The Elastic Universe

The Elastic Universe

Edwin Hubble’s main observation was that all galaxies that are not gravitationally bound to ours are speeding away from us and each other at greater and greater speeds depending on their distance from us. Tthis suggests certain deductions. Rewinding time back to the origin like a VCR recording, it is thought that this observation implies that the universe must have originated as a point particle with infinite density and an infinite gravitational field whereupon the absolute value of time must have started at exactly zero. According to this postulate, before “the Big Bang”, there was nothing, not even time.

But, there is an easy alternative notion that does not postulate new physics if one allows that spacetime itself may act as an elastic entity overall. Then, one may be able to rewind time only to the point where the universe had just rebounded from its last oscillation. This oscillating universe may still have had a finite size, density and gravitational field. What then?

The Sloan Digital Sky Survey has shown that the universe has structure. This fact alone has implications, but the structure itself makes a difference. It has the structure of an open celled foam. It has the structure of a crosslinked polymer. Its network of entangled connected filaments, if viewed in Einstein’s “block time”, may therefore act like an elastomer, like rubber, in a new time dimension.

We should not care what happened before the universe began oscillating nor what made the universe begin to oscillate. These are not proper questions because they make no logical sense. They presume too much. We have no idea of what “before” means in this case.

Contemplating this elastomeric universe rebounding from its last oscillation, we see that it may well have started its rebound in an extremely dense (not infinite) state with a very high gravitational field. As it proceeded to rebound, its integrity would have been conserved by its property of possessing a strong gravitational field. But, its observed apparent increasing kinematic motion among its parts would draw upon its inherent internal potential energy that would be latent in its compressed or distorted momentary initial instantaneous form.

Its early kinematic motion would have resulted from its sudden reversal of direction and so its gravitational force would have been very important at that time. But, its continuing expansion at an increasing rate will have to depend on the potential energy that has been stored within its structure. The rate may be increasing, but it should be increasing at a diminishing amount. The total available gravitational force might be called “Dark Matter”. The total available elastic potential energy might be called “Dark Energy”.

What is your idea concerning this possibility?

Frame dragging in a two dimensional gravitational field

If a massive spinning body possesses a strong gravitational field, that body will have a torque field around it that will act on external coorbiting pairs of objects. The torque field will apply a simultaneous torque to the coorbits of each pair, causing the ellipticity of each coorbit to precess in the same sense of the directions of their primary planetary orbital rotations.

That is: if , say, the Earth and the moon orbit each other with ellipticity e, and if the spinning Sun had sufficiently high mass, it  would possess a strong torque field concomitant to its gravitational field. This solar torque field would act on the Earth/moon system such that the moon's slightly elliptic orbit, e, would precess slowly in the anticlockwise direction consistent with the system's overall orbit about the Sun. If an highly elliptic orbit of a moon of Mars was observed for a long time, the ellipticity of its orbit would be seen to precess too. If a satellite was placed in an elliptical orbit about Venus in the plane of rotation of either the Milky Way Galaxy or the plane of the Solar system (rotational plane of the Sun), this orbit would be seen to precess slowly, more than could be accounted for by conservation of angular momentum (or lack of it) due to its own elliptical circumsolar orbit or to tidal forces.

The Earth/moon system has already been observed to possess such an inexplicable odd precession. Mars has two moons which may interfere with observations of individual ellipticities. But, Venus has no moons. It would be ideal for emplacement of an artificial satellite with properly oriented orbital ellipticity.

But, the Sun may not have enough mass to cause relativistic frame dragging of this type. But, the galaxy possesses a supermassive black hole (SMBH) with its two dimensional gravitational field confined to the galactic plane, mainly. The spacetime gravitational properties of black holes are conserved. So the torque field of a supermassive black hole must be concentrated and intensified in the galactic plane (the rotational plane of the black hole) and not spread out thinly over a sphere. So, its high intensity must reflect this focussed concentration, especially because gravitation must decline as 1/r for a two dimensional field, not 1/r^2 as for an ordinary three dimensional field. So, the influence of this torque field may be felt all the way out to the Earth and beyond.

In other words, relativistic frame dragging may reach much farther in the case of rapidly spinning SMBHs and this must be taken into account when analyzing orbital precession rates involving pairs of coorbiting objects simultaneously orbiting black holes.

That is, the moon/earth binary system exhibits anomalous changes in orbital eccentricity[1]. Its orbital eccentricity and precession change in a way that cannot themselves be easily explained. One explanation refers to the proposed 2 dimensional (2-D) gravitational field effect of relativistic frame dragging by the central supermassive black hole at the center of our galaxy. The short range usually attributed to frame dragging is not relevant to 2-D frame dragging because the proposed condensing of the black hole 3-D gravitational sphere of influence to a 2-D entity extends the radius of the frame dragging effect many orders of magnitude so that it affects the stars and other co-rotating systems as far out as earth and even farther.

