Alternative Explanation of Modified Newtonian Dynamics - MOND

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The effect that causes dark matter is merely the acceleration caused
by the accelerating expansion of the universe which is masked
by gravity until gravity lessens to the point that the
acceleration of the expansion can be detected.


Regarding an article in Science News 11/30/13, page 9,
Jefferey Miller of Los Angeles made the comment:
"Candidates for dark matter bite the dust
brought to mind a quote by Confucius that
The most difficult thing is to find is a black cat in a dark room,
especially if there is no cat.
(Above added to this website on January 25, 2014.)


This is an update to this website which was added on July 24, 2002, was itself updated first on July 26, 2002, and will continue to be updated as better ways to present this complex subject are found.

Background Information

Dark matter was hypothesized from observations made by astronomers which indicated more acceleration from gravity at extreme distances from various masses. Mordehai Milgrom, after extensive research, arrived at the equations which describe this phenomenon. Subsequently, it was discovered that the expansion of the universe is accelerating. However, no one bothered to incorporate this new data into Mordehai Milgrom's research. Below, it is shown how Milgrom's data perfectly fits into the hypothesis that the accelerated expansion is masked by gravity only up to a point - at which this acceleration is detected and mistakenly explained as the reason for the supposed gravitational acceleration attributed to dark matter. Thus, it may be said that Mordehai Milgrom is the first person to detect the acceleration of the expansion of the universe.   This is an oversimplified explanation - the details below provide a thoroughly convincing argument when understood.

The Details

The August issue of Scientific American features an article by Professor Mordehai Milgrom of the Weizmann Institute in Rehovot, Israel, called Does Dark Matter Really Exist. According to the article, the Professor is the "Father of MOND" and MOND means "Modified Newtonian Dynamics". MOND is a theory which began when Professor Milgrom "proposed a modification of Newton's second law that changed the relation between force and acceleration".

My own knowledge of MOND is limited to what I read in this article, so I am not commenting upon whether or not there should be a change in Newton's second law. However, I believe almost any alternative to "dark matter" is a refreshing change. Furthermore, the phenomenon which has led to the inference of dark matter has effects too precise to be thus attributed. These effects would require a certain distribution of dark matter that is anything but random. So it is appropriate, instead. to examine the possibility of a natural law at work.

Dark matter was proposed to explain the fact that stars and bodies of gas far from their galactic centers, and galaxies within galaxy clusters, move in in a manner which, according to the known amount of matter present, should cause them to escape. In a stable orbit, the velocity of an orbiting body creates centrifugal force which is balanced by the force of gravity at the orbital radius. If the velocity of the orbiting body is great enough to create sufficient centrifugal force to exceed the gravitational force, the orbiting body flies away from the attracting body. Observed mass usually creates enough gravitational force to prevent the orbiting body from flying away. However, the observed mass in the cases mentioned above is not sufficient to keep the orbiting bodies from flying away. So the concept of dark matter was provided as a solution.

Ordinarily, in a solar system such as our own, the orbital velocity of an inner planet will be greater than the orbital velocity of an outer planet. So the orbital velocity of Mercury is the highest, and the orbital velocities of the other planets decrease as we move outward. Venus has a lower velocity than Mercury, Earth has a lower velocity than Venus, Mars has a lower velocity than Earth, Jupiter has a lower velocity than Mars, and so on.

Distances within our solar system are small compared to distances within and between galaxies. According to the article, MOND would not begin to apply for our solar system until a body is 10,000 times more distant from our sun than the distance between Earth and the sun. Our sun is a very small one. For very large attracting masses, such as whole galaxies, the distance before MOND becomes effective is much greater.

When MOND applies, the velocities of orbiting bodies no longer decrease with distance but maintain a constant value. According to MOND, this is possible because a constant, with the dimensions of acceleration, manifests. This constant was there all along, but was masked by gravity at distances less remote from the attracting body (such as the sun). This constant, called ao, acts in the same direction as gravity (toward the attracting body) and has the effect once attributed to dark matter.

According to the article, MOND applies when the velocities of orbiting bodies cease to decrease. At this point, they reach a constant value, so for convenience I choose to call it the constant-velocity-point (CVP). The CVP occurs at different radii from different attracting bodies according to the mass of each attracting body, but in every case, the constant orbital velocity is proportional to the fourth root of the mass of the attracting body.

Professor Milgrom spent many years developing MOND and had the intestinal fortitude to introduce it to a the scientific community where, very likely, it was first regarded as too revolutionary. In my opinion, he is a genius in his field. His originality and persistence has resulted in what I believe is basically a valid theory. He did not have the true nature of gravity to use as a tool, so I decided to see what would happen when the nether (dynamic ether) theory of gravity was used along with his math. The results follow.

First of all, at the CVP the constant orbital velocity is proportional to the fourth root of the attracting mass.
In equation form, this is: mx/my = vx4/vy4 where the subscript "x" applies to one galaxy and the subscript "y" applies to another galaxy.
This equation can be rewritten as: mx/my = (vx2/vy2)2.

