G Anthony

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 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.

Hi Forrest, Let's keep to the thread! So the ability to formulate a Null Hypothesis is the key to crafting a theory according to the rigor of the scientific method. Not all of our thoughts require this rigor. Only the ones that we intend to publish so that others can figure out what we mean and duplicate our actions and thoughts in order to come to the same conclusions (to within some tolerance, I guess). Much that passes for science today fails when we can find no evidence that a proper Null was ever cobbled together. When it is suggested that the scientific method should be suspended in order to accept Dark Energy, I get worried.

Suppose you were imprisoned on Penitentiary Earth. You slipped out of the fortified walls somehow and you began to walk due West. When you encountered water, you found a boat or ship and continued on your journey being careful to compensate for seasonal changes in the position of the sun. Eventually you would wind up back at the 'Ol Pen, having traced a latitudinal great circle around the pole. The surface of a sphere has no end. To get out of, or off of, this surface, one needs to move in directions that are not properly "in" the surface. Try reading Flatland by Edwin A. Abbott. Analysis of the variations in intensities and their frequency distributions in the cosmic microwave background radiation (CMB) shows that the pattern matches a roughly random pattern that is originally "flat" before it is projected upon the sky by various kinds of digitally equipped radio-telescopes. The statistical pattern virtually matches that expected for inflationary Hubble expansion of the universe. Deep space telescopic probes find that "SNe 1a" supernovae are more distant than their Hubble redshifts would indicate, so the Hubble constant, Ho, must be increasing for these and other kinds of very distant bright objects. But, motion is relative, so what it really means is that Ho must be increasing here and now, for US. Maybe you could say that the universe is open ended only on our end. This is "acceleration" of Hubble expansion and it is ascribed to some form of potential energy that is pouring spacetime juice into our universe from some source or else it is due to "quintessence" which is supposed to be a fundamental force that is built into the fabric of the cosmos. Now, somehow Alan Guth got transported to a completely new and different universe where he was able to view our little world in "block time". That is, he was able to see us and all that we have done and all that we will ever do from his perch in his meta-universe, outside our own. His clocks followed "meta-time" while our clocks were seen to trace a complex static path according to frozen orbital motions of the earth, the sun, our galaxy and the expansion of the entire universe (our universe, that is). Our clocks appear to him like multiple mad computer screen cursors stopped in a panoramic all-seeing time exposure photograph. We cannot join him in his world because we are frozen in "block time", so we do not even want to. Guth sees our universe from beginning to end. All the objects that move or that have ever moved in it show like the contrails of fighter jets in a crazy dog-fight. The contrails seem like they are frozen in a big block of Jell-O. He sees how our universe began, how it suddenly jumped from a mere speck to cosmic dimensions in a short distance in "block time". All the objects that move in our universe leave contrails that seem frozen in ice. Guth observes our universe with a laser pointer that acts like a cursor as he moves the beam along a contrail to see what it is and where it leads. He can examine all the contrails in our whole universe from beginning to end. He is like God. He gets bored with our puny universe and moves on to examine another one that seems to be much more interesting. When he turns off his laser pointer, nothing happens ever again in our block of frozen continuum. We are like statues in the museum of the multiverse. Let us hope that there shall never be an all consuming fire or that no clumsy janitor will ever knock us off our pedestal! You finally return home to the Penitentiary where you finally come to live in peace with yourself. You have discovered that freedom is just walking around in bigger circles, anyway.

Dr R is such a wonderful delightful skeptic, I do hesitate to proffer this idea. http://www.fotothing.com/Gak/ image 96 Hyperbolic P.E. vs. Inverse Square P.E. <--- This web address points to an image of a graph of (1.) y = ln(x) compared to an equally scaled graph of (2.) the hyperbola y = -1/x + 1. These are supposed to represent the potential energies (P.E.) of the gravitational fields associated with (2.) the inverse square F = GMm/r2 and (1.) F = GMm/kr, k = the unit vector of r for dimensional integrity, where F is the hyperbolic ultra-massive black hole "inflaton" super-excited "inflaton field", the primordial hyper-excited gravitational field of Alan Guth's Inflation Hypothesis. Suppose, just for argument's sake, that (1.), as the P.E. stemming from a super-excited hyperbolic gravitational field, was the potential energy source that fueled inflation in the first place (see how much higher it, P.E. of F, is nearer the abscissa) and it was the source of potential energy that fuels "re-inflation" - acceleration of Hubble expansion seen in the latter era (see how it becomes significantly higher again to the right of x = y = 1). This P.E. of F in (1.) became available to objects in the universe which were under the influence of equation (2.) where its P.E. curve is seen to be generally significantly lower than in (1.). The mechanism of transition from (1.) to (2.) is the time dependent quantum transition of one excited state to a lower state. Such transitions release energy. This transition energy forces the expansion of space and thus the increase in kinematic properties of objects within it at an accelerating rate. There is a major objection. See the graphs here ---> http://www.fotothing.com/Gak/ image 97 Hyperbolic 1/kr versus inverse square 1/r2 gravitational fields. It is said that GR cannot tolerate a hyperbolic 1/kr gravitational field unless there are only two spatial dimensions in spacetime. Otherwise, Birkhoff's theorem applies and the inverse square gravitational field is de rigeur. But, Birkhoff and its sibling theorems and corollaries all presume that the black hole or other massive body is stationary and spherically symmetric. This is never the case. This is always grossly unreal. All Black holes rotate at great rates and they are always distorted massively by tremendous external gravitational fields. These theorems just do not apply. They are good only for approximate estimates of black hole properties, not for "precision cosmology". Furthermore, so what? If we must putatively endorse a 2-D spacetime continuum for the inflaton particle and the inflaton field, then fine. The holographic principle says that all relevant information may be stored on the 2-D surface or quasi-surface of any 3-D parcel of space. It is the basis for the black hole entropy law. So the inflaton ultra massive black hole singularity might have existed in a 2-D false vacuum continuum surface (an ultra massive black hole event horizon quasi-surface?) that began to unfold or deconvolve into our 3-D + time continuum thereby commencing inflation and fueling "re-inflation" in the current epoch. The hyperbolic field may reside comfortably on such a 2-D surface. And, such a surface need not be "flat", after all. And, there are ways to represent curvature that do not necessitate a 3rd spacial dimension. All that I am saying is that it may be worthwhile to consider the hyperbolic black hole singular gravitational field. The HBHF also explains every other phenomenon associated now with Dark Matter. It ratifies GR and Friedmann by "explaining" Dark Matter and even Dark Energy as well. DE is seen as purely a gravitational effect, not quintessence. But, Dark Matter is still real. The P.E. wrapped up in the hyperbolic gravitational field is real. It contributes to the total mass/energy of galaxies, galactic clusters and super-clusters. So, it adds to the inventory of matter and energy in the universe consistent with current formulations of the Friedmann equations according to comments under the image in (1.). What if the appearance of virtual particles, say, in a Casimir effect experiment, obeys an inverse square law too? Studies of virtual particles using particle accelerators also probe very small distances. If the Casimir effect falls off exponentially with distance or even much much faster, quantum electrodynamic extrapolation to cosmic distances would not be 10120 too large. If anything, the numbers would be too small. But, surely we could fudge that too. But, why does the continuum seethe with virtual particles in the first place? Because it CAN? This form of the anthropic principle is highly unsatisfying and physicists are loath to embrace it, Stephen Hawking notwithstanding.

