I love a good mystery, and recent astronomical observations have created a mind bending controversy. All galaxies rotate, and when astronomers began to measure the orbital velocity of individual stars within a galaxy, they noted something entirely unexpected. Some distance from the galactic center, individual stars moved with orbital velocities independent of their distance from the central mass. Rather than follow the basic gravitational rule that as distance from a central mass such as the sun increases orbital velocity must decrease, individual stars defied Newtonian rules and all moved at the same velocity. Such unorthodox behavior created a huge paradox for science, and only three possible choices could explain the observations. Either the data is faulty, or Newton was wrong about gravity, or there is some mysterious gravitational stuff out there that causes the stars to orbit faster than they otherwise should. The data has been confirmed by many astronomers using diverse instruments and methods, so the anomaly is real. The second possibility, that our gravitational theories are wrong, is offensive to most scientists who refuse to give this possibility credence. While most scientists will freely admit that we really do not understand gravity, it is scientific heresy to claim that Newton and Einstein were wrong describing this fundamental force. To preserve these time honored theories, most scientists have opted for the third possibility and assumed the existence of a deep space ghost; an enigma they call Dark Matter, so named because it is invisible, undetectable, and its nature uncertain.
Most scientists accept Dark Matter as a real despite the fact that they cannot see or measure it or even agree on what it is. It is theorized to be some enigmatic matter that gravitationally affects large-scale systems such as galaxies or galactic clusters, but does not interact in other ways with ordinary matter. All we know is there must be an awesome amount of it throughout the universe to account for our observations and theories. Without Dark Matter most of the universe is missing.
Dark Matter is ubiquitous yet displays no measurable attributes such as electrical charge, inertia, spin or other of the usual properties of matter. It does not absorb or emit electromagnetic radiation or interact with atoms or other subatomic particles; exchanges that might betray its presence. In other words, it will be very difficult to prove that it exists at all.
If Newton and Einstein’s descriptions of gravity are complete (and this may be a big assumption), all matter in the universe must follow these laws without regard to scale or distance. The laws of celestial mechanics dictate how an independent body such as a planet or spaceship should move inside a gravitational well. Einstein theorized that gravity is not a force between two objects but the bending of space-time as a property of mass. The further away an object is from a large central mass, the shallower the slope of the gravitational well surrounding that mass. In other words the further away from a mass, the weaker gravity field will be. Celestial mechanics requires an object nearby a central mass to move at a greater orbital velocity than if the same object were at a distance. If it moves slower than that required by its position in the gravitational well, the object will spiral into the central mass, and if it moves faster it will move away from the central mass. A popular way to describe this law is to imagine the central mass has less pull (less bending of space-time) on a body as it moves further and further away from the mass. For instance, because of its proximity to the Sun, Mercury races about its orbit in 88 days just to keep from spiraling into the Sun and burning up. Earth, being further away, orbits with a lower orbital velocity, and poor Pluto way out there in the boondocks of the solar system, has an orbital velocity that is the lowest of all the planets taking that frozen world hundreds of years to complete a single orbit. Newton’s laws of celestial mechanics are well understood, so much so that his equations are used to sling a spaceship from Earth to Saturn with the precision required to orbit that planet and send a probe to the surface of Titan. That is like firing a rifle at a target placed on the Moon and hitting the bull’s eye. If Newton’s equations work this well, most scientists argue that they must be a correct description of nature.
Nevertheless, for me the concept of Dark Matter to explain a fundamental process of the universe is nonintuitive and unsatisfactory. When scientists invent some mysterious substance to preserve their overall concept of the universe, one has to suspect the theory they are striving to protect could itself be fundamentally flawed. One infamous example was Einstein’s invention of the cosmological constant to explain an inevitable consequence of his equations that contradicted his intuition. Einstein believed that the universe was static, neither expanding nor contracting under the influence of gravity. A consequence of his theory demanded that the universe was expanding, and this was so unsatisfactory that he invented the cosmological constant (lambda) to preserve his idea of a static universe. Later on when Hubble proved that the universe was indeed expanding, Einstein called lambda his “greatest blunder”. The recent discovery that the universe is experiencing an accelerating expansion has revived the concept of a cosmological constant and thus change Einstein’s greatest blunder into possibly his greatest intuition.
In the 19th century scientists invented another mysterious substance they called the Ether. It was known that light traveled in the form of a wave, and the Ether was necessary to explain how an electromagnetic radiation such as light could travel through empty space. After all, what was waving in the vacuum of outer space? They reasoned it had to be an invisible substance, the Ether. The Ether could not been seen or measured, but it was necessary to preserve the electromagnetic wave theories in vogue at the end of that century. Sound familiar? By the 20th century, Einstein and Max Plank obviated the need of the Ether by explaining light as both a wave and a particle that traveled in packets or quanta. This explanation doomed Ether to a historical notation in textbooks.