An analysis of data records collected with the Lunar Laser Ranging (LLR) technique performed with better tidal models was unable to resolve the issue of the anomalous rate of change in eccentricity de/dt  of the orbit of the Moon, which has a magnitude of de/dt = (5±2)×10^-12 yr ^-1. Cosmological explanations fail: none of these is successful in reproducing the effect, since their predicted rates of change in lunar eccentricity are too small by several orders of magnitude.

Frame dragging declines as around 1/r³ for a normal classic theoretical unperturbed black hole, it appears. But a real supermassive black hole may have 2-D frame dragging declining as 1/r² or even 1/r. Relativistic analysis should provide an exact numerical estimate.

This suggests a critical test of the 2-D gravitational field proposal. The gist of the test is that anomalous changes in orbital eccentricity and orbital axis of rotation should be detectable in binary stars and perhaps even in the orbits of planetary moons such as Mars’ Phobos and Deimos.  The Mars system can be considered as a simple binary system because Mars’ moons are not massive enough to significantly affect each other and their relative distances a generally too far. A three body gravitational system may be too complex to analyze accurately.

There may be other candidates for planet/moon anomalous orbital precession and eccentricity if the many body model of gravitation obstacle could be overcome (with ultra precise measurements and supercomputer assistance, say). But, all the other planets either have many moons or else have no known moons (Venus and Mercury). We could put moons (satellites) into orbit around Venus (say) and track these orbits as precisely as with LLR.

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[1]  Anomalous precession of the axis of orbital rotation of earth/moon system, the lingering anomalous secular increase of the eccentricity of the orbit of the Moon: further attempts of explanation of cosmological origin,  Lorenzo Iorio,  http://arxiv.org/abs/1102.0212, submitted to Arxiv on 26 Apr 2014)

 

 

 

 

 

Black Hole Singularities and the Possibility of Two Dimensional Gravity

According to general relativity, in a 3-D universe with time, the gravitational field of all compact objects behaves as if the objects are point masses and the field strength must decline as 1/r². In a 3-D universe, therefore it is said, it is impossible to support a hyperbolic 1/r gravitational field. But, black holes are different.

 
Why bother with the whole concept of black holes if they are not different? Collapse of matter into a black hole must not only create a singularity (within the limits imposed by the Heisenberg uncertainty principle) but, the spin rate or orbital frequency of in-falling matter of the black hole must also increase without bound as radius r decreases to values near zero below the event horizon. Attempts to explain away these singularities on the basis of a non-existent quantum gravity scheme are vacuous extrapolations of tentative hypotheses that amount to pure conjecture.

 
Black hole singularities exist. Einstein through Schwarzchild and others say so. Who claims to be more brilliant than these fellows? I appeal to authority here only because it seems to be the only thing that impresses some. If you want to claim that BH singularities are mere artifacts of an inadequate theory, show me the Math.

 
Black holes are different. When matter and energy collapse under an infinitely strong gravitational field to a point mass that is as tiny as may be necessary to explain its properties (not necessarily to zero, the true meaning of infinity), the result is a phase change. Spacetime phase changes are S.O.P. in the repertoire of theoretical cosmologists, like Alan Guth. Let us adhere to the hydrodynamics metaphor used by Einstein in his development of GR. Flat spacetime is a massless superfluid. Helium IV is a superfluid but, it is not massless.

 
To extend the metaphor, it is not hard to imagine that spacetime could undergo a phase change, just as helium IV may. In a black hole this change involves a reduction in dimensionality. This is about the only change available to it. Analysis of the equations of GR shows that gravitational strength, F_g is proportional to 1/r^(n-1) where n = number of spatial dimensions. In a 3-D universe, F_g declines as 1/r². In a 2-D universe, F_g declines as 1/r.

 
So, a black hole must use the gravitational energy of in-falling matter to raise its gravitational potential, the gravitational energy level, to the 2-D “state”. We are starting to talk quantum language now.

 
The shape of this singular BH gravitational field strength diagram, as it is a 2-D entity embedded in a 3-D space, is a nominally flat disk or platter with a potentially infinite radius. Unlike Kerr, I call this topology of the event horizon a “spin disk” because it arises from the infinite rotational and orbital spin rate of matter that has in-fallen toward the singularity. As a spacetime entity, this new phase ignores the event horizon and propagates outward to beyond the edge of the galaxy. It emanates from the central core of the galaxy wherein resides any central supermassive black hole.



