are made regarding the type of "perfect fluid" of which the universe is made we cannot disregard exceptional circumstances like the presence of a froth of black-holes embedded within it. It matters little that there are good reasons for using approximations like the Cosmological Principle. Something must be done to allow the formulation of comprehensible theory giving the means for tractable calculation. But, this theory and such calculation must be regarded as only approximate. Unless steps are taken to greatly refine theory and bring calculations up to a much higher standard, there shall be no such thing as "precision cosmology".

The hyperbolic black-hole (HBH) gravitational fields, stemming from supermassive black-holes at the centers of galaxies, extend far beyond the visible boundaries of the galaxies themselves. The Modified Newtonian Dynamics (MOND) effect shows that these fields may be virtually infinite in extent. If this is so, the spacetime continuum that is actually present in the universe is very different from the one that Einstein assumed. These oversimplifications are implicit in the Friedmann LeMaitre Robertson Walker metric that Friedmann used to formulate the form of the General Relativity equations that cosmologists commonly use. In other words, the whole structure upon which is built the argument for acceleration of the rate of expansion of the universe and the existence of dark energy (not to mention dark matter) is deeply suspect.

It is just too bad, so sad, that so many physicists have devoted whole careers to mastering the mathematics of General Relativity from the perspective of the FLRW metric and the Friedmann equations. These anachronistic personalities will simply have to die off or retire before we can make progress. After all, there is some truth in the saying about physicists who see everything in terms of some simplifying assumption. "First, we assume a perfect sphere." is not how to do critical science deserving of massive funding.

Only spacetime itself is homogeneous and isotropic. But, once it becomes filled with supermassive black-holes and other dark naked singularities, it cannot be treated this way with any degree of precision or accuracy. Some investigators have already picked up on this fact. They are formulating new cosmologies with different metrics and are abandoning the oversimplified assumptions that were designed to make calculations easy. Much too easy. They have come to appreciate the power of supercomputers and advanced mathematical logic programs to handle more realistic models of the universe. This twenty-first century trend is only just beginning. The real revolution in cosmology has yet to come. It will be a counterrevolution, for the twentieth century is dead.
　
　
　

Modified Newtonian Dynamics

MODIFIED NEWTONIAN DYNAMICS AND THE BLACK-HOLE HYPERBOLIC GRAVITATIONAL FIELD

Albert Einstein easily derived and wrote a relativistic differential equation that was guaranteed to reproduce Newton's Law of Gravity when it was integrated. He could have just as easily written a differential equation that reproduced MOND, but he didn't. He just didn't. He had no reason to do so since the various MOND observations had not been made. So, let no-one say that MOND contravenes relativity.

So, relativistically speaking, if we consider the definition of a black-hole, it must be accompanied by a very characteristic and very different gravitational field. Because it is a singularity, a single point-mass with infinite density (at the limit as the center is approached), it must possess a gravitational field that is defined and determined by its single point, its singular property. Its gravitational field must therefore approach an asymptote at radius = 0 and, and by symmetry, it must approach another asymptote at radius = infinity. This is the definition of a hyperbolic field, NOT one that follows Newton's inverse square law, which is parabolic.

If black-holes posses hyperbolic gravitational fields, then there is no mystery in MOND. No big deal. Look at this image of a whiteboard derivation of the hyperbolic black-hole (HBH) gravitational acceleration and velocity profile near a galaxy containing a supermassive black-hole at its center. On the whiteboard, I also have written a synopsis of the MOND development.

NOTE: In the HBH segment, r must be multiplied by k. Here, k = 1m (S.I.) for dimensional integrity. In other words, F = GMm/kr, k = 1m (S.I.) all the extensions of F have the same caveat.

GO TO

HTTP://WWW.LONETREE-PICTURES.NET/

AND PRESS THE MOND BUTTON TO VIEW A BETTER VERSION OF THIS IMAGE.

Use the backarrow button <<--- to return here or else

you might close out of NEO-COSMOS

Of course, something must be done to compensate for the fact that (GM)^1/2 does not have the dimensions of a velocity, G x M not being divided by r. This could be resolved with the adjustable parameter ratio b/d having a dimension the same as 1/r. OR, better yet, multiply r by the absolute value of the unit vector of r, retaining the unit. This would be a mathematical acknowledgement that we are dealing with a singularity.

