This has been added to the compound posting on this blog, "The Lowest Information Point". We have seen some relationships involving the fundamental scales of the universe already.
In "The Chemical-Nuclear-Astronomical Relationship", which is part of "The Lowest Information Point", we saw that the relationship between the amount of matter that must collect by gravity to form a sphere in space and the far greater amount of matter that must collect by gravity before the mutual gravity is strong enough to overcome the electron repulsion between atoms and crunch atoms together to initiate the nuclear fusion of a star is essentially equal to the relationship between the energy released by chemical processes and the far greater energy per mass released by nuclear processes.
In "The Gem Formation Hypothesis", we saw that first, natural gems that refract light are very limited in size and second, that they are formed by geological processes. That can only mean one thing. Gems are made of atoms that are shaped into their final form by the processes in the earth. The practical limit to the size of gems that refract light must therefore be that the gems must be closer in scale to that of their component atoms than to the size of the earth. If the gem were closer to the scale of the earth than to the scale of the atoms, the geological processes would not be able to form the atoms into the neat rows so that light can be refracted by passing between the atoms.
Today we have another such scale relationship. We have seen that so much of the matter in the universe is in the form of dust because there is a bias toward dust. The universe is nearly infinite in scale but. according to my cosmology theory, it is composed of near-infinitesimal negative and positive electric charges. The reason that Planck's Length is so important in physics is that this is the scale of these charges. There is a universal bias toward dust because it's scale is exactly halfway between the scale of the universe and the scale of the electric charges of which it is composed. This halfway point in scale forms a "square" which is a lower information point than a rectangle because it's two sides are equal, thus is is the preferred scale for structures of matter.
Matter, like space, is formed of electric charges. The difference between the two being that space is a perfectly alternating checkerboard of negative and positive charges, in multiple dimensions, while matter is a concentration of like charges, held together against their mutual repulsion by energy. Atoms are the "zero unit" of matter, where negative and positive charges get together to form a structure with a net electric charge of zero. The number one rule of the universe is that the two electric charges must always balance out. This rule comes before always seeking the lowest energy state.
Atoms have accomplished the balancing of the electrically charged particles comprising matter to zero. But not completely. With most atoms, there is still some charge imbalance. The way that this is balanced out is a further development, that of molecules. The less-than-perfect electrical balance in atoms, leads most of those atoms to combine into molecules in order to completely alleviate any charge imbalance. It is only those atoms of the inert gases, with completely filled outermost electron shells, that have no remaining electrical imbalance.
But what is so surprising is just how many different molecules can form from so few atoms. At the Big Bang, there were four different original atoms. Ordinary fusion in stars of smaller atoms into larger ones brings about 26 different atoms, up to iron. Application of the energy that is released when a large star explodes in a supernova further fuses atoms together that could not have been formed by the ordinary fusion process. This brings about a total of 92 different atoms, up to uranium.
But out of this relatively few number of different atoms the number of different molecules that can form, no one knows exactly how many, is millions upon millions upon millions. The vast majority of all possible molecules includes carbon, because of it's outstanding ability to form molecules.
The reason that so many different molecules can form from so few different atoms, all because of the imperfection of atoms at resolving the imbalance of electric charges, is that there are two scales that do not coincide, but which must exist together. These two scales are those of space and matter.
The reason that there is a mismatch between the scales of space and matter can be explained by my cosmology theory. The two did not form together, as in conventional theories of the Big Bang. Space formed first, and then matter.
The place where the two scales meet is at the scale of dust, as described above. The scale of dust is halfway between the scale of the infinitesimal electric charges of which the universe is composed, and the scale of the entire universe. The scale of dust is thus based on the scale of space and matter, since it must exist within space, "meets" the scale of space at dust and this is why there is a bias toward dust in the universe and so much of the matter in the universe is in the form of dust.
The scale of matter is much smaller than that of space. The "halfway" scale of space, where the matter that is scattered across it comes to meet it, is the scale of dust. But the dominant structure of matter, atoms, is so much smaller in scale than that of dust.
One way of explaining this is my cosmology theory. Matter originated from a two-dimensional sheet of space that was within, but not contiguous with, the multi-dimensional background space. When one of the two dimensions of the sheet disintegrated in what we perceive as the Big Bang, the matter that originated with the two-dimensional sheet was scattered over four dimensions of the background space. So that is the reason for the great different in primary scale of matter, compared to space. The scale of atoms represents the two dimensions of the original sheet of space that formed matter and the scale of dust represents the four dimensions of space over which the matter was scattered by what we perceive as the Big Bang.
The vast majority of an atom is empty space. The purpose that they serve is to act as a structure that brings about the balance of electric charges. Atoms are composed of both positive and negative charges and the reason that they are the scale they are is the strength of the charges of which they are composed.
But because of this difference in scale between matter and the space that it inhabits, both being composed of the same set of electric charges, atoms do not completely accomplish their objective of being the structures that balance electric charges. That is why atoms group together into molecules and these atoms are attached together by the leftover charge imbalance of atoms.
The reason that just so many different molecules form from so few different atoms can thus be explained simply. There is a simple relationship here. The tremendous number of different molecules that can form, relative to the number of different atoms, is equal to the scale of dust which is the scale of space, relative to the scale of atoms, which is the scale of matter.
Put simply, there is a relationship here similar to the two that we saw in the beginning. The universe favors such relationships because they represent the lowest information point. Essentially as many molecules can form from the few number of atoms from which they form as there are of these atoms in the typical scale of a speck of dust.
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