Let us talk about the scientific method and why it is so important. This is really a philosophical discussion pertaining to the philosophy of science. There is already a philosophy forum. So, we can avoid going off the reservation by sticking to nuts and bolts. The key to my essay is the point made about the Null Hypothesis. Most scientific results are expressed statistically and the Null Hypothesis is supposed to be an expression of how apparently positive statistical tests could have been fooled by random noise or just plain chance. Then if a major source of noise is found or if chance is confirmed, Null is true and the alternate hypothesis is false. This is just insurance against bias: looking at the other side of the coin. All scientists are biased, but only a few admit it. Yet, if they hew to the scientific method, their conclusions may still be trusted. Motivation is irrelevant. Even biased scientists can remain ethical. The scientific method is a framework or skeleton upon which may be hung the musculature of such ethics.

Thanks AJB. I was starting to think I was beginning to see double from the mushroom sauce I just ate with my breakfast steak. Maybe I need a rest. I am starting to hallucinate from my intellectual diet of cosmology. Nah! I am not hooked. I can quit anytime!

The Z boson is the last particle needed to fill out the Standard Model. So, where does the Higgs boson come from if not from an ad hoc addendum to the Standard Model the purpose of which is to explain the phenomenon of "mass". That a version of supersymmetry can be invoked to "predict" the Higgs is not surprising. But, that this "mass" is not actually explained by the existence of the Higgs, but only certain "kinds" of mass, is suspect. The success of Alan Guth's Inflation Theory should be instructive. An excited state of an inflaton field gave rise to an inflaton "virtual" particle by means of its intensely high energy state that was much more probable than lower energy states because of the zero point cut-off. It appears that the inflaton field is an excited state of the vacuum (the Einstein Aether) called a "false vacuum". It and its associated particle came into existence as a probabilistic statistical inevitability. It possessed a gravitational field which may have been identical to the inflaton field itself. What would an excited gravitational field be like? In the meta-space implied by the existence of an inflaton field and particle, might not the excited gravitational field have rather different properties relative to a "ground state" gravitational field? This excited gravitational field engendered the whole mass and energy of the entire universe. An excited field like it might create the Higgs particle and imbue the particles with which this field can interact with some form of "mass". I have suggested that, given the correct assumptions and boundary conditions, a gravitational field (if it emanates from a singular infinitely dense point mass like a black hole) could operate with a hyperbolic attractive force. This rather than the usual inverse square or "exponential" force. Its fundamental basis for being could be a two dimensional version of our 3-D world, like the holographic principle implies that the information in a given volume of space can be represented on its surface. A 2-D gravitational field could be hyperbolic in nature without stretching general relativity too far. Two dimensions does not necessarily imply "flat". A hyperbolic gravitational field would be quantum normalizable and could fit with quantum mechanics/dynamics to allow quantum theoretical treatment of gravity and "mass" as an expression of the Einstein Aether - an acknowledgement of the fluid dynamics analogy in general relativity. In other words, might it be profitable to consider the Higgs boson and field from the perspective of general relativity with a few quantum principles mixed in to give a sort of quantum relativity? If the mass of the Higgs should be less than the Z, and the Z is about as massive as an iron atom, may it not be asking a bit much from the CERN super-collider? If the Higgs is not found, would not a brand new band-aid be found to slap onto the standard model? And, how can there legitimately be more than one "standard" model? Are we not formulating whole models as ad hoc fixes for the flaws we perceive? Like weathermen, we choose the model we prefer for the purpose we desire.

Why do particle physicists and cosmologists seem to be so very bent on totally ignoring John Wheeler and Hugh Everett? How can they embrace Alan Guth's Inflaton field and particle and at the same time dismiss the ramifications of a fully quantum universe? We are trying to meld quantum mechanics/dynamics and relativity into a GUT or TOE, spending hundreds of millions per year to support scientists, professors and graduate students. But, the consequences of a quantum universe seem to be just swatted away like an angry mosquito. If the universe was once a quantum entity, then it still is. And, if there was an inflaton particle, there was a virtual anti-particle that our universe has not yet met and annihilated. The John Wheeler style quantum interference of the inflaton wave form to give its anti partner may mean that there is a universe full of antimatter almost right beneath our feet. The superposition of states to give the universe that we see only means that we cannot sense the other state or states that may superpose to produce our reality. But quantum mechanics/dynamics demands that they are there. So, there is no paradox here. But, scientists have always been reluctant to extend quantum to macroscopic scales even though there is a lot of research to find ways to do precisely this and the correspondence principle demands that it should be possible. I guess it would be too disappointing for them to learn that it has already been done - at least 13.72 billion years ago and perhaps a lot more than 27.44 billion years ago. Maybe they fear the day when a GUT or TOE will spell the end of cosmology and particle physics. We may not have to wait another 30 billion years for our parcel of space to loose causal contact with the rest of the cosmos (LOL).