For MOND, Newtonian gravitational acceleration is denoted aN. The variant acceleration due to MOND expresses aN in terms of an acceleration that is modified by the function μ(a/a0), which is equal to 1 when the radius from the center is small enough for the overall gravitational acceleration to be large relative to the MOND constant, a0. When the putative acceleration is small relative to a0, μ is equal to a0 such that the equations on the lower left are satisfied. This happens when radius r is large enough for a2/a0 = aN = GM/r, and the total force of gravitational attraction enters the MOND regime. These values for r are equal to and beyond the point where the velocity distribution of stars encircling the galaxy in its outer regions becomes constant.

Remember, M = the mass of an entire galaxy with its black hole. M2 = the supermassive black-hole mass while M1 = mass of the stars in the disk inside the radius r, to a given star. This radius might enclose more than 95% of all the stars in the disk and so may as well be considered to enclose all of them. But, a graphical model would have to take a sliding percent enclosure into account in order to plot a theoretical velocity distribution. So, it will be a little while before I actually do this. Maybe I’ll just assume a Gaussian distribution for the number of stars with a given average velocity in the disc and a different Gaussian for the stars in the spheroidal bulge. The bulge must be chaotic and so it would follow different statistics. This is why the net velocity fades to zero in the bulge.

According to Newton’s inverse square law, velocity should fall off rapidly toward zero in this outer zone as the periphery is approached. But, observations show that it does not. Instead, it falls off much more slowly and becomes constant according to the vMOND equation on the lower right.

But, the hyperbolic field contribution to the overall galactic gravitational field shown as the blue curve, y2, in the graph above, gives precisely the same result. Thus, vMOND = vHBH. If it is admitted that black-holes are different, that they have special properties, among them that they are gravitational singularities, then this is not too surprising. In fact, it should have been thought of before, and it probably has. But, it is now being overlooked. I hope this effort on my part may prevent this oversight from being propagated indefinitely. Sorry, there will never be a Nobel for MOND.

Note that the usual depiction of the velocity profile of a spiral galaxy shows velocities rising to a maximum as one moves toward the center whereupon they fall off virtually to zero as one gets very close to r = 0. My simpler velocity distribution profile is for just one or for a very few stars. The standard picture of a maximum and fall-off in velocity occurs because stars get crowded approaching the center and their orbital paths become chaotic. As one moves closer in, just as many stars move clockwise as move counterclockwise (and on more nearly perpendicular trajectories relative to the galactic plane) and the net velocity declines. The stellar distribution becomes more spheroidal too, resulting in the classic galactic “bulge”. When I formulate my model, I will have to take all this into account as well. This is going to be fun.

It is interesting to imagine what a galaxy would look like if purely Newtonian F = ma = GMm/r2 ≠ GMm/r for large r. Then, v∞ ≠ (GM)^1/2 = constant. Instead, rotational velocity would rapidly fall off toward zero as r increases without bound. The stars would lag much further and further behind and the spiral arms would wrap around the center much more tightly, like the mainspring of an old wind-up clock. So, one can actually see the MOND effect by just looking.

This means that there may well be no such thing as dark matter or twin matter or any such Baroque complications festooning the simple picture of the universe that we, as scientists, should be looking for. It is in the nature of human beings to overdo. Dark matter and MOND are in danger of becoming vastly overdone.

So, now let me engage in a little bit of my own overdoing.

If this version of MOND is correct, there will never be a measurement of a0 obtained in the laboratory in a supersensitive Cavendish experiment. That is, not unless we can produce some sufficiently long-lived black-holes in the lab. Nor will evidence be found inside or just outside the solar system. HBH MOND requires participation of a black-hole. This prediction will never go over very well with a lot of important people, so it will not be readily accepted.