The equation for centrifugal force is Fc = mv2/r where Fc means centrifugal force, m is mass, v is orbital velocity, and r is the radius from the galactic center to the orbiting body. Note that the galactic center is used because it is very close to the center of mass for the galaxy and the CVP is a long way from that center - otherwise, the equation would not be so simple. F = ma where a is acceleration, so we can remove mass from the equation for centrifugal force and arrive at an equation
for centrifugal acceleration which is ac = v2/r.
Because ao is a constant that opposes centrifugal force and is thus equal to it,
we now can say: ao = vx2/rx = vy2/ry where again the subscripts are for two different galaxies, each v is the constant velocity for its galaxy, and each r is the radius to the CVP for its galaxy.

By substitution, mx/my = (vx2/vy2)2 becomes mx/my = (rx/ry)2
which is mx/my = rx2/ry2 which is also
mx/my = Ax/Ay where A is the area of a theoretical sphere surrounding a galaxy at the CVP of the galaxy. Gravity acts throughout a spherical area, A, and the product of A and g (where g is the acceleration of gravity at A) at any given radius is proportional to the mass at the center of the sphere.
So mx/my = Axgx/Aygy. But Ax/Ay already is the correct ratio for mx/my, so gx/gy must equal one,
and therefore, gx = gy. This means that the acceleration of gravity at the CVP for any galaxy or other attracting body is the same.

There is another effect at the CVP which is only evident when one knows what mass and gravity are in actuality. What we call "mass" is actually nether (dynamic ether) flowing into matter. Nether has a "Mass" with a capital "M" and what we call mass is given here as a small "m".
So m = M/t where t is time. At all levels of a gravity funnel (see Is There a Dynamic Ether? on this website) mass is the same because the same Mass must flow through any level of the funnel.

A theoretical spherical surface surrounding the attracting mass acts as a funnel cross-section for incoming nether (dynamic ether). The amount of nether flowing through the cross-section is equal to its incoming velocity and density at that cross-section. So the mass at any level of a gravity funnel for one of our example galaxies is found by the equation:
m = ADv where A is the area of the funnel cross-section, v is the velocity of the flow, and D is the density of the Mass flowing through.
This means mx/my = AxDxvx/AyDyvy and once again, since Ax/Ayalready is the correct proportion,
Dxvx/Dyvy = 1, and therefore Dxvx = Dyvy. The density of Mass here is the same as the amount of Mass, so Dv is actually the same as Mv (momentum). So Mv for nether at the CVP is the same for all masses. Why? In addition, where the product of g and A is proportional to the attracting mass at any radius, the product of M and v is proportional to the attracting mass only at the CVPs. Again, why?

The Simplified Explanation

In nether theory, there is an inertial reference frame (IRF) within which our universe exists. This IRF is a fundamental which is not caused by our universe, contains our universe within it, and may contain many universes or none at all should anything happen to erase our own. The big bang occurred because nether came into being in a concentrated form within which was pressure, and this pressure caused the universe to expand rapidly at an accelerating rate just as air does when there is an explosion. It is the pressure within the nether versus the lack of pressure in the IRF which creates the accelerated expansion of our universe (not dark energy - although the nether is the container of our electromagnetic energy).

The expansion of the universe is given in incremental form by the Hubble constant which is the velocity of a distant object as it moves away from us divided by the distance to it. I call this a unit velocity and it is v/d. The acceleration of the expansion can be found in the same manner by dividing the acceleration of a distant object as it moves away from us by the distance to it. I call this the unit acceleration and it is a/d.

F = ma = m(d/t)(1/t) = mv(1/t). For nether at a point at the CVP, m is M and a is g.
So F = Mg = M(d/t)(1/t) = Mv(1/t).
v = d/t, so v/d = 1/t.
Thus, Mg/Mv = Mv(1/t)/Mv = 1/t = v/d. When this v/d is equal to the v/d that is the unit velocity we call the Hubble constant, the velocity of nether is zero relative to the galactic center. This is why Mv is so important at the CVP.

The acceleration of the expansion of the universe is caused by the pressure difference between the nether and the empty IRF. The pressure difference constitutes a force.
F = ma, so this force equals MTa where MT is the total Mass being pushed by the force and a is the acceleration produced. The unit acceleration is a/d where d is a unit of distance. MTa/d is the total Mass multiplied by the unit acceleration. If we multiply this product by ro (the distance to the CVP) we have the total acceleration of the nether expansion relative to the galactic center.

This acceleration relative to the galactic center is what MOND theory calls ao. However, it is not a true constant and it is working in the opposite direction (accelerating outward from the galactic center). It is being opposed by the inertia of each orbiting body which is attempting to be affected by the IRF to maintain its same orbit. We are part of the expansion of the universe. As we view the galaxy from our own perspective, we do not see the universe expanding. Instead, we see the apparent acceleration of the inertia-bound orbiting body toward the galactic center.

This apparent acceleration is always proportional to and opposite to the acceleration of the expansion of the universe as we see it relative to the galactic center at the CVP. Although ao changes so slowly with distance that it appears to be constant, it is actually proportional to r, the distance from the galactic center. But v2/r is proportional to 1/r and it is the acceleration due to centrifugal force. So as we move outward, the orbital accelerations outward increase in proportion to 1/r and the inward acceleration, ao, increases in proportion to r. This causes the orbital velocities from the CVP outward to remain the same.

