This publication has trouble with large numbers and the interactions between the large numbers of fundamental particles involved. Magnetism and gravity work very differently and have been the subject of many of my blog posts. In previous posts I normally prefer to use Maxwell's equations with Heaviside's telegrapher's equations to make points about the real nature of electromagnetic interactions.
Ampere worked to give us a model for magnetism. If we spin electrons in the right way we will create a field of spinning electrons due to the interactions between electrons and the nucleus. The telegrapher's equations point to the mechanism by-which the electrons create spinning fields (L) and more linear electron fields (G and C). The spinning fields beget more positive ions that come in to charge balance the spinning electrons. Ampere's wires are thus forced apart.
Static magnets work in a very elegant manner. The magnet's ejected electrons are what some call the magnetic field. Really electrons are just moving in a circular manner determined by the magnet's electro-molecular geometry. When a magnet is flipped pi radians it's electrons have the opposite spin and the magnet is pointed in the opposite direction. Therefore, the magnet will attract the opposite pole of another magnet. The spinning electron field will line up atoms and molecules and the biggest and dense molecules of the opposing magnet will be attracted to charge-balance spinning electrons in a gas (or vacuum).
Gravity attracting matter has a more subtle explanation than the mechanical explanation as to how magnets attract. Gravity attracts slower moving matter and is an effective back-fill to electrons moving upwards. As matter attracts more matter to itself a positive feedback cycle is produced. Negative charged electrons will repel each other closer to the core of any mass. The escape route for this charge will always be towards the outer shell of the mass. There will be an acceleration of charge towards the outer shell of the mass. The electron ejected from the mass will need to be charge-balanced. This charge balance as ions of all sorts fall back towards the center of mass is what we feel as the force of gravity.
True understanding of the nature of the force of gravity rests on the understanding of how many molecules are involved. While a small number of molecules will exhibit the London Force ten to the twenty-fifth power number of molecules presents a stronger attraction depending on the specific electro-chemical interactions of the constituent molecules. Astro-physicists seem to write a lot about iron.
If paper-clips are the great mystery of physics perhaps we can put to rest the mechanism by-which a paper clip is attracted to a magnet against the force of gravity. Because the mechanisms of these two forces are so different the organized force around a magnet can overcome a very disorganized but statistically relevant force around an entire planet.
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