In elliptical and globular galaxies wherein the MOND effect may be observed, HBH MOND will require that one or more supermassive black-holes shall be found, naked black-holes at that. The intragalactic black-hole presence in galactic clusters and superclusters may not be enough to account for MOND in these objects either, so some naked black holes may well be found to be embedded within them too. Nobody is looking for them now, so it is not surprising that they have not yet been found.

The hyperbolic field concept can be extended to the entire universe, too. If it can be verified, it may go a long way toward an accounting for the mistaken interpretations of acceleration and dark energy in the universe. This would require that the primordial black-hole, the mother of all black-holes or MOAB, must have persisted in some form, probably greatly diminished, for a long time after it started to decay into the universe that we see now. In other words, the highly excited inflaton particle may have taken some time to deconvolve, decompose and collapse, so it may even still persist today, along with its hyperbolic field in which we may still be embedded.

But, if the inflaton paticle decayed and its hyperbolic gravitational field collapsed with it, a transitional Newtonian field rose up to replace it almost instantly. These would be other cases where entities expanded or contracted at many times the speed of light. In other words, the inflation process had reflections or reverberations that we still see today. The old hyperbolic field is not finished collapsing. The new Newtonian field is not finished rising. This would have subtle relativistic effects in their own right.

Let’s just hitch a ride on a really fast space-ship heading on a straight line for deep space in any direction with a destination rather more than 13.72 billion light years away and we just may be able to find out. But, it will take us considerably more than 13.72 billion years. More than 27.44 billions years. Still, surely by then, the MOAB hyperbolic field will have completely dissipated with little or no residual effects.

The good news is, if strange, weird science is needed to justify grant funding, this is it.

INEXPLICABLE REVISIONISM

Some of Our Best Scientists

Have Shown Genius Level Negative IQs

Recently there has been an inexplicable reversal in the usual recitation of facts that scientists have been giving regarding the evidence for dark energy. Here is a quote from a current article on dark energy and dark matter that appears on a NASA website: "Then came 1998 and the Hubble Space Telescope (HST) observations of very distant supernovae that showed that, a long time ago, the Universe was actually expanding more slowly than it is today."

This is grossly untrue. If this is what Saul Perlmutter and Adam Riess have been saying, it is a gross distortion. In them, I am disappointed almost to tears. But, what else can I expect from the antigeniuses among us?

I have been tracking measurements of the Hubble constant for many years. The Hubble Space Telescope has measured H0 for the deep space SNe 1a as the highest yet recorded except for H0 determined for the cosmic microwave background radiation, which is even more "distant" and even older. As one plots H0 measurements against the average distances from Earth to the midpoints of the ranges of objects used in the observations, one obtains a very precise straight line in this scatter diagram. This linear regression line has a very high correlation coefficient (0.98) and a NEGATIVE slope stretching from the origin at t = 0 to now at t = 1.

Given that H0 is not really a constant, older accepted data along with current measurements of H0 show that H0 for very distant and old objects is larger than for nearer and younger objects. Nowhere in any of the peer reviewed publications of Perlmutter nor Riess is there explicit argument for acceleration or dark energy that does not subtly assume what it purports to prove. They never explain exactly how the reversal of common sense occurs that says the universe expansion rate is accelerating in the present era. They do not even acknowledge the reversal.

Commonly accepted facts have to be rewritten to accommodate this circular conclusion. History has to be revised. Accepted data clearly show that the expansion rate is decelerating. See http://www.lonetree-pictures.net/Graphical%20Model%20of%20the%20Universe.htm .

There is lots of evidence against dark energy. Recent papers casting doubt on the Cosmological Principle should be taken seriously. If we should be prepared to accept the many patches and ad hoc band-aids that dark energy requires, why can we not entertain some patches to explain away the so called "evidence" for it and help save the Scientific Method?

One does not validate a scientific principle by accumulating circumstantial evidence. Such are just anecdotes. One must formulate an antithesis; an opposite or negative hypothesis, and attempt to perform a critical or crucial experiment that would confirm or deny it. If this “null hypothesis” is confirmed, the original hypothesis is falsified or nullified. Dark energy is incapable of falsification and is thus as ineligible as a scientific hypothesis as Santa Claus or God Himself. To hold otherwise is to open the gate to superstition.