The More Complex Explanation (As I see it)

The *inertial reference frame (IRF) within which our universe exists, consists of three spatial dimensions (the x, y, z straight-line types found in elementary geometry). The laws within the IRF are Newton's, and the dimensions of the IRF are infinite.

Inertia is a passive "force". The "law" of inertia merely states that something does whatever it is doing until something else changes it. This is simply logic. Why should anything change unless there is something to make it change? So inertia is a very "passive" and logical "force".

One plus one equals two and energy in one direction plus energy in another direction should result exactly in the sum of the two energies. This is conservation of energy which is like one plus one equals two. It is fundamental. The Pythagorean theorem makes this conservation possible and thus defines the three dimensions of the IRF. So the IRF is a consequence of two very logical and passive laws: (1) that for inertia, and (2) that for simple math (conservation of energy). The constituency of the IRF itself is simply nothing. The IRF is merely two basic, passive, mental concepts.

The universe was probably begun at a point where nothing was divided into "positive" and "negative" nether (dynamic ether). Our universe was one point, and the opposite universe was another point, probably separated from ours by time. The total Mass of the two universes adds up to zero.

When our universe began, the nether of which it was formed was concentrated so that relative to the surrounding nothingness, it was under extreme pressure. The pressure caused it to expand in all directions from the starting point. Just as any explosion within a body of air causes the air to expand at an accelerating pace which lessens with time, the nether of our universe expanded at an accelerating pace which lessened with time (and is still lessening with time). This is a consequence of inertia and pressure which is more than I wish to go into here.

The phenomenon we call gravity creates greater nether density as the nether falls into the gravity funnel (see the mechanism for gravity in nether theory) so that matter is composed of nether that is more dense than nether in "free space". The more mass within a given volume, the more dense the nether within that volume. Matter has inertia proportional to its mass, and this inertia opposes acceleration. So more massive matter accelerates more slowly than less massive matter, and all matter accelerates more slowly than nether that is far from gravity funnels (matter). Therefore, the components of the universe accelerate at different rates.

Gravity is an acceleration caused by a "funnel" in which nether moves from all directions toward the body creating the funnel. When there is no nether motion external to the gravity funnel, the inward acceleration is balanced and the body creating the funnel does not move. However, when there is nether motion external to the gravity funnel, we can think of that motion as if it were a wind. There are two types of this nether wind that we should examine.

First, we should examine a wind of nearly constant velocity over a period of time. A truly constant wind never occurs because this wind is caused by either another gravity funnel (in which all nether motion inward is acceleration) or by the expansion of the universe (which is accelerating). However, there are places within our universe where this wind is relatively constant. A constant nether wind would tend to create an effect on the upwind side of a gravity funnel. There would be more inflow from that direction. The nether on the downwind side must turn to come into the gravity funnel and the turning causes centrifugal acceleration of the nether which tends to lessen the inflow from that direction. This is balanced by the greater inflow from the upwind side, and the gravity funnel maintains its position. Of course, a constant wind which appears suddenly is an acceleration and would have an effect at the time of its sudden appearance, but this belongs in the second classification which follows.

Second, we should examine a wind that is an acceleration of the nether. This type of situation is the reality we see in our universe. The acceleration upon a gravity funnel causes the funnel to attempt to increase its own speed in the direction of the external acceleration.

An object in the gravity funnel experiences the second type of situation and the acceleration is what we call gravity. Due to inertia, there is a very slight hesitation before an object moves with the accelerating nether. Thus, the object is always accelerating slightly behind the nether acceleration around it. This effect is very minor and is masked by the effect of gravity beyond our ability to detect it - until the nether acceleration we call gravity is reduced sufficiently for us to do so.

It is this inertial hesitation that we see opposing the outward acceleration of the expansion of the universe from our locale.

The expansion of the universe and its acceleration as we see it are only contributing vectors of the resultant expansion as seen from the place where the expansion began (the point of the big bang). This is why there can be acceleration away from a galaxy while the galaxy is also accelerating away from its outer portions, and why an object outside the CVP can be accelerating away from a galaxy while also accelerating away from a point farther outside the CVP.

Furthermore, the acceleration of the expansion of the low-density nether, which occupies most of the volume between galaxies and between the galactic centers and their outlying stars is slightly greater than the accelerating expansion between these concentrations of matter. So the redshift we see will indicate slightly greater accelerating expansion than the distances between masses would indicate.

The result of all this is that in almost every respect, MOND is correct and there is no dark matter. Professor Milgrom has my thanks and admiration.

For all the details on the nether (dynamic ether) theory regarding dark matter, see The "Big Bang", Dark Energy, & Dark Matter by Lew Paxton Price in the essay section of The General Science Journal.

A Proposed Alternative

In the March 2003 issue of Scientific American is an article by David B. Cline, a professor of physics at the University of California in Los Angeles. He states that another particle may explain the dark matter problem (Does this sound familiar?). This new particle, christened the neutralino, is based upon supersymmetry.

