# Dark (Missing) Matter

## What Was Missing

Dutch astronomer Jan Oort first discovered the 'missing matter' problem in the 1930's.  By observing the Doppler red-shift values of stars moving near the plane of our galaxy, Oort assumed he could calculate how fast the stars were moving. Since the galaxy was not flying apart, he reasoned that there must be enough matter inside the galaxy such that the central gravitational force was strong enough to keep the stars from escaping, much as the Sun's gravitational pull keeps the planets in their orbits.  But when the calculation was made, it turned out that there was not enough mass in the galaxy. And the discrepancy was not small; the galaxy had to be at least twice as massive as the sum of the mass of all its visible components combined. Where was all this missing matter?

In addition, in the 1960's the radial profile of the tangential velocity of stars in their orbits around the galactic center as a function of their distance from that center was measured.  It was found that typically, once we get away far enough from the galactic center all the stars travel with the same velocity independent of their distance out from the galactic center. (See the figure below.)  Usually, as is the case with our solar system, the farther out an object is, the slower it travels in its orbit.

Figure 1.  A typical star's tangential velocity as a function of its distance from the galactic center.

To visualize the seriousness of the problem cosmologists face, we need to consider just a bit of Newtonian dynamics:

• To change a body's velocity vector - either in direction or magnitude or both, a force must be applied to the mass of the body.  The resulting acceleration is equal to the ratio of the applied force divided by the mass of the object; i.e.,  = m  a,  where f is the force applied to the body, m is the mass of the body, and a is the resulting acceleration (change in velocity). Both f and a are vectors;  the change in direction of the velocity will be in the direction of the applied force.
• When an Olympic athlete, starting to do the hammer throw, swings the hammer around himself in a circle, the force he feels stretching his arms (the force he is applying, pulling on the hammer) is the 'centripetal force'.  That force is equal to the product of the hammer's mass, m1, times the centripetal acceleration (which in this case is the acceleration that continually changes only the direction, not the magnitude, of the velocity vector of the hammer - inward - so as to keep it in a circular orbit around the athlete).  This acceleration is equal to the square of the hammer's tangential velocity, v, divided by the radius of the circle. So, the inward force the athlete needs to exert to keep the hammer in its circular path is:  f = m1 v^2/R.
• Newton's law of gravitational force says that the force between two masses is equal to G (the gravitational 'constant') times the product of the two masses divided by the square of the distance between them.  f = G(m1 x m2)/R^2.

Consider the case of a star on the outskirts of a galaxy.  Its radius from the galactic center is R.  Its mass is m1, and m2 is the total mass of everything else (all the other stars and matter) inside a circle whose radius is R, the distance of the star from the galaxy's center.  Newtonian dynamics assumes all that combined mass, m2, acts as if it were located at a single point at the galaxy's center.  For the star to remain in a fixed orbit, the necessary inward (centripetal) force, m1 V^2/R, must be exactly equal to the available (gravitational) force pulling inward, G(m1 x m2)/R^2.  Setting these two expressions equal to each other results in the expression:

m2 = (V^2) R /G

This says that for the tangential velocity, V, to remain constant as R increases - as it does in figure 1 (as we look at stars farther and farther out from the galaxy's center) the included mass, m2, must increase proportionally to that radius, R.  But we realize that, if we move far out from the center, to the last few stars in any galaxy, included mass will not increase proportionally to the radius. So there seems to be no way the velocity can remain the same for the outermost stars as for the inner stars.  Therefore, astrophysicists have concluded that, either some mass is 'missing' in the outer regions ("halos") of galaxies, or the outer stars rotating around galaxy cores do not obey Newton's law of gravity.

There were problems, too, at a larger scale.  In 1933 astronomer Fritz Zwicky announced that when he measured the individual velocities of a large group of galaxies known as the Coma cluster, he found that all of the galaxies that he measured were moving so rapidly relative to one another that the cluster should have come apart long ago. The visible mass of the galaxies making up the cluster was far too little to produce enough gravitational force to hold the cluster together.  So not only was our own galaxy lacking mass, but so was the whole Coma cluster of galaxies.

