MOND and Other Theories on Dark Matter and Dark Energy


The Prevailing Theory

The most common viewpoint on dark matter is that is it made of WIMPS, or Weakly Interacting Massive Particles. These particles can pass through normal matter (known as baryonic), move at a slow rate, are generally unaffected by forms of electromagnetic radiation, and can clump together easily. Andrey Kravtsov has a simulator that concurs with this viewpoint and also shows that it helps clusters of galaxies stay together despite the expansion of the universe, something that Fritz Zwicky postulated about over 70 years ago after his own observations on galaxies noticed this peculiarity. The simulator also helps explain small galaxies, for dark matter allows the clusters of galaxies to remain in close proximity and cannibalize on each other, leaving small corpses behind. Furthermore, dark matter also explains the spin of galaxies. Stars on the outside spin as fast as stars near the core, a violation of rotational mechanics because those stars should be flung away from the galaxy based on their velocity. Dark matter helps explain this by having the stars contained within this strange material and preventing them from departing our galaxy. What it all boils down to is that without dark matter, galaxies would not be possible (Berman 36).

As for dark energy, that is still a great mystery. We have little idea as to what it is, but we do know that it operates on a grand scale by accelerating the expansion of the universe. It also seems to account for almost ¾ of all that the universe is made of. Despite all this mystery, several theories are hoping to sort it out.

Mordehai Milgrom
Mordehai Milgrom

MOND, or Modified Newtonian Dynamics

This theory has its roots with Mordelai Milgrom, who while on sabbatical went to Princeton in 1979. While there, he noted that the scientists were working on solving the galaxy rotation curve problem. This refers to the before-mentioned properties of galaxies where the outer stars rotate as fast as the inner stars. Plot the speed versus distance on a graph and instead of a curve it flattens out, hence the curve problem. Milgrom tested many solutions before finally taking a list of galaxy and solar system properties and comparing them. He did this because Newton's gravity works great for the solar system and he wanted to extend it to galaxies (Frank 34-5, Nadis 40).

He then noticed that the distance was the biggest change between the two of them and began to think about that on a cosmic scale. Gravity is a weak force but relativity is applied where gravity is strong. Gravity is dependent on distance, and distances make gravity weaker, so if it behaves differently on larger scales then something needs to reflect this. In fact, when the gravitational acceleration became less than 10 -10 meters per second (100 billion times less than Earth's), Newton's gravity wouldn't work as well as relativity's, so something needed to be adjusted. He modified Newton's second law to reflect these changes to gravity so that the law becomes F = ma2/ao, where that denominator term is the rate it takes you to accelerate to the speed of light, which should take you the lifetime of the universe. Apply this equation to the graph and it fits the curve perfectly (Frank 35, Nadis 40-1).

Graph showing traditional Newtonian vs. MOND.
Graph showing traditional Newtonian vs. MOND. | Source

He began to do the hard work in 1981 alone because no one felt this was a viable option. In 1983 he publishes all three of his papers in the Astrophysical Journal with no response. Stacy McGaugh, from Case Western University in Cleveland, did find a case where MOND did predict results correctly. She wondered about how MOND worked on "low surface brightness galaxies" which had low star concentrations and were shaped like a spiral galaxy. They have weak gravity and are spread out, a good test for MOND. And it did great. However, scientists generally shy away from MOND still. The biggest complaint was that Milgrom had no reason why it was right, only that it fit the data (Frank 34, 36-7, Nadis 42).

Dark matter, on the other hand, attempts to do both. Also, dark matter began to explain other phenomena better than MOND even though MOND still explains the curve problem better. Recent work by a partner of Milgrom, Jacob Bekenstein (Hebrew University in Jerusalem), attempts to explain all that dark matter does as he accounts for Einstein's relativity and MOND. Called TeVeS (for tensor, vector, and scalar), the 2004 work takes into account gravitational lensing and other consequences of relativity. Whether it takes off remains to be seen. Another problem is how MOND fails for not only galaxy clusters but also for the large scale universe. It can be off by as much as 100% (Ibid).