Supersymmetry postulates "a whole new family of particles - one `superpartner' for every known elementary particle." All of these new particles are heavier than known particles. The best candidate for dark matter is the neutralino which is actually supposed to be the lightest supersymmetric particle. It must be stable because it is the lightest and cannot decay into something lighter. It has no charge. Its only quality necessary for communication with other particles is gravity - which is very weak.

Although many attempts are in progress to catch a neutralino, there is no credible evidence, to date, that they exist. More time and money are being expended to try to create better detectors.

It appears that the particle physicists will be able to create new particles to explain anything that they wish to explain. Where does it end? The number of new particles can extend to infinity and each will be just as valid as their foundation of fantasy. Most science fiction writers can do better than that. Isn't it amazing what brainwashing can do?

Regardless of neutralino theory, the article is a good one in that it explains the theories for dark matter which are currently considered to be better band-aids for today's prevalent particle theory. The author seems to be capable of assimilating different ideas and weighing their merits.

The Earliest View of the Universe

In the February 15, 2003, issue of Science News, is a photo of what is supposed to be the oldest view of the infant universe. It is said to be what the universe looked like 380,000 years after the Big Bang, and the light from it is supposedly 13.7 billion years old. However, I wonder if the acceleration of the expansion of the universe was considered in this age estimate of the light.

According to the article, "Cosmic Revelations", the images of the Big Bang's afterglow, known as the cosmic microwave background, also delineates cosmic composition: 4 percent is ordinary matter; 23 percent is invisible stuff called cold dark matter, which prompted the galaxy to coelesce; and 73 percent is so-called dark energy, which has accelerated the rate at which the universe expands.

Conclusions Derived from the Above

Of course when one acknowledges the fact that we live in a universe of dynamic ether, the cold dark matter is merely a theorized substitute for the truth. The effect supposedly created by "dark matter" is the acceleration of the universe, the "dark energy" is the dynamic ether, and the matter is merely combinations of vortices of dynamic ether.

This is a "postscript" added on May 5,2006

The article below from New Scientist indicates that the supposed "field" (which causes the acceleration that some attribute to "dark matter") may be detected if a satellite is placed where the gravity from the earth is equal to the gravity from the sun. In my own opinion, the acceleration of the expansion of the universe is everywhere so that supposed evidence for such a "field" might be detected as hypothesized. However, the place proposed for its detection is one where the nether (dynamic ether) is very dense as opposed to its density at empty places between or far from galaxies. This density will cause the effect of the acceleration to be very small for essentially the same reasons found in the part of this site called Why Ether Detection Has Yielded Lower Velocities.

The ether expands equally per "amount" of it. The "amount" of it per volume is its density. If it is more dense by a factor of ten at one point than it would be at a point in intergalactic space, then the visible expansion would be one-tenth what it would be where the effects of MOND are found. Actually, the density at the proposed point of measurement would be much greater than ten times that of intergalactic space. Consequently, it is unlikely that the instruments used will be able to detect the acceleration - and if it were to be detected, the expansion would appear to be much less than expected.

The proposal of two new "fields" to complement Einstein's gravitational field (caused by the curvature of space according his general theory of relativity) is markedly more cumbersome than simply realizing that the effects of dark matter are caused by the accelerating expansion of the universe as shown above. Of course, it would appear that Occam's razor was discarded long ago by most theoretical physicists.

My comments will be more comprehensible once one has read the article below.

Gravity: Were Newton and Einstein wrong?
29 April 2006
From New Scientist Print Edition.
David Shiga

Catching cosmic waves

A GOOD bit of our universe - 23 per cent of it, to be exact - seems to be made up of stuff we can't even see. Except, what if it isn't?

The leading cosmological theory says that invisible "dark matter" lurks in the hearts of galaxies, its extra gravity keeping the outermost stars from flying off into the void and generally making clusters of galaxies look the way they do. Nobody knows what this mysterious matter is, but it must be there, because all the visible stars, planets and other bodies do not have enough mass to account for the celestial motions we observe, according to Newtonian gravity.

But what if Newton was wrong? It's a long-standing question whether his law of gravity, supposed to explain everything from falling apples to spinning galaxies, might actually be flawed. That is the claim of a growing number of physicists who support a controversial alternative theory called modified Newtonian dynamics, or MOND. The theory has recently overcome some serious problems that had plagued it since its inception - such as how it fits with general relativity - and it is now able to make surprising predictions about the evolution of the universe.

Suddenly, people who used to scoff at the renegade theory are giving it a second look, sparking one of the hottest debates in astrophysics. If MOND is correct, it will pull the rug out from under the established view of gravity and dark matter, which together underpin almost everything we know about astronomy. "From being really out in the cold from a theoretical point of view, MOND is now being taken very seriously," says University of Oxford physicist James Binney.

What has made people sit up and take notice is a 2004 paper by Jacob Bekenstein of the Hebrew University of Jerusalem in Israel (New Scientist, 22 January 2005, p 10). His paper, the culmination of a 20-year quest to reconcile MOND with relativity, seems to have stood the test of time and has convinced several other groups to work on the theory and test its predictions. Their results suggest Bekenstein is on to something deeper: a theory of gravity that preserves the best aspects of relativity, but with modifications that could make dark matter obsolete - even as efforts to find it are heating up.

