This post is entered in 5 parts because it is long, segmenting makes it easier to reply and easier to read.
………………………..Critique and Fate of the Universe (continued, part 4)……………………..
It is well known that a point mass having the size of many hundreds or even thousands or millions of suns will have a very different gravitational field from the normal star, planet or galaxy because its mass is not distributed in 3D space - it must exist as a 1D singularity. Singularities do not possess the usual parabolic gravitational field potential that is assumed by Newtonian Dynamics. Such a black hole field must have a shape that is infinitely deep as the origin or center of mass is approached since a black-hole has infinite density with all its mass compressed into a single point. An infinitely deep gravitational potential has the 2D profile of a hyperbola, not Isaac Newton's parabola.
The gravitational attraction around a black hole must fall off with distance from the center as 1/r, r being the distance. Newtonian Dynamics assumes that the field is parabolic, falling off as 1/r^2. The fact of this difference is huge. So, when the centripetal acceleration of stars in the periphery of spiral galaxies is computed, it does not agree with ordinary Newtonian Dynamics because the centers of most spiral galaxies contain super-massive black holes. The mass of the galactic disk may actually contribute to the effective mass of the black hole in the nucleus, making the 1/r relationship even more pervasive.
The acceleration difference between the 1/r versus the 1/r^2 relations, at large r, is virtually a constant, just as Mordehai Milgrom observed in 1983. The “MOND effect” is real.
But, the inference of "Dark Matter" is unnecessary to explain the MOND effect, nor is a modification of Newton's Law. There is no Dark Matter. No WIMPs or "weakly interacting massive particles" will ever be found in any particle accelerator now or in the future. The theories of subnuclear physics do not have to be rewritten to accomodate an odd new particle. General Relativity does not have to be revised. Newtonian Dynamics survives with only the ADDITION of a footnote: when a black hole is involved, Newton's Law of Gravity must include a term in 1/r as well as, perhaps (as in galaxies) one in 1/r^2. That is all.
As far as Dark Matter is concerned, I report only what Milgrom says he discovered after carefully considering data from many many spiral galaxies. I am saying only that he ignores the fact that nearly all spiral galaxies and most other types have supermassive black holes embedded in them. This makes a huge difference. Black holes and the whole mass of the galactic disk will behave like a non-Newtonian entity having a gravitational potential that falls off as 1/r, not as 1/r^2.
Comparing a graph of this hyperbolic versus a Newtonian parabolic potential profile one sees that there is a virtually constant difference at large r. This is the source of Milgrom's residual centripetal acceleration constant that he says he sees in most of the galaxies he studied.
I am not arguing with Milgrom's findings. Far from it. I say he is probably right. But, he needs to consider the implications of the existence of relativistic supermassive black holes.
This comment is just that, a comment on the cosmological meaning of relativity in regard to black holes in galaxies.
Milgrom proposes a new model for gravity. He calls it modified Newtonian dynamics (MOND). But, MOND will require a rewrite of general relativity, one of the most validated theories in all science (only quantum mechanics is better verified). My comment leaves GR intact. My comment is simple, direct and jibes with the facts while being more parsimonious than MOND.
One does not observe the rotation of galaxies directly against the background of other galaxies. They rotate too slowly. One observes red-shifts from stars in different regions of each galaxy. Plotting rotational velocities got this way versus distance from the center of a galaxy, one should see a monotonic drop in velocity to near zero as one approaches larger r. Instead, velocity reaches a constant nonzero plateau. This contradicts Newton's Law of Gravity.
Milgrom wants to add his tiny, residual acceleration constant to Newton's Law. All I am saying is that it would be better to take into account the non-Newtonian hyperbolic black hole gravitational potential that general relativity says simply must exist in almost all spiral galaxies and also in other types of galaxies that may harbor black holes.
Galaxies that do not happen to show the MOND effect probably do not have supermassive black holes, or else their black holes have formed so recently that there has not been enough time for the effect to propagate all the way to and beyond the periphery.
Yes, Saul Perlmutter and Adam Riess both depended on the same Lambda/Cold-Dark-Matter model of the universe that uses the Friedmann equations as a basis. So, they really didn't have to coordinate their results. But, they did. And, they used the model to predict the model, the ultimate retrodiction.
The same thing is done when cosmologists use the model to interpret gravitational lensing effects, the SZ effect and other observations that they say give credibility to the same dark energy and dark matter contained in the model.
I do not say there is any attempt at fraud here. In fact, I say that they all are clearly acting as honest scientists. But, the scientists who reported positive cold fusion results were all honest too. They did not realize that there were inherent flaws in the neutron detection devices that they employed to observe "fusion" in deuterium oxide electrolysis cells using palladium electrodes. Honest scientists fall for pseudoscience too. But, fudge is fudge and no-one is immune to wishful
thinking. Perlmutter and Riess wished for a more exciting result and they got it.
See Part 5 for the implications to the fate of the universe.