Some recent work has been promising, however. In 2009, Milgrom himself revised MOND to include relativity, separate from TeVeS. Though the theory still lacks a why, it does better explain those large scale discrepancies. And recently the Pan Andromeda Archaeological Survey (PANDA) looked at Andromeda and found a dwarf galaxy with weird star velocities. A study published in The Astrophysical Journal by Stacy McGaugh found that revised MOND got 9/10 of those correct (Nadis 43, Scoles).

The Scalar Field

According to Robert Scherrer of Vanderbilt University in Tennessee, dark energy and dark matter are actually a part of the same energy field known as the scalar field. Both are just different manifestations of it depending on what aspect you are examining. In a series of equations he derived, different solutions present themselves depending on the time frame we solve for. Whenever density decreases, volume increases according to his work, much like how dark matter operates. Then as time progresses density remains at a constant as volume increases, much like how dark energy works. Thus, in the early universe, dark matter was more plentiful than dark energy but as time goes on, dark matter will approach 0 with regards to dark energy and the universe will accelerate its expansion even further. This is consistent with the prevailing viewpoints on cosmology (Svital 11).

A visualization of a scalar field.
A visualization of a scalar field. | Source

John Barrows and Douglas J. Shaw also worked on a field theory, though theirs originated by noticing some interesting coincidences. When evidence for dark energy was found in 1998, it gave a cosmological constant (the anti-gravity value based on Einstein's field equations) of Λ = 1.7 * 10-121 Planck units, which happened to be almost 10121 times larger than the "natural vacuum energy of the universe." It also happened to be close to 10-120 Planck units which would have prevented galaxies from forming. Finally, it was also noted that Λ is almost equal to 1/tu2 where tu is the "present expansion age of the universe," which is about 8 * 1060 Planck time units. Barrows and Shaw were able to show that if Λ is not a fixed number but a field then Λ can have many values and thus dark energy could operate differently at different times. They were also able to show that the relation between Λ and tu is a natural result of the field because it represents the light of the past and so would be a carry-through from the expansion of today. Even better, their work gives scientists a way to predict the curvature of space time at any point in the Universe's history (Barrows 1,2,4).

The Acceleron Field

Neal Weiner of the University of Washington thinks dark energy is linked to neutrinos, small particles with little to possibly no mass that can pass through normal matter easily. In what he calls an “acceleron field,” neutrinos are linked together. When the neutrinos move away from each other, it creates tension much like a string. As the distance between neutrinos increases, so does the tension. We observe this as dark energy, according to him (Svital 11).

The Josephson Junction in red.
The Josephson Junction in red. | Source

Josephson Junctions

A property of quantum theory known as vacuum fluctuations could also be an explanation for dark energy. It is a phenomena where particles pop in and out of existence in a vacuum. Somehow, the energy that causes this disappears from the net system and it is hypothesized that that energy is in fact dark energy. To test this, scientists can use the Casimir effect, where two parallel plates are attracted to each other because of the vacuum fluctuations between them. By studying the energy densities of the fluctuations and comparing them with the expected dark energy densities. The test bed will be a Josephson junction, which is an electronic device having a layer of insulation squeezed between parallel superconductors. To find all the energies generated, they will have to look over all frequencies, for energy is proportional to frequency. The lower frequencies so far support the idea, but higher frequencies will need to be tested before anything firm can be said of it (Phillip 126).

Rogue Planets, Brown Dwarfs, and Black Holes

Something that most people don't consider is objects that are just hard to find in the first place, like rogue planets, brown dwarfs, and black holes. Why so hard? Because they only reflect light and do not emit it. Once out in the void, they would be practically invisible. So if enough of them are out there, could their collective mass account for dark matter? In short, no. Mario Perez, a NASA scientist, went over the math and found that even if models for rogue planets and brown dwarfs were favorable, it wouldn't even come close. And after researchers looked into primordial black holes (which are miniature versions formed in the early universe) using the Kepler Space Telescope, none were found that were between 5-80% of the mass of the moon. Still, theory does hold that primordial black holes as small as 0.0001 percent of the moon's mass could exist, but it is unlikely. Even more of a blow is the idea that gravity is inversely proportional to the distance between objects. Even if a lot of those objects were out there, they are just too far apart to have a discernible influence (Perez, Choi).