The story goes back to 1933, when Swiss astronomer Fritz Zwicky noticed that galaxies in certain clusters were moving so fast that the clusters shouldn't be able to hold onto them - yet they did. To explain this, Zwicky suggested that extra, unseen matter in the clusters provided the gravitational glue. He called this stuff dark matter. By the 1970s, astronomers realised there was a similar problem for individual galaxies: they are spinning so quickly that they should tear themselves apart. Here too, dark matter was invoked.

In 1981, physicist Mordehai Milgrom hit upon the alternative theory of MOND. He was at Princeton University at the time but soon moved to the Weizmann Institute near Tel Aviv, Israel, where he remains today. He went to visit Bekenstein, then at Ben-Gurion University in Beersheba in the south of the country. "He said he had something very interesting to show me," recalls Bekenstein, who was best known for his work on the thermodynamics of black holes. Milgrom set out his idea that galaxies and galaxy clusters might remain intact not because of unseen matter but because gravity itself does not weaken with distance as quickly as Newton's law says it should. Intrigued, Bekenstein began working with Milgrom on the theory.

The name MOND contrasts the theory with Newtonian gravity, even though this was essentially replaced by Einstein's general relativity in the early 20th century; the name makes sense because astronomers still use Newton's equations for most situations. However, Milgrom and Bekenstein were effectively challenging relativity too. That's because MOND would have to be different enough from relativity to make gravity noticeably stronger in the outskirts of galaxies, yet not so different that it contradicted aspects of relativity verified in observations stretching back to 1919.

Rethinking relativity

That was a problem. Milgrom published his theory in 1983, but no one could see how to reconcile it with Einstein's well-tested model. Also, it seemed too ad hoc in that it simply modified gravity below a certain strength, thereby altering its behaviour typically at large distances. So in 1984, Milgrom and Bekenstein published a version that attempted to explain MOND as a modified version of general relativity. They took relativity and added a second gravitational field to provide the extra pull needed to keep spinning galaxies stable.

There was a snag, however: disturbances in this extra field would travel faster than the speed of light, creating a breakdown of cause and effect. Neither Milgrom nor Bekenstein knew how to fix this, so they both gave up the quest for a while. "When you see a big mountain in front of you, the first feeling you have is that it's the end. I mean, you're not going to get over this," Bekenstein says.

Ten years on and things had grown worse, with the discovery of new evidence for dark matter. Astronomers had been examining the way gravity bends light as it passes by galaxies, a phenomenon called gravitational lensing. The lensing they saw was much stronger than what the galaxies' ordinary matter should have caused, but consistent with what general relativity predicted from galaxies filled with dark matter. Either galaxies really had hidden mass, or MOND would have to provide extra light-bending too.

Bekenstein didn't give up. In 1994, he and Robert Sanders of the University of Groningen in the Netherlands proved that you could never satisfy all the demands facing MOND if you restricted yourself to adding just one field on top of the standard gravitational field in relativity. Instead, a workable relativistic version of MOND would have to contain at least three fields.

Frozen field

In 1997, Sanders published a three-field version of MOND. The third field provided extra gravitational lensing and also got rid of faster-than-light waves, but again there was a catch. The field was a type called a vector field, which at each point in space has a magnitude and a direction. To get the right lensing results, Sanders froze the vector field so that it would always point in a particular direction: the direction of time. In relativity's four-dimensional universe, time is just another direction, like up, down, left or right. The frozen field violated the symmetry principle that space-time should have no preferred direction. "That's in a sense throwing the baby out with the bath water," Bekenstein says.

And so things stood until 2003, when Bekenstein finally found a way forward. Stuck at home with an illness, he realised he could unfreeze the vector field in Sanders's theory but still get it to point in the right direction. It isn't against the rules of relativity for the field to wind up pointing in a particular direction, as long as this behaviour is not locked in beforehand. The vector field in Bekenstein's version is free to point in any direction, but it tends to align itself in the time direction through its interactions with the other fields, the way a compass needle homes in on north.

Here at last was a version of MOND in harmony with well-established parts of relativity, yet different in a way that made dark matter unnecessary. Bekenstein named it "Tensor Vector Scalar" theory, or TeVeS, after the three kinds of fields it employs (Physical Review D, vol 70, 083509). The tensor field, from general relativity, describes the usual gravity arising from the curvature of space-time. The scalar field gives gravity extra strength in places such as the outskirts of galaxies. The vector field enhances gravitational lensing.

It may still sound ad hoc, but with the theory finally on a relativistic footing, even long-time sceptics are giving it a second look. "For me, MOND was a dirty word for years," says astrophysicist Pedro Ferreira of the University of Oxford. The big problem was that you couldn't address cosmology under MOND because it lacked a relativistic framework, he says. "What changed my mind was Bekenstein's paper."