Here is one of the non-intuitive consequences of GR. It is known that matter in-falling toward the event horizon must experience time dilation. From our external perspective, we would perceive time for this matter as having slowed and even stopped at the event horizon. Viewed from any point outside the event horizon, time really does stop there. But from its own perspective time does not stop and such matter does indeed drop through the event horizon where it may take part in whatever processes it might (time reversed or not).


There is simultaneously an inverse square gravitational field set up by this time-frozen matter at the event horizon and an inverse gravitational field set up by this same matter that has already in-fallen to the singularity. There is no violation of conservation laws here because no object can feel these separate effects simultaneously. If an object orbits the galactic center in the plane of the galactic disk, it feels the inverse 1/r field. If it orbits on a trajectory not aligned with the galactic plane, if it orbits chaotically, it feels the inverse square 1/r² field.


This has consequences for the analysis of the orbital motion of close-in Milky Way bulge stars like S2 for the determination of the MW’s supermassive black hole mass according to Kepler’s laws. Kepler is valid for the 2-D case as well as for the 3-D case. But, it has to be adjusted for the 1/r gravitational field as does Newton’s law. No deep relativistic calculations are needed. One can determine what changes must be made in Newton’s law and Kepler’s laws by inspection.


Above, I explained how a 2-D gravitational field can exist in our 3-D universe. It must be associated with a black hole having an infinite spin rate as well as infinite density and infinite gravitational field strength. Within the bounds of Heisenberg uncertainty, these singularities must exist. There is no point in trying to explain them away using some kind of unfalsifiable overly advanced unintelligible gravitational quantum sophistry.

 
I show that the hyperbolic 1/r inverse gravitational field can exist as a spin disk surrounding any black hole with said disk extending far beyond the event horizon toward infinite radius. This explains MOND and the anomalous velocity dispersion because hyperbolic 1/r gravity means that orbital velocity, v, around a galactic center containing a black hole, v = (GM_bh)^1/2. That is, v becomes constant dependent only on M_bh and G. This v is not only constant for a given galaxy, it is constant from galaxy to galaxy. This means that GM_bh must itself be a constant, a new fundamental physical constant.


But, G may not be the same G that applies in 3 dimensions. So, I call it G*. Besides by an extension of GR, one might get G* from the M‑sigma relation as well as by the anomalous velocity dispersion. But, the mass of the central galactic supermassive black holes must first be refigured on the basis of the hyperbolic field if very many of the orbits of the bulge stars that were used to get M_bh were coincident with the galactic plane. If all or most of these orbits were chaotic and not aligned with the galactic plane, the BH mass determinations may be okay.


The new fundamental physical constant should actually be written G*M_bh such that G* and M_bh are not independently variable but together form this constant that I call Ḡ. Ḡ is constant only under the influence of the gravitational field of a given black hole.

 
The meaning of the hyperbolic gravitational field of black holes is that MOND (Modified Newtonian Dynamics, suggested by Mordehai Milgrom) is explained without recourse to Dark Matter or to modifications of Newtonian dynamics. Newton and Kepler must be understood in two dimensions, that is all.

 
All of the observations that are said to support Dark Matter as being, say, a huge halo of WIMPs engulfing galaxies and galactic clusters also support the hyperbolic (1/r) gravitational field postulate, even the Bullet Cluster effect.  Dark Matter 3-D maps obtained by analysis of gravitational lensing also follow logically from the Postulate.

The hyperbolic (1/r) supermassive black hole gravitational field is indeed a postulate. This means that there can be no argument against it. It must be taken at face value and carried to its logical extreme whereupon it will be either reduced to absurdity or else found to be correct.

 
When extrapolated to the entire universe, the hyperbolic field mimics Dark Energy too. If Alan Guth’s inflaton particle originated in 2-D space and began to roll down its own hyper-gravitational super-potential slope toward a lower energy 3-D state, the higher energy 2-D potential energy would be progressively transformed in a time dependent quantum-like transition to the new 3-D “ground state”. This potential energy would show up as apparently increasing kinematic momentum of all stars and galaxies in the universe. That is, the universe would appear to be expanding at an accelerating rate.

 
This is an exciting idea because the whole universe is thus to be regarded as a quantum object. It may provide a route to a falsifiable certifiable theory of quantum gravity because 2-D gravity does not lead to a gravitational catastrophe as r tends to 0, and it is renormalizable, a prerequisite for any quantum theory of gravity. This Postulate may point to a means to prove the existence of the multiverse. If Guth is right, Hugh Everett could be right.

 

 

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.