The Beginning

Rest assured that these just scratch the surface of all the current theories about dark matter and dark energy. Scientists continue to gather data and even offer up revisions to out understandings of the Big Bang and gravity in an effort to solve this cosmological conundrum. Observations from the cosmic microwave background and particle accelerators will lead us ever closer to a solution. The mystery is far from over.

Works Cited

Ball, Phillip. "Scepticism Greets Pitch to Detect Dark Energy in the Lab." Nature 430 (2004): 126. Print.

Barrows, John D, Douglas J. Shaw. "The Value of the Cosmological Constant” arXiv:1105.3105

Berman, Bob. "Meet the Dark Universe.” Discover Oct. 2004: 36. Print.

Choi, Charles Q. "Is Dark Matter Made Of Tiny Black Holes?" Huffington Post, 14 Nov. 2013. Web. 25 Mar. 2016.

Frank, Adam. "Gravity's Gadfly." Discover Aug. 2006. 34-7. Print.

Nadis, Frank. "Dark Matter Deniers." Discover Aug. 2015: 40-3: Print.

Perez, Mario. "Could Dark Matter Be...?" Astronomy Aug. 2012: 51. Print.

Scoles, Sarah. "Alternate Theory of Gravity Predicts Dwarf Galaxy." Astronomy Nov. 2013: 19. Print.

Svital, Kathy A.. "Darkness Demystified.” Discover Oct. 2004: 11. Print.

© 2013 Leonard Kelley

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Comments 3 comments

sparkster profile image

sparkster 3 years ago from United Kingdom

I don't have a particularly scientific mind but I am very interested in this kind of thing. I have previously written about "the neutrino universe" after watching a discussion with Senior Research Scientist for Lockheed Skunkwords Boyd Bushman.

So, if this dark matter is responsible for the expansion of the universe can it then be used for anti-gravity propulsion? And is it the same as zero-point energy?

Here is quote I found at NASA:

Zero Point Energy (ZPE), or vacuum fluctuation energy are terms used to describe the random electromagnetic oscillations that are left in a vacuum after all other energy has been removed. If you remove all the energy from a space, take out all the matter, all the heat, all the light... everything -- you will find that there is still some energy left. One way to explain this is from the uncertainty principle from quantum physics that implies that it is impossible to have an absolutely zero energy condition.

For light waves in space, the same condition holds. For every possible color of light, that includes the ones we can’t see, there is a non-zero amount of that light. Add up the energy for all those different frequencies of light and the amount of energy in a given space is enormous, even mind boggling, ranging from 10^36 to 10^70 Joules/m3.

In simplistic terms it has been said that there is enough energy in the volume the size of a coffee cup to boil away Earth’s oceans. - that’s one strong cup of coffee! For a while a lot of physics thought that concept was too hard to swallow. This vacuum energy is more widely accepted today.

What evidence shows that it exists?

First predicted in 1948, the vacuum energy has been linked to a number of experimental observations. Examples include the Casimir effect, Van der Waal forces, the Lamb-Retherford Shift, explanations of the Planck blackbody radiation spectrum, the stability of the ground state of the hydrogen atom from radiative collapse, and the effect of cavities to inhibit or enhance the spontaneous emission from excited atoms."

Reynold Jay profile image

Reynold Jay 3 years ago from Saginaw, Michigan

I'll need to look into this and come up with a theory too! Just kidd'n. Heck I was a scince teacher however my students never got to this point. Well done UP and awesome to even think of all this theory.

1701TheOriginal profile image

1701TheOriginal 3 years ago Author

sparkster, several people have wondered about the connection between "negative energy" and dark energy. I recommend reading Physics of the Impossible by Michio Kako for more about the science behind it.

Reynold Jay, I am glad to hear from a science teacher that this post is good. Good luck on any theory you start to work on!

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