Now several groups are using the theory to make cosmological predictions. Ferreira worked on a 2005 study led by Constantinos Skordis of the Perimeter Institute in Waterloo, Ontario, to predict how the large-scale structure of the universe would turn out under TeVeS following the big bang (Physical Review Letters, vol 96, 011301). Despite the cobbled-together nature of Bekenstein's theory, it naturally solves a fundamental problem in cosmology that is usually solved by invoking dark matter.

Galaxies are thought to have formed from relatively dense pockets of matter in the wake of the big bang. These dense patches were part of a pattern of giant acoustic waves that rippled through the universe, compressing and rarefying the soup of hot matter. The puzzle is how these variations could persist long enough for galaxies to form: in the white heat of this early era, countless photons zipped around and bounced haphazardly off particles of matter, and this should have blown the dense pockets apart before they could develop into galaxies. The standard explanation for what held the pockets together is - you guessed it - dark matter.

In Bekenstein's universe, however, the pockets survive even without dark matter. "The effect of MOND is to kind of sustain these structures through this smoothing phase, so the seeds of galaxies aren't wiped out through that period," Ferreira says. With TeVeS, the extra scalar field develops variations of its own that reinforce the dense pockets of matter, preserving them long enough for galaxies to form.

Although the cosmic sound waves behave in roughly the right way under Bekenstein's theory, there is debate over whether their detailed behaviour is correct. To see how the real waves behaved, astronomers look at the cosmic microwave background, the radiation emitted by the hot matter at around that time in the universe's history. We can detect this faint glow all over the sky, but it is not uniform. It is finely mottled, with some areas slightly brighter than others, and these variations correspond to where the waves made matter denser in some regions (see Graph). This even allows us to see what different frequencies of wave existed.

Sceptics argue that relativistic MOND gives fewer high-frequency waves than is implied by observations. "I think it's very difficult to reconcile what we've observed in terms of the amplitude fluctuations in the microwave background with the MOND theory," says astrophysicist David Spergel of Princeton University. In particular, he says, the theory underestimates how strong acoustic waves with wavelengths of about 100,000 light years must have been.

MOND proponents counter that measurements in this wavelength region are not yet very precise, and so it's not clear that Bekenstein's theory is at odds with them. Future missions such as the European Space Agency's Planck spacecraft, scheduled to launch in 2007, will map out the microwave background to higher precision and should help resolve the ambiguity.

Who needs it anyway?

Scepticism, however, runs much deeper than that. Spergel doesn't see the need for the theory in the first place, even in the realm where MOND has traditionally been strongest. "I have not seen any really convincing case for the need for MOND-like physics on galaxy scales," he says, because the stability of galaxies can be explained with dark matter. Indeed, even if MOND does well in future tests, its creator Milgrom thinks many experts will continue to support dark matter. "This is their livelihood. This is their claim to fame," he says. "They will never change their mind."

Conversely, the only thing that could rule out MOND in the near future would be direct detection of dark matter. About 20 different experiments are under way, or about to begin, that could detect dark matter particles within five years. One group of US universities is running the Cryogenic Dark Matter Search II, which is monitoring silicon crystals to look for small vibrations created by the impact of dark matter. They have not detected any so far, but they are gradually improving the sensitivity of the detectors. If any experiment finds dark matter particles in sufficient abundance - whether neutrinos or something else - then out go the alternative gravity theories.

Until then, MOND will remain a thorn in the side of the astrophysics establishment. If the theory survives and garners supporting evidence from future missions (see "A good MOND is hard to find"), astronomers will still face a long road ahead. Over the years, they have built a comprehensive picture of the universe using dark matter as a key ingredient. "That stuff rests on 25 to 30 years of laborious work," says Binney. "To do a comparable job with a much more tricky theory is going to be a long haul, and people are only beginning on it at this point."

Bekenstein concurs and goes even further. "All that we have learned about the universe in the last 300 years since Newton was learned really by combining the universal law of gravity of Newton with various pieces of physics," he says. "If you're going to change this, and you say that the law doesn't work, literally, in galaxies and bigger systems, then our picture of the universe is going to get changed drastically."

Either way, the picture will probably include a more fundamental theory of gravity. Even Spergel, despite his criticism of MOND, finds Bekenstein's theory interesting in a deeper sense, as a variation of relativity. "General relativity, while it's been a very successful theory, may not be the complete theory," he says. "Most people think it is not the final theory." When the dust settles, we may find that dark matter, Newton's law of gravity and even Einstein's most famous theory are all things of the past.

David Shiga is a science writer based in Toronto, Canada A good MOND is hard to find Where do you go to look for modified Newtonian dynamics (MOND)? Try our own solar system. Since the early 1980s, NASA's Pioneer 10 and 11 space probes have been coasting away from the sun in the outer solar system. Puzzlingly, they have been decelerating more quickly than Newton's law of gravity would predict. The cause of this "Pioneer effect" is hotly debated, but the rate of deceleration is about what you would expect if Jacob Bekenstein's theory were correct. Still, most physicists won't accept the modified gravity explanation unless a dedicated mission confirms the Pioneer effect is real.

MOND might be more definitively tested through NASA and ESA's Laser Interferometer Space Antenna (LISA) project, designed to look for gravitational waves - ripples in space-time created by cataclysmic events like the collision of neutron stars. In 2008, a test mission called LISA Pathfinder will wind its way outward in larger and larger orbits around the Earth, carrying devices that sense very small accelerations.