The observed constant velocity of stars within a galaxy may help explain another mystery that has been debated for years; the diverse spiral shape of galaxies. Intuition and experimentation can be used to help explain galaxy formation and geometry. Let a bucket of white paint simulate the spiral formation of independently moving particles in a viscous material. Gently stir the paint until the entire bucket of paint assumes a constant rotational velocity, then pore a cup of black paint into the center. Note the black paint begins to form spiral arms as propelled by centrifugal force it moves out from the center. Spiral arms of black paint form because those individual particles further away from the hub have a longer distance to travel to complete a revolution than those closest to the center. Because of the viscosity of the paint, the black particles at the leading edge attain a certain terminal velocity and at some distance from the center they all move with the same velocity, a velocity that is not fast enough to remain synchronized with the inner particles. A spiral arm forms as distant black paint particles lag behind, taking longer and longer to make a complete revolution. On the other hand, if the particles were locked into position and unable to move independently as they are in a wheel, the particles at the periphery of the wheel will have a greater velocity than those nearest to the hub, each making a complete revolution in equal time. If the particles were allowed to move slower and slower as they moved from the center, spiral arms would not form. Another example of this is a line of ice-skaters performing a rotation about a central point. If the skater at the end of the line cannot increase his or her speed proportional to the distance from the center, they will lag behind and the entire line will sag. If the skater can keep balanced and assume the required speed, the line will remain straight but the end skater will be traveling faster than they might wish. They will also have to hold tight to their companion (an analogy of gravity) or the affects of centrifugal force will tear them away from their friends and fling them out of the rink. If the skaters were allowed to move independently, slower and slower as their distance from the center increased, then they all would assume asynchronous positions around the ring.
I also have a problem with the explanation that Dark Matter forms a halo outside of each visible galaxy. This halo of Dark Matter’s is presumed to gravitationally attract individual stars and cause them to move faster than they otherwise should. Nonetheless, what force keeps this halo of Dark Matter in place outside the main body of the galaxy? When the galaxy originally condensed from a presumed cloud of both normal and Dark Matter, why would Dark Matter remained outside the main body of the galaxy and not migrate toward the central mass along with ordinary matter and stars? Conversely, how could the galaxy form in the first place with a massive halo of matter opposing the gravitational pull of the central mass on migrating matter? It seems likely that a halo of Dark Matter, many times the mass of the visible galaxy, would tear the galaxy apart.
Finally, we must explore the third possibility, the one that admits we do not fully understand gravity. Did Newton and Einstein have it wrong about the nature of gravity? The anomalous velocity of stars rotating in a galaxy can be explained equally well by a tweak to a famous equation, Newton’s second law of motion. Newton’s law of motion linearly relates force, mass and acceleration in the formula F=ma. This formula is valid on the scale of our solar system, yet may need to be tweaked on a galactic scale. One scientist, Mordehai Milgrom proposed just such a tweak to Newton’s second law of motion. He calls his theory MOND, or MOdified Newtonian Dynamics. This theory conjectures Newton’s second law is incomplete for extremely small accelerations, those less than 10 billionths of a meter per second each second. This sounds like an infinitesimally small number, one that can be easily ignored in everyday life. Yet even a small tweak can have profound effects for galactic distances and masses. MOND adjusts the second law to be F=ma2/a0 Within our solar system, Newton’s conventional formula works well to the 6th decimal place, but at galactic radii MOND predicts the observed the flat line velocity verses distance data that astronomers measure.
MOND explains another dilemma that has puzzled scientists for decades. As the Pioneer 10 and Pioneer 11 spacecraft climbed out of the Sun’s gravitational well, something inexplicable was observed. They are not following the gravitation law that dictates the velocity as their distance from the Sun increases. The variation from the law is small, at the limits of our ability to measure, but the further those spacecraft move away from the Sun, the more their speed deviates (speeds up) from the predicted value. Unless something is wrong with our measurements, the only other explanation is that gravity is stronger at the limits of the solar system than Newton and Einstein formulas predict and the spacecraft are being accelerated from the predicted values.
However, all is not well with MOND. MOND is itself a contrived mathematical solution (as was Lambda, Einstein’s cosmological constant) and as such seems nothing more than another convenient fudge factor. MOND is best described as a math adjustment rather than a theory. It has not been derived from basic physical principles such as E-mc2 or F=ma has. Milgrom simply adjusted the value of a0 until the results agreed with the measured velocities of galactic stars. Nevertheless, it is interesting that if we divide the speed of light by the age of the universe, we arrive at the value of a0 . This may have some cosmological significance, or just be a coincidence. At this point no one knows. Another sticking point is that MOND cannot be easily related to relativity, although there has been some recent success by another researcher in doing so.
As in the history of other controversial theories, MOND has yet to gain wide acceptance among Physicists or Astronomers. It is considered too radical and Dark Matter has been able to solve other cosmological problems such as the “missing mass” of the universe. Another example where Dark Matter can explain observations is with the phenomenon known as Einstein lensing, where the mass of a galaxy cluster placed between the observer and a distance object causes that object to be magnified or split into multiple images. Such lensing requires many times the amount of visible mass in those clusters, but adds in copious amounts of Dark Matter and the results match observations.
Much about the behavior and origin of gravity has yet to be discovered, and to presume that we know all there is to know about this mysterious force (or the bending of space-time) is arrogant. Presently the fact remains that Dark Matter lacks existence proof. Essentially, we have no idea what it is or how it originated. The conjecture is that we are bathed in a flood of seldom interacting subatomic particles, yet after spending hundreds of millions of dollars and years of dedicated work to build and operate huge instruments designed to detect them, no one has captured a single Dark Matter event. If these mysterious particles exist in such huge and ubiquitous numbers, where and what are they? Elusive as these particles may be, I have a problem accepting the existence of Dark Matter until scientists can prove WIMPS (Weakly Interacting Massive Particles) or some other exotic “stuff” actually exist in sufficient quantities to explain astronomical observations. In the meantime, I consider Dark Matter in the same category as the Ether of the 19th century; a theoretical speculation designed to preserve historic theories.
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Originally Posted by Richard L.
So, MOND appears even more contreived.
