In 1933 Fritz Zwicky a Swiss astronomer, was trying to measure the mass of a galactic cluster using two different methods. First he tried to infer it from the rational speed of the galaxies around the center of the clusters. Just like kids on a merry-go-round have to hold on to avoid being ejected, galaxies are held together in a spinning galactic cluster by the gravitational force provided by the matter it contains because if there were not enough matter to create this force, the galaxies would simply scatter.
He then compared his result with the mass evaluated from the light the galaxies shed. He realized that there was way more matter in the cluster than what was visible or baryonic matter. This matter of an unknown type generated a gravitational field without emitting light; hence its name, dark matter.
Further observations suggest the baryonic or visible forms of matter in the universe only comprise approximately 5 to 10% of the mass required to account for the total gravitational energy in the universe.
However, the fact that 90 to 95% of the mass of the universe is invisible or “Dark” even with the recent advancements in particle detection technology suggests that it may be made up some else.
Einstein’s may have given us a clue as to what this could be when he defined gravitational forces and the quantity of mass in a give volume of space-time in terms of its field properties and not in terms of the particle or physical properties of mass.
This means the additional gravitational forces over and above that associated with the visible matter Fritz Zwicky measured in 1933 may be related to geometric property of space-time and not to the particle properties of baryonic or visible mass.
One can understand why by use the example Einstein gave us of a rubber sheet to visualize how a curvature in a space-time results in a gravitational field.
For example if one places a heavy ball in the middle of a flexible rubber sheet and then pushes a smaller ball the general direction of the heavy ball, will follow a curved path, as if “attracted†by the mass. In other words the small ball is attracted to the focal point of the depression caused in the surface of the sheet by the heaver one.
However this does not accurately describe the gravitational fields associated with spiral galaxies because their rotational energy causes then to occupy a spatially extended region around its center.
Again one can understand the effects of the flattening of space caused by their rotational energy has on their total gravitational potential by using the example of a marble on a rubber diaphragm.
For example if one places a heavy ball in the middle or a rubber sheet and then pushes several smaller balls in the general direction of the heavy ball, will follow a curved path, as if “attracted†by the mass. However the curvature in the sheet associated with each individual marble will be greater than what it would if it was just resting on the rubber sheet because the kinetic energy of their rotation will flatten and therefore increase the overall the curvature in its surface.
The rotation energy of the individual stars in galaxies would have the same effect the curvature in space-time.
However Einstein told us that the magnitude of a curvature in space defines the magnitude of the gravitational forces and therefore the total mass of in a volume of space.
Therefore to be valid representation of the gravitational forces in a galaxy one would have to analyze what the flattening of the bottom of a displacement in space-time does to the magnitude of the slope of the curvature in its surface.
Einstein told us what the effects of this would be when he defined the equivalence between energy and mass in terms of the equation E=Mc^2 because that tells us that the kinetic energy of the stars motion also posses gravitational potential.
If one flattens the distribution of the marbles around their original focal point while keeping their overall depth the same as it was before that flattening it would make the curvature steeper than it would be if no flattening had occurred.
Similarly because of the *flattening* of space by the rotation energy of the individual stars in galaxies the magnitude of the slope of the displacement in space-time associated with gravitational forces would be greater than it would be if one only viewed the sum of that associated with the individual stars as if they were not in relative motion with respect to each other. In other words the gravitational potential Einstein with the Kinetic energy of individual stars in galaxies would increase the magnitude of the curvature in space time over and above that caused by their visible mass.
However, as mentioned earlier Einstein define gravitational force and the quantity of mass in a given volume of space in terms of the magnitude of a curvature in space.
Therefore, one would measure the total gravitational potential and mass of a galaxy or galactic cluster to greater than that associated with the individual stars or visible baryonic matter they contain.
Additionally because the gravitation potential due to spatial flattening of space-time would be cumulative and linear with respect to the distance from the galaxy’s center the gravitational forces experienced by each star orbiting it would increase as its distance from the center does. This also means that there should be linear relationship between a stars distance from the center of a galaxy and its orbital velocity.
In other words Einstein predicted the existence of Dark Matter when he defined gravitational potential in terms of a geometric property of space-time.
However this means that some of the gravitation potential associated with Dark Matter in galaxies galactic clusters and supper clusters and the recently observed dark matter web may not be due to baryonic matter but to the distortion or flattening of in space-time caused by their rotational energy.
One could observational verify the above hypothesis by determining the ratio of Dark matter to the orbital dynamics of galaxies. If it is found that spiral galaxy have a larger ratio of dark matter to visible matter than globular clusters it would suggest that flattening of space does contribute the total gravitational potential in of a given volume of space. This is because the rotational velocity of stars in spiral galaxies would have a slightly greater flattening effect on space than globular ones.
Another way of observational verifying this hypothesis would be to determine where the gravitational nodes would be located in the space between galactic clusters and determine if they match the patterns associated with the dark matter web. If it does it would go a long way in confirming it.
Later Jeff
Copyright Jeffrey O’Callaghan 2013