MACHOs, WIMPs & MOND

At first, cosmologists decided to leave Newton's laws inviolate and to postulate the existence of some invisible dark entities to make up the missing mass.  Apparently it never ocurred to anyone to go back and examine the basic assumption that only gravity was at work in these cases. It was easier to patch up the theory with invisible entities.  (Remember the invisible gnomes in my garden?)  To quote Astronomy magazine (Aug. 2001 p 26):

"What's more, astronomers have gone to great lengths to affectionately name, define, and categorize this zoo of invisible stuff called dark matter.  There are the MAssive Compact Halo Objects (MACHOs) - things like ... black holes, and neutron stars that purportedly populate the outer reaches of galaxies like the Milky Way.  Then there are the Weakly Interacting Massive Particles (WIMPs), which possess mass, yet don't interact with ordinary matter - baryons such as protons and neutrons - because they (the WIMPS) are composed of something entirely foreign and unknown.  Dark matter even comes in two flavors, hot (HDM) and cold (CDM)....." (A great number of other "flavors" have been proposed too.)

1. Cold dark matter - supposedly in dead stars, planets, brown dwarfs ("failed stars") etc.
2. Hot dark matter - postulated to be fast moving particles floating throughout the universe, neutrinos, tachions etc.

"And all the while astronomers and physicists have refined their dark matter theories without ever getting their hands on a single piece of it.  But where is all of this dark matter? The truth is that after more than 30 years of looking for it, there's still no definitive proof that WIMPs exist or that MACHOs will ever make up more than five percent of the total reserve of missing dark stuff."

Of course, the second possibility mentioned above (that the outer stars rotating around galaxy cores do not obey Newton's Law of Gravity) was thought to be impossible.  But the first alternative - the fanciful notion that 99% of the matter in the universe was invisible - began to be worrisome too.  It was stated that WIMPs and MACHOs were in the category of particle known as "Fabricated Ad hoc Inventions Repeatedly Invoked in Efforts to Defend Untenable Scientific Theories" (FAIRIE DUST).   Even such an august authority as Princeton University cosmologist Jim Peebles was quoted as saying,

"It's an embarrassment that the dominant forms of matter in the universe are hypothetical..."

So the second alternative, radical as it is, was chosen by some astrophysicists and called "MOdify Newton's Dynamics" (MOND) This paradigm shaking proposal to alter Newton's Law of Gravity - because it does not seem to give correct answers in the low density regions of galaxies - was first put forward in 1983 by astrophysicist Mordehai Milgrom at the Weizman Institute of Science in Israel. It has recently been given more publicity by University of Maryland astronomer Stacy McGaugh.  Milgrom, himself, has recently ("Does Dark Matter Really Exist?", Scientific American, Aug. 2002, p. 42-52) said, "Although people are right to be skeptical about MOND, until definitive evidence arrives for dark matter or for one of its alternatives, we should keep our minds open."  One wonders what alternatives was he referring to?

Some other astrophysicists have grasped at the announcement that neutrinos, that permeate the cosmos, have mass.  This, they say, must be the previously "missing matter".  But the "missing mass" is not missing homogeneously throughout the universe - just in specific places (like the outer "halo" reaches of galaxies). The neutrinos are homogeneously distributed. So this last ditch explanation fails as well.

The dilemma presented by the fact that Newton's Law of Gravity does not give the correct (observed) results in most cases involving galaxy rotation can only be resolved by realizing that Newton's Law of Gravity, by itself, is simply not sufficient in these situations.  Galaxies are not held together by gravity only.  They are formed, driven, and stabilized by dynamic electromagnetic effects.

# Cosmic Plasmas Connect Galaxies in a Galactic Web

Ninety nine percent of the universe is made up of tenuous clouds of ions and electrons called electric plasma.   Plasmas respond to the electrical physical laws codified by James Clerk Maxwell and Oliver Heaviside in the late 1800's.  An additional single law due to Hendrick Lorentz explains the mysterious stellar velocities described above.

d/dt(mv) = q(E + v x B)

Simply stated, this law says that a moving charged particle's momentum (direction) can be changed by application of either an electric field, E, or a magnetic field, B, or both.  Consider the mass and charge of a proton for example.  The electrostatic force between two protons is 36 orders of magnitude greater than the gravitational force (given by Newton's equation).  It's not that Newton's Law is wrong.  It is just that in deep space it is totally overpowered by the Maxwell-Lorentz forces of electromagnetic dynamics.

Notice, in the equation in the previous paragraph, that the change in a charged particle's momentum (left hand side of the equation) is directly proportional to the strength of the magnetic field, B, the particle is moving through.  The strength of the magnetic field produced by an electric current (e.g., a cosmic sized Birkeland current) falls off inversely as the first power of the distance from the current.  Both electrostatic and gravitational forces fall off inversely as the square of the distance.  This inherent difference in the spatial distribution of electromagnetic forces as compared to gravitational forces may indeed be the root cause of the inexplicable velocity profiles exhibited by galaxies.