I have constructed a model of inflationary big bang expansion of the universe from simple assumptions similar to Alan Guth's model. But, he does't provide a model that stretches all the way from the first plausible and treatable instant to the present and beyond as my model does. And, by means of a single adjustable parameter, I can mimic acceleration, steady expansion or deceleration. In the case of acceleration, my model naturally passes through a short pause of perhaps about 100 - 200 minutes or maybe more, not exactly as your calculation suggests, but the duration of this period is subject to the choice of somewhat arbitrary initial conditions. This period also provides time for equilibration of temperature and density differences in the inflationary expansion. Because the universe was still very small, when all the regions or arbitrarily small parcels were still in causal contact, this pause is essential to the inflationary scenario. This pause is necessary and most fortunate because this simple model does not provide for a lag or "induction" period initially, as Guth assumed, even though the model is a fully exponential growth process. When I saw this expansion rate curve come down from a maximum, turn right around and then go through a minimum and turning around again to resume its upward trajectory, I was amazed that such a simple equation could produce such odd behavior. I wondered if there was any consequence other than to offer a time period long enough to allow equilibration. Now, I see that it may have been crucial to BBN. My model is posted on my website, www.lonetree-pictures.net , but this site is temporarily down because the index.htm main page has become corrupt and I cannot access it until I figure a way to replace the bad code on this page. In addition, my website host has issues recognizing my password for uploading. So, it is difficult to replace the corrupt page. But, I can post the details on my blog http://neocosmology.blogspot.com . So, this has just become a priority on my agenda. As I recall, I posted it there a long time ago, so if you check older posts, it may show up. In the meantime, I have posted images on FotoThing.com: http://www.fotothing.com/Gak/ , images 94 to 96.

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 1916. An hyperbolic field will give constant rotational 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 seem to move at constant velocity because rotational acceleration does not drop to near zero as with a !/r2 inverse square law. 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 so. 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. Any entity that possesses rest mass or mass by virtue of its motion will be influenced by the gravitational fields that it encounters. It is not so much that a gas may be very much colder than other gases that such a body might encounter, but whether it may be much denser. But absolute zero is absolute. Only translational motion and ground state vibration modes are allowed for gases at absolute zero, and such modes are only for multi-atom molecules. Intergalactic gas is almost non-existent, is not denser and is not a factor.

I get paid by the word.

Very many people do not believe that science is actually practiced this way. Many believe that Science is not only ideological, it is Myth. The problem is with scientists themselves. Too often, they forget that all math, all science, is metaphor. All language is ultimately just metaphor. It is impossible to fully capture reality with any kind of human language. This is what many people mean when they claim that scientists are insufferably arrogant and naive. These critics go too far though, when they claim science is Myth. They create the Myth. We should endeavor not to do so ourselves. I do not dismiss good suggestions. My style is what it is. Take it or leave it. Off putting? What kind of style is this? No style. Read it again. I do not necessarilly endorse faith. I simply say that it is a reality and those who dismiss it make a big mistake. For starters, they dismiss 5 or 6 billions of people worldwide. I do not say Science is faith, although this is exactly what many critics of Science say. In a way, I think they have a point. But, do I have faith that if I jump out the window, Isaac Newton's gravity will drag me down to my most dismal fate? Do I have faith that there is dangerous electricity all around my house? I do have faith in Faraday's laws, so I avoid electectrocuting myself. I have faith in the rules governing radioactivity so that I can faithfully depend on the nuclear power that lights up my home. We all operate largely on faith. We do not have time to personally verify the science that we accept, often blindly. Such blind acceptance is faith. Evidence? We must accept evidence for ideas based on our faith in the integrity and competence of the scientists who present said "evidence". There is an element of some sort of faith in all that we do. What is the difference, and who should care, and who should judge if faith is in an ill defined God or in The Bomb? We are not all atheists, thank God. Education does not mean Godlessness. But, SwansonT will be here shortly because we are not supposed to talk religion on this forum.

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 samereality. If we try to merge the two, we shall go blind. The GUT or TOE is afantasy. 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 . . . 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. Guth says that suddenly, it decays. But, 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"). There must be such a "process" involved. 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 invokingacoustic anomalies, quantum instabilities or other forms of additionalturbulence to give the energy/mass distribution we see today, especially in theCMB. 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 that 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 set was non-physical. However, a greater understanding of general relativity led to the realizationthat such singularities were a generic feature of the GR theory and not just an exotic special case. Such solutions are now believed to actually exist and are termed black-holes. Because they certainly are gravitational singularities, they must have a unique gravitational field profile. By simple analytic geometry, they must be distinguished by a hyperbolic (1/r) fall-off in their 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. Mordechai Milgrom is a reputable careful worker. His data are used to support the idea of Dark Matter (DM), not MOND (Modified Newtonian Dynamics). 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 (weakly interacting massive particles) are even more hypothetical and unfalsifiable than DM or MOND. DM itself is just a patch used to fill in the blanks in the Friedmann model. If Einstein can derive Newton from GR, then one can derive the hyperbolic (1/kr) black-hole galactic gravitational field using the right assumptions about black-holes. These would be interesting in themselves. . . Unfalsifiable hypotheses cannot be used to refute facts, as forum respondents often do. TeVeS theory is such an hypothesis like 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 (or especially) Scripture. It is utterly impossible to fully capture reality with any kind of human language. Professionals' unawareness of this objection 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 that science itself is just Myth. They create this Myth. Let us endeavor NOT to do so ourselves. No cynic is happy.

The case r = 0 is different, however. If one asks that the solution 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 theory and not just an exotic special case. Such singular solutions are now believed to actually exist and are termed black holes. The event horizon of a black hole is not really what defines it. It is defined by its singular mathematical nature. However, according to the Heisenberg Uncertainty Principle, the precise location of the center of a black hole cannot be known. Therefore, the matter in a black hole cannot actually be measured as infinitely dense nor its gravitational field as infinitely strong. But, mathematically, they may be treated this way.

You do not believe in Science? (Upper case "S") Science has always been embroiled with religion. Not so long ago, they were hardly distinguishable. Isaac Newton justified doing his kind of work by appealing to Scripture. But this misses the whole point of my post which is to outline some initial version of the scientific method. Please, may we not address this? This post is written for a discussion forum. It is written in a conversational style deliberately. It is not intended for an English rhetoric professor to grade. Please address the actual content of this post, not its style. I intended to get a discussion going on the implications of the Scientific Method. I should not have even included the poll.

If I wrote in this format, I would not publish here, I tell you! You cannot be serious. Do you really expect a full blown journal ready paper in the traditional format? This is just a DISCUSSION forum. For discussion! I write in a conversational style because this is what most people expect.