Scientists are considering sending Pathfinder through the point in space where the gravity of the Earth and sun balance out precisely. Under Newton and Einstein, the gravitational force at that point should be zero. Under Bekenstein, however, there should still be a slight force. It is not clear whether Pathfinder will be sensitive enough to detect this force, but if it does, it will be a victory for MOND.

The main LISA mission in 2015 might also shed light on MOND if it succeeds in measuring gravitational waves. Unlike such waves in general relativity, gravitational waves in Bekenstein's theory move more slowly than light because one of the extra fields slows them down. If LISA were to find that the waves do indeed move more slowly than light, it would be strong evidence that MOND is on the right track.

The rivals

When it comes to alternative theories of gravity, MOND isn't the only game in town. Other proposed ideas:

Brans-Dicke theory (1961)

Carl Brans of Loyola University Chicago and Robert Dicke of Princeton University proposed that the gravitational constant of general relativity depends on an additional scalar field. The strength of gravity varies in time and space according to the strength of this field.

Scalar Tensor Vector Gravity (2005)

Joel Brownstein and John Moffat at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, described a theory in which quantum fluctuations alter the strength of gravity from place to place, giving rise to MOND-like effects.
  Bi-Scalar Tensor Vector Theory (2005)

Robert Sanders of the University of Groningen in the Netherlands put forward this model, which is like Bekenstein's relativistic MOND, but with two scalar fields altering gravity instead of one. Vibrations in the second field give rise to a kind of dark matter.

Supernovae make dark matter bloat

* 02 August 2006
* Exclusive from New Scientist Print Edition.
* Hazel Muir

Computer simulations showed that dark matter should be densest at the centres of galaxies, like this one, but observations show it is constant over thousands of light years - supernovae could be to blame (Image: NASA/Hubble Heritage/AURA/STScI) < 33.900-1_250.jpg>

The invisible dark matter at the centre of galaxies is not as dense as we would expect - and now we know why. It seems that the explosions of exhausted old stars are to blame for puffing out dark matter. These supernovae can also account for a mysterious shortfall in the universe's quota of dwarf galaxies.

More than 80 per cent of the matter in the cosmos is in some strange undetected form. We can see the gravitational effect of this dark matter, but cannot identify it. Computer simulations have reconstructed how dark matter clumped together with normal gas in the early universe to form small galaxies and how these small galaxies merged over billions of years to create huge star systems like the Milky Way.

The simulations raised one mystery, however. They showed that the density of dark matter should spike sharply at the centre of galaxies, while observations of the motions of stars reveal that the dark matter cores of galaxies today are much more puffed out, with densities that are constant over thousands of light years. "We have known about this problem for more than 10 years," says Sergey Mashchenko from McMaster University in Hamilton, Ontario, Canada.

Astronomers have suggested several possible fixes for this anomaly. For instance, they thought that dark matter might puff outwards because some kind of exotic force between the particles - other than gravity - makes them collide and scatter off each other like snooker balls. Now Mashchenko and his colleagues have shown that the smoothing of the density of dark matter is down to the explosions of massive stars at the end of their lives. At their peak, these supernovae can outshine their host galaxies.

Mashchenko thought that shock waves from supernovae should churn up interstellar gas in a galaxy, and that the gravitational disturbances created by this sloshing gas should in turn smooth out the spike of dark matter at the centre. To test this, his team used a supercomputer to simulate the evolution of a small, primordial galaxy that started off with a central spike in the density of dark matter. Sure enough, just 80 supernovae explosions per million years - typical of values expected in dwarf galaxies today - were enough to smooth out the dark matter spike to match observations if they continued for at least 100 million years or so (Nature, vol 443, p 539).

The same model can also solve another conundrum. The cosmos has far fewer dwarf galaxies - which contain several billion stars compared with the hundreds of billions in larger galaxies - than cosmological simulations predict. In Mashchenko's simulations, because supernovae smoothed out the spike in dark matter density at the centre, dwarf galaxies were less tightly bound together by their own gravity. Any encounters with bigger galaxies would therefore have easily torn many dwarfs apart, and this may explain their paucity.

>From issue 2563 of New Scientist magazine, 02 August 2006, page 12

Comments on the Above

1.   Mordehai Milgrom succeeded in establishing a mathematical relationship for the distance in which dark matter begins to manifest its effects.   This distance appears to be a function of gravity.   Although the puffing-out theory above appears to be generally tenable, it is doubtful that it will be as precise mathematically as MOND.

2.   The number of supernovae that would occur near a galactic center (where there is a black hole) would increase with the amount of mass near that galactic center.   Therefore, it is obvious that the same approximate relationship would exist between (1) numbers of supernovae and the distance to the dark-matter-doughnut effect - that exists between (2) mass near the galactic center and the constant velocity point where gravity diminishes so greatly that it can no longer mask the acceleration of the expansion of the universe.   The latter (2) is the contention supported by nether theory as applied to Mordehai Milgrom's work.

