If you are wondering what on earth electrons and elevations on the earth's surface have to do with each other the answer is an amazing example of how information flows through the universe, from the lowest to the highest levels, as described in the compound posting on this blog, "The Flow Of Information Through The Universe" January 2016. This posting has been added to that.
What the flow of information through the universe means is that the higher-level structures in the universe must be composed of the same information as the lower-level structures of which they are composed, simply because there is no new information from anywhere on which to base them. A simple and obvious example is that our Solar System is made of atoms, and the orbits of planets around the sun very much resemble the orbitals of electrons around the nucleus of the atoms of which the Solar System is composed.
There are two basic elevations on the earth's surface, the ocean floor and the elevation of land above sea level. The average land elevation on earth is 840 meters above sea level and the average ocean depth is 3700 meters so there is a difference of about 4.5 km between the two levels.
But this difference in elevation is information, and information must come from somewhere. We know that the earth is composed of atoms, and we know that the information in larger-scale structures must somehow come from the smaller-scale structures of which they are composed. So atoms might be where we look to find out why this difference in elevation on earth is as much as it is.
As it turns out the answer is fairly easy to find. Electrons are in orbitals around the nucleus of the atom. The nucleus is composed of positively-charged protons and neutrally-charged neutrons. The electrons have negative electric charges that are equal, but opposite to the positive charge on a proton.
But the electron and the proton are not equal in mass. While the two are equal in charge the mass of a proton is 1,836 times that of an electron. This difference is information and we know that, since atoms are lower-level structures of which higher-level structures are composed, we might expect that this fundamental difference in mass of the atom's component particles may well be reflected in higher-level structures that are composed of atoms.
The average difference between the two basic levels of the earth's surface, the elevation of the land and the depth of the ocean floor, is about 4.5 km. The radius of the earth is about 6,000 km. If we divide the latter by the former we get 1,333, which is less than 1,836.
But we are dealing with the information in atoms here so the density of the earth counts, not just simply distance. The earth is not of uniform density, with higher density toward the center. The iron core has the highest density. The rock of the lower mantle is more dense than that of the upper mantle. The rock of the earth's crust, where the difference in elevation is located, is the least dense.
If we consider density multiplied by distance, rather than just distance, the difference between the two basic elevations on the earth's surface is just about exactly 1,836 times the radius of the earth, and this is the information in the atoms of which the earth is composed, the difference in mass between the proton and the electron.
Of course the earth's surface, whether land or seafloor, is far from being of even elevation. But that is because more information was added later, my impacts from space, tectonic collisions and glacial movement caused by the earth's rotation, and volcanic activity caused by heat energy from radioactive decay that is trapped within the earth.
But I find this to be an excellent example of how information flows through the universe, from the lowest to the highest levels, and the information in the lower-level structures must be used to construct the higher-level structures because there is no new information from anywhere else.
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