Speculation or fringe theory is really what we are all about here on this forum, no? In someway 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 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 is always that the hyperbolic (1/kr) black-hole singular galactic gravitational field is acknowledged to be for real and is being 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, what 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 mass, there is no validated implicit 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 B to follow as a reply: 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 daughter black holes they generate this way should follow a "normal" or "Poisson"distribution, perhaps. Statistically, this might be verified. 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 result in very ancient super-massive BH masses following a Poisson distribution, after all. If I was a mathematical physicist, I am sure I could derive it. But, I am just a modeler. Now for Black-Hole existence: the singularity case of a mass with radius r = 0 is different, however. If one asks that the solutions to the simultaneous nonlinear 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 actually 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. Part C is in the next reply: Mordechai Milgrom is a reputable careful worker. His data are used to support the idea of Dark Matter, not MOND. DM is taught 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 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 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. It is impossible to fully capture reality with any kind of human language. This 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. replies consolidated...

No mention of variations on the anthropic principle. Like, we ARE the extraterrestrials. Trivial, it's true. But, there is another thing, we have been seriously looking for only a few decades. Why is it surprising that we have not yet found what we are looking for? Give us another few hundred years and then come back to me and say there is a true paradox here.

Bulloney. I define my own terms, not Kierkegaard or you! Insult is in the eye of the beholder. I respect all religion. See Theosophical Society founders' tracts. I am not a Theosophist. I am a Christian. I believe in God. Everybody believes in God or some god. I know that there is already a term called "Christian Existentialism. I said "Primary" Christian Existentialism just for this reason. It is as though key words do not count with you. If your shirt gets any more stuffed, we will have to mount you on a pole as a scarecrow. I have no bone to pick with you. Actually, though, I have a revised version of this essay that is a bit more pithy. As a matter of fact, many will insist that science itself is dogma as sure as the Pope sits in the Vatican. Yeah, yeah. Science evolves and truth is relative. Bull honkey. To me, as a Christian, there is Truth. Truth is next to Godliness. Cleanliness is over rated. This section is here because there certainly is a place for faith to any open minded scientist. This is an essay about the scientific method, after all. I want to make a distinction between science and faith. Is that wrong? Scientific Method (revised) Wolfram Math World: A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true (usually that observations are the result of chance). The concept was introduced by R. A. Fisher. The hypothesis contrary to the null hypothesis, usually that the observations are the result of a real effect, is known as the alternative hypothesis. Most science knowledge is statistically validated. The scientific method requires scientists and all others who claim to think rationally to answer knotty questions by means of EXPERIMENT or careful direct observation. In order to do this effectively, one must formulate a hypothesis, a statement of the putative principle that engages all the known implications (an alternative hypothesis) . These implications must also be rather direct. Circumstantial consequences are just that - circumstantial and cannot PROVE a hypothesis. These better implications must suggest experiments that will verify them or not. It is good if there are subservient implications of the alternative hypothesis that can be tested. It is better if a complete and utter negative statement of the hypothesis can be formulated as well that has testable implications (null hypothesis). Then, the net sum of the original hypothesis and the negative hypothesis should be zero, a "zero sum" result in Game Theory terms. Logically, the negative completely cancels the positive hypothesis when the statements are added together. This negative hypothesis is called the"null" hypothesis not only because it would nullify the other if it proves to be true but, it would otherwise tend to validate the positive or "alternative" hypothesis if it is iteself proven to be "null". Still, it would fail to PROVE the alternate to be true, if Null was shown to be false in small ways.. Then, if direct evidence can also be found that tends to corroborate the original positive alternative hypothesis, we can begin to regard it as a good logical beginning. THEN, if this confirmed positive hypothesis can be combined with statements that have already been proven and the combined implications can be verified experimentally or by observation, we have the beginnings of proof. The key to this process is our ability to form an experimentally testable Null Hypothesis. The evidence FOR the positive alternative statement of the hypothesis is insufficient in itself because circumstances may combine to fool our little experiments. We are human. If an appropriate robust Null Hypothesis cannot be formulated, the original alternative hypothesis is unsuitable to merit the attention of the scientist. This is relevant to the debate about Dark Energy, quintessence and Dark Matter. To call one's self a scientist, one must respect the scientific method. It is not a scientist's dogma any more than is it such to be a fireman; one must respect the power of fire - or else you die. An unfalsifiable hypothesis (unable to be cast in terms of a null statement) has no business occupying the time of the scientist. Whole theories have often been constructed from unfalsifiable hypotheses. Such theories are often fun to think about, even edifying and inspiring - but they are not science. There is indeed a place for faith. But, if a person of faith needs experimental proof, he has little of either. We all need faith. We all use faith in some way. In times of trouble and sorrow, sometimes it is all we have. God loves us, we believe. Our belief makes it so. If we can say sincerely that a principle of human conduct or relations should be true, then it is. Human reality is what we can say it should be. This is called Primary Christian Existentialism. All men and women of faith are Primary Christian (or Hindu, or whatever) existentialists. Since this post is ultimately about the scientific method, it does really belong somewhere. It belongs here because the science of cosmology is in dire need of being reminded. Some have said the scientific method should be suspended when Dark Energy is discussed. Those who suggest this should rejoice. The Pope shall now re-ascend to the Throne! Cosmologists are always wrong, but never in doubt. – Lev Landau