3.   No one has ever seen dark matter and this at least implies that it may not exist.   However, time will tell.

My contention and proof that dark matter does not exist seems to be confirmed by the following article.   Note that it mentions that a "new solution for the missing mass must be found."   If anyone would pay even minimal attention they would realize that the solution has been found and that the acceleration of the expansion of the universe is the cause of the supposed missing mass per my explanation and the math to prove it.   My thanks again to Mordehai Milgrom for the initial discovery even though he did not realize what he actually discovered.

European Southern Observatory - ESO (2012, April 18). Serious blow to dark matter theories? New study finds mysterious lack of dark matter in Sun's neighborhood. ScienceDaily. Retrieved April 18, 2012, from

ScienceDaily (Apr. 18, 2012) — The most accurate study so far of the motions of stars in the Milky Way has found no evidence for dark matter in a large volume around the Sun. According to widely accepted theories, the solar neighbourhood was expected to be filled with dark matter, a mysterious invisible substance that can only be detected indirectly by the gravitational force it exerts. But a new study by a team of astronomers in Chile has found that these theories just do not fit the observational facts. This may mean that attempts to directly detect dark matter particles on Earth are unlikely to be successful.

A team using the MPG/ESO 2.2-metre telescope at the European Southern Observatory's La Silla Observatory, along with other telescopes, has mapped the motions of more than 400 stars up to 13,000 light-years from the Sun. From this new data they have calculated the mass of material in the vicinity of the Sun, in a volume four times larger than ever considered before.

"The amount of mass that we derive matches very well with what we see -- stars, dust and gas -- in the region around the Sun," says team leader Christian Moni Bidin (Departamento de Astronomía, Universidad de Concepción, Chile). "But this leaves no room for the extra material -- dark matter -- that we were expecting. Our calculations show that it should have shown up very clearly in our measurements. But it was just not there!"

Dark matter is a mysterious substance that cannot be seen, but shows itself by its gravitational attraction for the material around it. This extra ingredient in the cosmos was originally suggested to explain why the outer parts of galaxies, including our own Milky Way, rotated so quickly, but dark matter now also forms an essential component of theories of how galaxies formed and evolved.

Today it is widely accepted that this dark component constitutes about the 80% of the mass in the Universe [1], despite the fact that it has resisted all attempts to clarify its nature, which remains obscure. All attempts so far to detect dark matter in laboratories on Earth have failed.

By very carefully measuring the motions of many stars, particularly those away from the plane of the Milky Way, the team could work backwards to deduce how much matter is present [2]. The motions are a result of the mutual gravitational attraction of all the material, whether normal matter such as stars, or dark matter.

Astronomers' existing models of how galaxies form and rotate suggest that the Milky Way is surrounded by a halo of dark matter. They are not able to precisely predict what shape this halo takes, but they do expect to find significant amounts in the region around the Sun. But only very unlikely shapes for the dark matter halo -- such as a highly elongated form -- can explain the lack of dark matter uncovered in the new study [3].

The new results also mean that attempts to detect dark matter on Earth by trying to spot the rare interactions between dark matter particles and "normal" matter are unlikely to be successful.

"Despite the new results, the Milky Way certainly rotates much faster than the visible matter alone can account for. So, if dark matter is not present where we expected it, a new solution for the missing mass problem must be found. Our results contradict the currently accepted models. The mystery of dark matter has just become even more mysterious. Future surveys, such as the ESA Gaia mission, will be crucial to move beyond this point." concludes Christian Moni Bidin.


[1] According to current theories dark matter is estimated to constitute 83% of the matter in the Universe with the remaining 17% in the form of normal matter. A much larger amount of dark energy also seems present in the Universe, but is not expected to affect the motions of the stars within the Milky Way.

[2] The observations were made using the FEROS spectrograph on the MPG/ESO 2.2-metre telescope, the Coralie instrument on the Swiss 1.2-metre Leonhard Euler Telescope, the MIKE instrument on the Magellan II Telescope and the Echelle Spectrograph on the Irene du Pont Telescope. The first two telescopes are located at ESO's La Silla Observatory and the latter two telescopes are located at the Las Campanas Observatory, both in Chile. A total of more than 400 red giant stars at widely differing heights above the plane of the galaxy in the direction towards the south galactic pole were included in this work.

[3] Theories predict that the average amount of dark matter in the Sun's part of the galaxy should be in the range 0.4-1.0 kilograms of dark matter in a volume the size of Earth. The new measurements find 0.00±0.07 kilograms of dark matter in a volume the size of Earth.

More information

This research was presented in a paper, "Kinematical and chemical vertical structure of the Galactic thick disk II. A lack of dark matter in the solar neighborhood," by Moni-Bidin et al. to appear in The Astrophysical Journal.

The team is composed of C. Moni Bidin (Departamento de Astronomía, Universidad de Concepción, Chile), G. Carraro (European Southern Observatory, Santiago, Chile), R. A. Méndez (Departamento de Astronomía, Universidad de Chile, Santiago, Chile) and R. Smith (Departamento de Astronomía, Universidad de Concepción, Chile).

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The above story is reprinted from materials provided by European Southern Observatory - ESO, via AlphaGalileo.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

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