Density/Dimension clarification

[3D Sunset]

Two questions about this. What do you mean when you say that a Euclidean universe is flat? And why does coalescing due to its own gravity require elliptical geometry?

It is interesting to note, that the amount of matter/energy known is amazingly close to the amount necessary to make a flat universe. After that the simple addition or subtraction of a single atom is all that is needed to make it elliptical or hyperbolic.

Whoah! How does that work, exactly? Can you elaborate on this at all?

Both of these questions are related, so let me try to address them together. It is an interesting fact that Euclidean vs non-Euclidean geometries result in open, closed, or flat universes, but it is true. Before the 19th Century, when Lobachevsky and Bolyai independently discovered non-Euclidean geometries which are based upon curved, rather than flat surfaces, the only geometry that anyone knew was Eucledian, or flat, in which parallel lines stay a constant distance apart, and the angles of a triangle always add up to 180 degrees. In a spherical (aka elliptical) universe, the angles of a triangle add up to slightly more than 180 degrees and parallel lines meet eventually before infinity. In a hyperbolic universe, the angles of a triangle add up to slightly less than 180 degrees and parallel lines diverge prior to infinity.

Einstein used these geometries to mathematically represent his relative universe with curved space/time, and afterward, his concept of a closed, spherical universe, was generally accepted until they started trying to find all the matter that was necessary to close it. Up to now, there is still matter "missing" that would be required to close the universe, so it is generally accepted as being based on a hyperbolic geometry. It is interesting to note though, that several methods for measuring the flatness of the universe that are independent of the amount of matter indicate that it is so close to flat, that we can't currently tell if it is flat or ever so slightly curved.

Thus, for Dewey's tenet of geometries being Euclidean to be correct, the universe would have to be exactly flat, which means that the fate of the universe would be for it to expand forever at an ever decreasing rate. In this case, the universe is open and not closed, so there is no Big Crunch. I think, however, that the inclusion of a non-Euclidean geometry on RST, would complicate his simple, straightforward (he wrote, tongue-in-cheek) math enormously. Thus, my conflict between the aesthetic beauty of RST and the aesthetic beauty of my intuitive view of cosmology.

To finish the thought for the fate of non-Euclidean universes: A spherical universe is closed and would eventually coalesce. And a hyperbolic universe is open and would expand forever at an ever increasing rate.

By the way, the flatness of the universe has also been referred to as "The Omega Factor" (where Omega refers to the density factor of the universe). If Omega = 1, then there is exactly the right amount of matter to make the universe flat, if Omega >1 then the universe is closed and spherical, if Omega <1 then the universe is open and hyperbolic.

Ra said that Dewey Larson didn't understand gravity. I wonder if that might be relevant here.

Is this the quote that you're referring to? I always saw that as Ra scolding Don a little and reminding him not to overlook the spiritual aspects of physical phenomena.

Questioner: Then because of these rotations there is an inward motion of these particles which is opposite the direction of space/time progression as I understand it, and this inward progression then is seen by us as what we call gravity. Is this correct?

Ra: I am Ra. This is incorrect.

Questioner: Can you tell me how the gravity comes about?

Ra: I am Ra. This that you speak of as gravity may be seen as the pressing towards the inner light/love, the seeking towards the spiral line of light which progresses towards the Creator. This is a manifestation of a spiritual event or condition of livingness.

This sounds much more like the metaphysical definition of gravity, rather than the physical. That said, I'm not really sure why Ra said that Dewey's definition of gravity was incorrect, but I couldn't glean anything tangible from his description, so I settled on the above interpretation.

For what it's worth, Dewey Larson himself did not accept the Big Bang theory, and he scoffed at many of what he considered "imaginative" attempts by theorists to get themselves out of sticky situations that their fundamental misunderstanding of time, space, and motion had gotten them into. I'm not sure, but I'm guessing that inflation might be one of those imaginative attempts.

Note that Dewey's concept of a universe of motion ever expanding at unit speed is actually similar to the Big Bang concept. The primary difference (as I see it, and note that this is my interpretation, not Dewey's) being that in the Big Bang, all matter and energy are formed simultaneously at a singularity, whereas Dewey would have matter and energy generated whenever and wherever it is needed in order to keep the universe flat as space expands out over time. This resolves several issues with current cosmological theory, such as the need for inflation and would also explain why there is exactly enough matter available for the universe to be flat. My only problem with it is that it still conflicts with my intuitive concept of a closed universe.

Ultimately, I feel that I will need to abandon one or the other, I'm just not sure which it will be yet. In the mean time, I continue to gather data and refine my understanding of all the theories.

I hope that helps,

3D Sunset