Origins, emergence and eschatology of the Universe: Dark Energy & Dark Matter Should we mean "the universe" or "the meta-verse" or "the multi-verse"? (Hugh Everett) Presumably, when the universe formed from an ensemble of some sort of "inflaton" point particles (Alan Guth) as a statistically inevitable child of an extremely excited field, possibly the gravitational field itself, its hyperbolic (proportional to 1/r) field began to collapse into a parabolic (1/r2) one. That collapse continues to this day. But, the process is almost done. There cannot be an infinite amount of energy sequestered in the hyperbolic 1/r field that would be available to fuel acceleration of the Hubble expansion rate by such a transformation. Transition to a lower potential energy parabolic field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the (1/r) potential energy mainspring has almost run down by now. The remaining (1/r) potential energy is called Dark Energy. It accounts for the "missing mass " or "Dark Matter" and "Dark Energy" in audits of universe contents and provides a convenient, theoretically rigorous and parsimonious basis for "acceleration". Dark Energy could account for around 80% of the universe's total mass, but audits are not so accurate. Dark Matter accounts for another 15% perhaps. Still, The Mainspring may still have enough oomph to last for at least 140 billion years more! (at least 10x what has come so far). The total mass, including Dark Matter, of the universe is enough to "flatten" it while acceleration may creep to a stop, but Hubble expansion will not. The hyper-excited gravitational field sprang into existence simply because it could. It came to "be" in a tremendously excited state because very high excited states are much more probable than lower ones, because of the zero point cut-off. This is just like virtual particles come to exist and to be annihilated all the time on the quantum level (this is confirmed by experiment). None of them become universes, though, because there is already one here. It's a sort of a Pauli exclusion principle. There has been some confusion about "variable labels". So, let us switch definitions of "r" in the following. For now, r is the rate of acceleration of expansion of the universe (or rotational acceleration around a black-hole). If the acceleration of the expansion rate is called a, and its present value is called P, then a = P at any given time, including the present. The simplest equation for the expansion rate's effect on P would be an exponential decay expression, P = ho e(-rt), where ho is an initial value for h, r is the rate of increase in this expansion and t is time. We can get an estimate of a value for ho from Alan Guth's formulation of the theory of simple inflation. The present values of both the expansion rate, P1, and acceleration rate, r, is observable. We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation, R = Ro e(rt),where R is the putative instantaneous "radius" or scale factor of the universe. The current value of the expansion rate is Ho, the Hubble "constant", so P1 = Ho. Rigorously, one should extrapolate back to t = t1 through all the older values of Ho that have been got so far, using the midpoints of their domains and ranges. They are all good values. But Ho is not constant. This is what "acceleration" means, after all! See http://www.lonetree-pictures.net the COSMOS sub-sites. OR, I may post to one of my blogs. Look for it soon, but this site is temporarily unavailable right now due to a glitch in my version of FrontPage. It deleted the index master page when uploading an update. It deletes it even when saving to a folder on my own computer. Reloading FrontPage does not help. I think uninstall does not really uninstall everything. I need to get another hard drive going and use it instead. It is frustrating - even maddening! I may have to use an FTP connection. Back to our original definition of r (not R) as a radius or scale factor: Exponential decay equations exhibit what is called a "dormancy" period or late plateau region. In this part of the discussion, here, "r" refers to distance from a center of rotation. Sorry. I missed this inconsistency in previous posts. I need a nicer symbol for the exponential period, another name for r; maybe Cyrillic backward "R"? Maybe a lower case Cyrillic "r"? Using "r" as a radius or scale factor: the hyperbolic 1/r curve levels off to near zero and continues to subside gently almost linearly for an indefinite time. Plot a graph yourself on the back of an envelope! Use mass M = 1, the smaller mass, m, drops out for acceleration. And, assume G is any self consistent constant like G = 1 (units!). This is just for comparison purposes, so it matters not. The equation for orbital acceleration around a galactic center, say, levels off to a constant, even at infinity, for a hyperbolic 1/r black-hole galactic gravitational field potential diagram. (You have just DERIVED modified Newtonian Dynamics or MOND!) You must multiply r by the constant k = 1m (Systeme Internationale) for dimensional purity. NOW, let us MIX the "r" metaphors. The current state of the universe itself may be considered as being of this (1/r) condition – implying both of the ways we have defined "r" - scale factor and exponential decay late dormancy or plateau period. The conclusion here is that acceleration of expansion may continue for a long time while very slowly decreasing nearer to zero. The black-hole rotational acceleration connection implies that the universe may be rotating very very slowly right now. But, we cannot know. We would have to observe the universe from the outside, from the perspective of the meta-universe, to tell. From the standpoint of general relativity, we simply cannot tell from our perspective here and now. Yet, in other words, even with acknowledged acceleration of the Hubble expansion rate, there does not necessarily have to be a "Big Rip" wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point. By the way, "M Theory" doesn't exist. M Theory is just an "ideal". Brane Theory is not M Theory. Neither one has ever predicted anything that can be experimentally verified and neither one is falsifiable. Therefore, they cannot qualify as legitimate scientific propositions. Not one single unique result has ever come from either. Furthermore, they are both unnecessary. Shrewd development of general relativity and quantum are slowly causing both to merge. What's the hurry? Let true "M Theory" and "Brane theory" grow organically directly out of quantum and GR. Each step will be independently validated, then. No worry. Origins, emergence and eschatology are fertile fields for philosophers. This is why we scientists are sometimes called "Doctors of Philosophies", Ph.D. Philosophi Doctori. I took Latin for three years and I am still not sure of this. German and Russian too, but this is no help. What happened to my old Latin grammar texts?