Cosmologists are always wrong, but never in doubt. - Lev Landau
September 11th, 2011, 01:46 PM
Originally Posted by Gary Anthony Kent
"The gravitational fields of any supermassive black hole and its associated galactic disk are perfectly and precisely co-axial. This means that the gravitational fields will be indistinguishable from a distance, say, at and beyond the periphery of the disk. The fields merge into one, especially at the coaxial center. The fields must reinforce each other. So, the effective mass of a supermassive black hole at the center will not be just a few hundred to a few million suns, it will be a few tens of billion suns."
Show it! Show us the math. What you are saying here is wrong and disproved by the analysis of Keplerian motions of stars around the centre of the Milky Way. These motions were the very measurements that determined the mass of the central BH. If your claim were true, the analysis would have indicated the mass you are claiming. The orbits of objects in galaxies are determined by the mass that is encircled by these orbits.
You cannot first say that a BH produces a gravitational field that is proportional to 1/r and the rest produces something that goes like 1/r^2 and then claim that the global field goes like 1/r anyway. It is either the one or the other. How would a million solar mass BH with a 1/r field surrounded by matter that produces a 10 billion solar mass 1/r^2 field merge into a 10 billion solar mass 1/r field?
And even if this were all true, you have yet to demonstrate that this is the cause for the flat rotational curves or, if you will, the cause for the new MOND a0 constant. Remember that for a gravitational field you need the mass or mass distribution and the shape of the potential.
What you are proposing is yet another version of the Dark Matter mass conspiracy that would now turn into a BH mass/disk mass conspiracy. Both masses would have to be very finely tuned in order to produce flat rotation curves. This phenomenon would require that all galaxies have the same BH/disk mass ratio in order to be universal. How should this be possible?
In addition, a BH is spherical if not singular, i.e. the resulting gravitational field is radially symmetric. The gravitational field of a galactic disk is different, because the mass is distributed across a large disk, i.e. the resulting field is not radially symmetric, rather cylindrically or toroidally symmetric.
Come up with some simple math, and you might have a point.
Last edited by Dishmaster; September 11th, 2011 at 02:14 PM. Reason: typos
I said that the gravity fields of the two entities overlap and superpose only at or beyond the periphery of a galaxy AND at the exact asymptotic center of the Supermassive Black Hole (SBH). I insist that the SBH simply must be situated at the exact center of the nucleus of a galaxy. The nucleus itself could be off-center, I suppose, in some cases. But, not for long – tidal forces and other losses will soon cause the centers to again coincide.
If the SBH that is said to exist in the nucleus of most spiral galaxies is not precisely at the barycenter of the symmetric structure, with its gravitational field exactly co-axial with the field of the whole galaxy, then it must be “off center” or “eccentric”. In this discussion, we are talking about only two entities, the supermassive black hole and the whole rest of the galaxy. So, if it is in an eccentric position, as it orbits the barycenter existing at the time, the SBH must be producing regular shock waves of gravitational energy – gravity waves. If they exist by general relativity, these gravity waves (especially at smaller distances) should be of an intense kind that would be readily detectible by the several laser interference gravity wave detectors (LIGOs) that have already been built here on Earth.
Not one single gravity wave has ever been detected yet, even though these instruments have been in operation for years. And, if gravity waves are being emitted, the “system” is losing energy at a prodigious rate. The separate centers of mass will be in-falling toward a common barycenter until the centers become indistinguishable and exactly co-incident with the barycenter. They will again become co-axially superposed.
I am not going to be sidetracked into mathematical discussions that most readers will never understand and that will turn them right off. I could go into group theory and discuss the ways that point groups (not space groups) could be used to categorize galaxies. Much can be said about the physical properties of objects conforming to a point group irreducible representation (IR).
Consider this, however. The IR of a galaxy and its resident SBH will be directly related and very similar, if not identical. One’s IR matrix will be the same or a subset of the other – I forget which sense would apply. This means their major properties will overlap too, given their relative spatial configurations.
What properties do they have that could overlap? SBHs have no other properties but their total entropy, total mass, spin and gravitational field. How many spiral galaxy nucleus SBHs spin retrograde? The event horizon is undetectable directly. So too, is the entropy state.
The gravity is measurable though, because INSIDE a galaxy, >greatly within the perimeter of its total mass< one may artificially consider the SBH and an orbiting star as “the system” and analyze it by Newton’s Law (NH) or by the hyperbolic black hole (HBH) field postulate. (But, at small radius, HBH and NL will be indistinguishable.) Larger radius will require consideration of the whole rest of the galaxy. See the whiteboard presentation of my mathematical analysis at http://www.lonetree-pictures.net under the MOND sub-site heading.
Here is some of the math that you demand, but it is meant to be accompanied by a more complete and exhaustive PowerPoint lecture – you know – like the ancient old professor with his brand new laser pointer that he hasn’t figured out yet. I am indeed preparing for the lecture circuit. These posts may help.
I love your replies because they make me clarify issues before I make a fool of myself in front of an audience.
Cosmologists are always wrong, but never in doubt. - Lev Landau