Electrical engineer Dr. Anthony L. Peratt, using Maxwell's and Lorentz's equations, has shown that charged particles, such as those that form the intergalactic plasma, will evolve into very familiar galactic shapes under the influence of electrodynamic forces.  The results of these simulations fit nicely with the observed values of the velocity contours in galaxies.  No missing matter is needed - and Newton can rest easy in his grave.  The electromagnetic force is many orders of magnitude stronger than the force due to gravity and it distributes itself more widely throughout space.  But present day astrophysicists refuse to recognize the existence of any cosmic force other than gravity.  That mind-set is the cause of their mystification.

An allegory:

A farmer and his young daughter are driving along a dusty road.  They are almost home when the car breaks down.  The farmer walks to the barn and gets his horse, Dobbin.  He harnesses Dobbin to the front bumper of the car and begins to drag it along the road toward home.  The young daughter takes a piece of string and attaches it to the bumper and says, "I'll help drag the car, Daddy."
Anyone who cannot see horses will think the daughter must possess "missing muscle" and that the string is infinitely strong. Or, as in Moti Milgrom's MOND proposal, they might suggest that Newton's Laws of motion needed "modification". In any event, they would be puzzled.

In 1986, Nobel laureate Hannes Alfven postulated both an electrical galactic model and an electric solar model.   The simple application of the Lorentz force equation described above ("crossing" the direction, v, of the current into the direction, B, of the magnetic field) yields a rotational force.  Not only does this effect explain the mysterious tangential velocities of the outer stars in galaxies, but also (in scaled down version) the observed fact that our Sun rotates faster at its equator than at higher (solar) latitudes.

Up to now astronomers and cosmologists have not given consideration to any sort of electrical explanation for the above observations.  This is inexcusable because all these electrical principles have been known and studied for decades.  They have been applied in the solution of problems in plasma laboratories here on Earth and have been used successfully in the invention of many practical electrical devices - such as industrial electrical arc machining, particle accelerators, etc.   The correct, simple, solution to the "mysteries" of galaxy rotation lies in Plasma Electro-Dynamics - not in the invention of imaginary, fanciful entities such as WIMPs and MACHOs or in the trashing of a perfectly valid law of physics as is proposed in MOND.

Recently, scientific attention is becoming focused on discoveries of linkages among galaxies previously thought to be isolated from one another.  Wide field telescope observations of the remote universe have revealed an immense string of galaxies about 300 million light-years long. New research suggests that galaxies are connected to one another by filaments of thin ionized gas (hydrogen plasma) called the inter-galactic medium or IGM.

This IGM is a leading candidate for what constitutes the filamentary connections that constitute a network of almost all galaxies. This network has been dubbed the "Galactic Web". Cal Tech's new Cosmic Web Imager has already detected one possible spiral galaxy in-the-making that is three times the size of our Milky Way.

Fig. 2 The Inter-Galactic Web

The solution to the mystery of the shapes of the stellar velocity profiles (plots of the velocities of stars vs their radial distance out from the center axis) lies in realizing that the velocity profiles of most spiral galaxies are extremely similar to the velocity profile of a force-free ("Birkeland") current. The details of the solution to the "problem" are included in a paper I wrote in 2018 Birkeland Currents and Dark Matter.

In that paper it is made clear that the velocities plotted in both the observed galaxies and the Birkeland Current model are almost identical.

## Conclusion

There is no mystery. If galaxies form on cosmic Birkeland Currents (and therefore have the same velocity profiles that those currents do) the shapes of the resulting stellar velocity profiles we are measuring are exactly what we ought to have expected, But Birkeland currents are electrical phenomena as as such are an anathema to mainstream astrophysics.

Present day astronomy/cosmology seems to be on the horns of a very painful dilemma.  This dilemma is caused by the fact that Newton's Law of Gravity alone does not give the correct (observed) results in most cases involving galaxy rotation.  The "missing matter" proposal attempts to balance the equation by increasing one of the variables (one of the mass terms).  The second proposal (MOND) is to change Newton's equation itself.  (If you are losing the game, change the rules.)

But, the ultimate resolution of the dilemma lies in realizing that Newton's Law of Gravity is simply not, by itself, applicable in these situations.  Maxwell’s and Lorentz"s equations are!  Why do astrophysicists continue to grope wildly for solutions in every possible direction except the right one? Theirs is an embarrassing Quixotic Quest that will never lead to a real-world solution.

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