What's this got to do with Dark Matter? Is DM supposed to be due to chunks of neutron stars floating around and inside galaxies and galactic clusters? How do they get there? If a piece of a neutron star is taken out of its context within the star, its gravitational field would still be enormous, but not great enough to keep neutrons bound. It would fly apart into component neutrons, protons and electrons (basically, hydrogen). It would become just another puff of gas. Look: Origins, emergence and eschatology of the Universe: Dark Energy & Dark Matter Should we mean "the universe" or "the meta-verse" or "the multi-verse"? (Hugh Everett) Presumably, when the universe formed from an ensemble of some sort of "inflaton" point particles (Alan Guth) as a statistically inevitable child of an extremely excited field, possibly the gravitational field itself, its hyperbolic (proportional to 1/r) field began to collapse into a parabolic (1/r2) one. That collapse continues to this day. But, the process is almost done. There cannot be an infinite amount of energy sequestered in the hyperbolic 1/r field that would be available to fuel acceleration of the Hubble expansion rate by such a transformation. Transition to a lower potential energy parabolic field must provide a distinctly limited supply of extra impetus. Surely, after 13.72 billion years, the (1/r) potential energy mainspring has almost run down by now. The remaining (1/r) potential energy is called Dark Energy. It accounts for the "missing mass " or "Dark Matter" and "Dark Energy" in audits of universe contents and provides a convenient, theoretically rigorous and parsimonious basis for "acceleration". Dark Energy could account for around 80% of the universe's total mass, but audits are not so accurate. Dark Matter accounts for another 15%. Still, The Mainspring may still has enough oomph to last for at least 140 billion years more! The total mass, including Dark Matter, of the universe is enough to "flatten" it while acceleration may stop, but Hubble expansion will not. The hyper-excited gravitational field sprang into existence simply because it could. It came to be in a tremendously excited state because very high excited states are much more probable than lower ones, because of the zero point cut-off. This is just like virtual particles come to exist and be annihilated all the time on the quantum level (this is confirmed by experiment). None of them become universes, though, because there is already one here. It's a sort of a Pauli exclusion principle. There has been some confusion about variable labels. So, let us switch definitions of "r". In the following, r is the rate of acceleration of expansion of the universe (or rotational acceleration around black-hole). If the acceleration of the expansion rate is called a, and its present value is called P, then a = P at any given time, including the present. The simplest equation for the expansion rate's effect on P would be an exponential decay expression, P = ho e(-rt), where ho is an initial value for h, r is the rate of increase in this expansion and t is time. We can get an estimate of a value for ho from Alan Guth's formulation of the theory of simple inflation. The presentvalues of both the expansion rate, P1, and acceleration rate, r, is observable.We can set t = 1, for the present value of t. So, we can summarize all relevant observations with this simple equation or the associated exponential expansion equation, R = Ro e(rt),where R is the putative instantaneous "radius" or scalefactor of the universe. The current value of the expansion rate is Ho, the Hubble "constant", so P1 = Ho. Back to our original definition of r (not R) as a radius or scale factor: Exponential decay equations exhibit what is called a "dormancy" period or late plateau region. In this part of the discussion, here, "r" refers to distance from a center of rotation. Sorry. I missed this inconsistency in previous posts. I need a nicer symbol for the exponential period, another name for r; maybe Cyrillic backward "R"? Maybe a lower case Cyrillic "r"? Using "r" as a radius or scale factor: the hyperbolic 1/r curve levels off to near zero and continues to subside gently almost linearly for an indefinite time. Plot a graph yourself on the back of an envelope! Use mass M = 1, the smaller mass, m, drops out for acceleration. And, assume G is any self consistent constant like G = 1. This is just for comparison purposes, so it matters not. The equation for orbital acceleration around a galactic center, say, levels off to a constant, even at infinity, for a hyperbolic 1/r black-hole galactic gravitational field potential diagram. (You have just DERIVED modified Newtonian Dynamics or MOND!) You must multiply r by the constant k = 1m (Systeme Internationale) for dimensional purity. NOW, let us MIX the "r" metaphors. The current state of the universe itself may be considered as being in this (1/r) – implying both of the ways we defined "r" - exponential decay late dormancy or plateau period. The conclusion here is that acceleration of expansion may continue for a long time while very slowly decreasing nearer to zero. The black-hole rotational acceleration connection implies that the universe may be rotating very very slowly right now. But, we cannot know. We would have to observe the universe from the outside, from the perspective of the meta-universe, to tell. From the standpoint of general relativity, we simply cannot tell from our perspective here and now. Yet, in other words, even with acknowledged acceleration of the Hubble expansion rate, there does not necessarily have to be a "Big Rip" wherein the fabric of the cosmos is irreparably torn apart as expansion proceeds beyond a certain point. By the way, "M Theory" doesn't exist. M Theory is just an "ideal". Brane Theory is not M Theory. Neither one has ever predicted anything that can be experimentally verified and neither one is falsifiable. Therefore, they cannot qualify as legitimate scientific propositions. Not one single unique result has ever come from either. Furthermore, they are both unnecessary. Shrewd development of general relativity and quantum are slowly causing both to merge. What's the hurry? Let true "M Theory" and "Brane theory" grow organically directly out of quantum and GR. Each step will be independently validated, then. No worry. Origins,emergence and eschatology are fertile fields for philosophers. This is why we scientists are sometimes called "Doctors of Philosophies", Ph.D. Philosophi Doctori. I took Latin for three years and I am still not sure of this. German and Russian too, but this is no help. What happened to my old Latin grammar texts?

My reply is a definition of the scientific method, not an exposition detailing characteristics of the universe. It is not my idea. It is an old old method to compensate for human failure, our disability to learn the truth directly, that is, by just looking and thinking. The theories of relativity and quantum mechanics/dynamics are theories only insofar as they are composites of many hypotheses that have all passed the scientific method's test. They are "falsifiable" and they have been experimentally confirmed. They have also been logically combined with other well established principles and the combinations have also passed the SM tests and experimentally confirmed. General relativity and quantum science are confirmed everyday. For instance your GPS device would not work properly if it did not take into account relativity. Your computer and your LCD HDTV liquid crystal displays would not work if quantum principles had not been used in their invention and design. Large scale integrated circuits for computer central processors & RAM and digital cameras depend on quantum phenomena that are well studied and deeply understood. Sure we still have questions, but we are certain that we have made a good case, so far. The Universe may be simple, but people are not. The scientific method is for people, not robots nor computers. It is a prescription for action. It is a technique of investigation and inquiry. Basically, it was pulled together and made formally a foundation of science by Galileo Galilei - you know, the guy who "invented" the telescope, discovered the moons of Jupiter and helped overturn the geocentric model of the universe that held sway for thousands of years. He was tried for heresy and suffered house arrest until he died in 1642. This is the heroic ideal of the scientist. We are not mere academics creeping around our ivory towers. We are practical people who value results and practical applications. If you do not respect the scientific method, then you should not respect the atom bomb, nuclear power, the discovery of DNA, the "theory" of natural selection, x-rays or nuclear magnetic resonance tomography. Almost everything in our modern culture is deeply in debt to the scientific method. You ideas are not different from the ideas of so many others before you. Their ideas had to pass the SM tests and so do yours. So, you should learn more about it and apply it, if you can. The way you have stated your message, it does not seem possible that it could be phrased in a way that could satisfy the SM. Then, where are your experimental observations? Experiment is essential to the scientist. Any hypothesis that is experimentally untestable is junk. Scientists do not waste their time with experimentally unfalsifiable hypotheses. See http://en.wikipedia....ientific_method .

The Scientific Method The scientific method requires scientists and all others who claim to think rationally to answer knotty questions by means of experiment (or careful observation). In order to do this effectively, one must formulate a hypothesis, a statement of the putative principle that engages all the known implications. These implications must be rather direct. Circumstantial consequences are just that -circumstantial and cannot PROVE a hypothesis. Those former better implications must suggest experiments that will verify them or not. It is good if there are direct elements of principle and subservient implications of the hypothesis. It is better if a complete and utter negative statement of the hypothesis can be formulated. Then, the net sum of the original hypothesis and the negative hypothesis should be zero. Logically, the negative completely cancels the positive hypothesis. This negative hypothesis is called the "null" hypothesis because it would nullify the other if it proves to be true and it would tend to validate the positive hypothesis, at least it would fail to PROVE it false, if it was shown to be false in any way. Then, if direct evidence can be found that tends to corroborate the original positive hypothesis, we can begin to regard it as a good logical beginning. THEN, if this positive hypothesis can be combined with statements that have already been proven and the combined implications can be verified, we have the beginnings of proof . The key to this process is our ability to form an experimentally testable Null Hypothesis. The evidence FOR the positive statement of the hypothesis is insufficient in itself because circumstances may combine to fool our little experiments. We are human. If an appropriate robust Null Hypothesis cannot be formulated, the original hypothesis is unsuitable to merit the attention of the scientist. This is relevant to the debates about Dark Energy, quintessence and Dark Matter. Dark energy is the reservoir of potential energy that is supposed to exist as an underlayment or foundation of the universe. Quintessence is supposed to be a new force field that is just another component of the universe. All fundamental force fields have an associated particle. So, if there is quintessence, there should be a quintessence particle also. Invisible Dark Matter is supposed to account for the anomalous rotation velocity distribution seen in galaxies and galactic clusters. To call one's self a scientist, one must respect the scientific method. It is not a scientist's dogma any more than is it such to follow a firefighter'scode; one must respect the power of fire - or else you die. An unfalsifiable hypothesis has no business occupying the time of thescientist. Whole theories have often been constructed from unfalsifiablehypotheses. Such theories are often fun to think about, even edifying and inspiring - but they certainly are not science. There is a place for faith. But, if a person of faith needs experimental proof, he will have little of either. We all need faith. We all use faith in some way.In times of trouble and sorrow, sometimes it is all we have. God loves us, we believe. Our belief makes it so. If we can say sincerely that a principle of human conduct or relations should be true, then it is. Human reality is what we can sincerely say it should be. This is called Primary Christian Existentialism. All men and women of faith are Christian existentialists. All scientists hew to a code of honor as well as to the scientific method.Truth is not just a buzzword. Truth is meaning. Truth is the scientist's life.Truth is noble. In a very real sense, to the scientist, "Truth" is the next bestthing to God.

The Scientific Method The scientific method requires scientists and all others who claim to thinkrationally to answer knotty questions by means of experiment (or carefulobservation). In order to do this effectively, one must formulate a hypothesis,a statement of the putative principle that engages all the known implications.These implications must be rather direct. Circumstantial consequences are justthat - circumstantial and cannot PROVE a hypothesis. Those better formerimplications must suggest experiments that will verify them or not. It is goodif there are direct elements of principle and subservient implications of thehypothesis. It is better if a complete and utter negative statement of thehypothesis can be formulated. Then, the net sum of the original hypothesis andthe negative hypothesis should be zero. Logically, the negative completelycancels the positive hypothesis. This negative hypothesis is called the"null" hypothesis because it would nullify the other if it proves tobe true and it would tend to validate the positive hypothesis, at least itwould fail to PROVE it false, if it was shown to be false in any way. Then, ifdirect evidence can be found that tends to corroborate the original positivehypothesis, we can begin to regard it as a good logical beginning. THEN, ifthis positive hypothesis can be combined with statements that have already beenproven and the combined implications can be verified, we have the beginnings ofproof. The key to this process is our ability to form an experimentally testable NullHypothesis. The evidence FOR the positive statement of the hypothesis isinsufficient in itself because circumstances may combine to fool our littleexperiments. We are human. If an appropriate robust Null Hypothesis cannot beformulated, the original hypothesis is unsuitable to merit the attention of thescientist. This is relevant to the debates about Dark Energy, quintessence and DarkMatter. Dark energy is the reservoir of potential energy that is supposed toexist as an underlayment or foundation of the universe. Quintessence issupposed to be a new force field that is just another component of the universe.All fundamental force fields have an associated particle. So, if there isquintessence, there should be a quintessence particle also. Invisible DarkMatter is supposed to account for the anomalous rotation velocity distributionseen in galaxies and galactic clusters. To call one's self a scientist, one must respect the scientific method. It isnot a scientist's dogma any more than is it such to follow a firefighter'scode; one must respect the power of fire - or else you die. An unfalsifiable hypothesis has no business occupying the time of thescientist. Whole theories have often been constructed from unfalsifiablehypotheses. Such theories are often fun to think about, even edifying andinspiring - but they certainly are not science. There is a place for faith. But, if a person of faith needs experimental proof,he will have little of either. We all need faith. We all use faith in some way.In times of trouble and sorrow, sometimes it is all we have. God loves us, webelieve. Our belief makes it so. If we can say sincerely that a principle ofhuman conduct or relations should be true, then it is. Human reality is what wecan say it should be. This is called Primary Christian Existentialism. All menand women of faith are Christian existentialists. All scientists hew to a code of honor as well as to the scientific method.Truth is not just a buzzword. Truth is meaning. Truth is the scientist's life.Truth is noble. In a very real sense, to the scientist, "Truth" is the next bestthing to God.

Some good points posted elsewhere to which I must respond: Originally Posted by OnlyMe in scienceforums.net 26/11/11 > " 1) The infinitely deep gravitational wells and thus infinite gravitational potential of such is not consistent with experience. Infinite remains infinite despite the method of reduction. It is more likely that in practice a black hole does have volume and is not a point mass singularity. 2) We have no empirical evidence that the gravitational potential of a BH ever exceeds that requiring an escape velocity equivalent to . 3) There are many things described mathematically that we do not find in experience, observation and experiment. 4) By framing your argument based on the theoretical point singularity, you introduce the potential for, not only and infinite mass density, but also an associated infinite mass. Which could theoretically support the underlying conclusions. 5) It could be argued just as successfully that since GR describes space as dynamically interacting with matter/mass, and the Lense-Thirring or frame-dragging effect can be considered confirmed, that over time and regular orbital motions of the matter contained within a galactic system, the very weak interaction between matter and space responsible for the frame-dragging effect has a cumulative effect and that in mature galactic systems the involved space must be considered to be essentially inertially involved. 6) In such a circumstance, from within such a system the inertial aspect of the involved space would be unobservable, while from any frame of reference external to the galactic system it would be observed as a component of the orbital velocities of the involved galactic matter. This too could be argued to be not only consistent with GR but also with a view of Newtonian dynamics, where space is a dynamic component of the whole system. GR requires that space be dynamic and the Lense-Thirring or frame-dragging effect demonstrates that the dynamic nature of space cannot be limited to a cuvature we experience as gravitation. 7) The observed anomalies in the orbital velocities involving galactic rotation, are theirselves a problem of dynamics. A dynamic interaction from which the dynamic nature that GR bestows on space cannot be excluded from consideration. 8) No matter what trail we follow in an attempt to explain the involved anomolous observations, the inclusion of dark matter, MOND or viewing the whole as an inertial system composed of both matter and space, we are left with the same fundamental questions... What is inertia and gravitation and how are they related or connected? Personnally I believe the answer will lie in a hybrid of GR and QM. " < OM, thanks again for taking the time to compose your reply. My response: 1) At very least, the necessary experience is Milgroms raw observations. What other relevant hard experience do we have concerning purported actual black holes? The galactic rotation anomaly must be explained. Milgrom wants to modify Newtonian dynamics in a way that would vastly complicate general relativity. I want to introduce the simple expedient concept of the hyperbolic black-hole gravitational field effect, which preserves and even enhances GR. Which of us has the more extreme proposal? Infinite remains infinite despite the method of reduction. This means that infinities cannot be explained away (the ultimate reduction). The existence of infinities in the Math surely has meaning. Schwartzchild thought so. He did not attempt to explain his infinities away. Okay, there could be limits on the idea of infinity in this case. Perhaps there are quantum mechanical constraints such as the fact that pinpointing the center of a black-hole would violate the Heisenberg Uncertainty Principle. But, if a black hole compresses to a diameter as small as a Planck distance, it would serve the same purpose as an infinitely dense point mass. That is, there would be no way to tell that a black-hole was not infinitely dense. Milgroms observations indicate that it really does behave this way. Whether it may actually be so is a theoretical point that Schwartzchild has already considered. I know that infinites are anathema to mathematicians. Their squeemishness is misplaced in cosmology, however. What if it happens that it is actually more likely that a BH is a real point mass, as close as we can tell by QM, having as near to an infinite density that may be required to provide the proper effect (the real meaning of infinite). 2) Actually, this is irrelevant. We are speaking of the geometry of BHs and the influence this geometry must have on the structure of spacetime in the vicinity. The consequences are to be determined by observation and experiment. If the escape velocity does not actually exceed c nearer to the center of a BH, then there is no such thing as an event horizon anyway. Karl Schwartzchild would object. If the escape velocity may be exceeded only by a smidgen determined by the Heisenberg Principle, why not by something rather more than just a smidgen? We need only to suppose that the effective radius of a BH is small enough to produce the required effect, which we may then consider to approach that needed to give effectively infinite density. Effectively is the keyword. 3) The nausea experienced by some professional mathematicians upon contemplation of infinity is not matched by the feelings of some others who revel in the concept. In fact, there is a whole branch of mathematics devoted to it. I do not believe that professionals would devote their whole careers to studies that do not have even theoretical practical consequences. Math is beautiful, but is no 10. And, it is a whore. The mathematics of infinities engendered by the Schwartzchild analysis of GR serve as a flag signaling that there is something going on here. What we find in experience now does not equate to what may be found in the future. And, Milgroms observations are still extant. No revision of Newtons Law of Gravity is needed. No Dark Matter is needed either (Dark Matter is based on Milgrom). Just a liberal tweak upon the concept of what it really means to be a black hole is all that is required. Sometimes liberalism makes sense. 4) Speaking of infinite mass, one would have to refer to the whole universe, at minimum. What if BHs are wormholes leading to this very same universe, but from a different perspective? Might it not then have an effectively infinite mass? But this is all an unnecessary complication. The potential need not be realized. 5) Okay. Now we have another possible alternative to Dark Matter. 6) Well, of course. Do we not always observe external galaxies from afar? It seems far fetched that we should ever observe the Milky Way from beyond. So, your idea means that it should be futile to try to detect the effect in our own galaxy. But, is not GR all about the curvature of spacetime and the dynamic effects that we can expect from such a curvature. Remember, the vector and tensor math of GR is derived from techniques used in hydrodynamics. The dynamic nature of fluids has a frame dragging equivalent. In other words, you are saying that GR is dynamic, not static. Even Newtonian dynamics is really static in nature because it cannot treat transitions between states which are time dependent. Time dependent variations between fluid states is often referred to as turbulence. Is there turbulence in the behavior of spacetime? 7) You amplify your comment that frame dragging style wrinkles on the face of GR could explain MOND and explain away Dark Matter. What if BOTH these wrinkles and the giant scar of the hyperbolic field effect should apply? 8) Wonderful. Fundamental questions are what science is all about. But, the anomalies do indeed need to be explained. Good luck finding a valid hybrid of GR and Quantum. Instead of M Theory, maybe we can call it OM Theory. Thanks for taking the time to read this. Further response would be appreciated. 27/11/11 P.S. This reply is also in response to all the other objections expressed by some readers. I would love to see more responses that build on what I have said. The other account now belongs to my wife, who is not much interested in physics or cosmology. She likes my avatar. The account is not a sockpuppet as defined in the rules. Administrative approval may be forthcoming. Naked singularities are not what this discussion concerning MOND and Dark Matter is all about. Far from it. The Black-hole singularities referred to here are cloaked in spiral galaxy disks or other conglomerations of stars. Usually, they are surrounded by infalling stars that sometimes result in phenomena of their own like jets. Also, the central supermassive black hole in any spiral galaxy is too small to have this putative effect of MOND that mimics Dark Matter. They have masses of "only" a few million sols, at most. While the galaxies contain masses of over 200 billion sols. But, since the central black holes rotate congruently with the disk having a center of rotation that is coaxial with the disk's, their gravitational fields superpose. If this is not so, geometry is not valid. Superposed, the combined gravitational field would be sufficient to provide the effect. One need not have an actual singularity anyway. All that is required is that the compact diameter of a black hole is less than or equal to the Planck distance implied by the Heisenberg Uncertainy Principle. This is really all that we can ever postulate, in fact. The references to my external site are mere references FYI for the reader. Do you mean that one may never quote material placed on one's own website? Confinement to "Speculation" is equivalent to effective censorship because, by Pareto'sa 8o/20 rule, at least 80% of all readers will avoid the Speculation category. I do. This category should be eliminated. I wish your ideal of science was really true. But, don't kid yourself. You know that it is not. Give students a little more credit. We have to make a distinction? Why? You put too much faith in the peer review process and journal editors, who are only human (at least at present). I do not admit that the idea of the hyperbolic field effect is not firmly established. The solidity of the concept is what my posts are all about.