A two dimensional surface current can also produce a three dimensional magnetic field pattern that does not radiate. All that is required is that the current remain constant at every point within the surface if radiation must be avoided.
You can visualize atomic structures where atoms are bound by magnetic forces arising from the electron current distribution effecting the near fields if you stretch your imagination. I would not be overly surprised to find that it is magnetic attraction instead or in cooperation with electric field forces that allow for the construction of covalent bonds. After all, the movement of charges generates the magnetic fields that are evident throughout nature. I would question the non constant charge distribution in time assumption concerning far field radiation balance. You are left asking how high in frequency must the harmonics be tracked in order for the balance to exist? There are an infinite number of harmonics for any fundamental frequency that you choose. What happens as you approach infinity, does the balance still occur? With DC this is not a problem. We are going to require a better understanding of Mills' theory before the non radiating, non-constant charge distribution is understood. So far it has been my understanding that he can construct a complex sphere out of smaller loops which is consistent with what I am proposing. I do not see how individual loops would be consistent with AC harmonic balancing in all directions. After all, RF antennas can be built in this manner. The balancing of the far field radiation pattern may not be the only requirement, but it is one of the main requirements. If this is not achieved then energy will continue to leak from the electron into space until it finally reaches that state. DC current distribution is also consistent with steady magnetic near fields. It is easy to see how the magnetic moment of an atom can be constructed in such a manner. If you assume AC currents then there would be very little if any steady magnetic moments generated. I suppose one could suggest a combination of DC and AC currents to overcome this particular problem but why is AC required at all? Dave -----Original Message----- From: Eric Walker <[email protected]> To: vortex-l <[email protected]> Sent: Wed, Jan 20, 2016 12:14 pm Subject: Re: [Vo]:quantum knots accomplished! On Wed, Jan 20, 2016 at 10:14 AM, David Roberson <[email protected]> wrote: The bottom line is that it is easy to produce a non radiating structure of any degree of complexity as long as the currents flowing within that structure are constant. An orbitsphere such as Mills appears to refer to is a simple example. Stefan Israelsson Tampe explained sometime back that the orbitsphere is characterized by a non-constant charge distribution in which the charge is proportional to the real value of one of the spherical harmonics: https://www.mail-archive.com/[email protected]/msg105034.html If Stefan is correct, it seems that Mills is proposing a current that varies along the surface of the orbitsphere, i.e., is not constant. Stefan in a later email says that the non-radiation condition is not the only requirement that must be met: https://www.mail-archive.com/[email protected]/msg105060.html I mention this not because I was persuaded of anything by that thread, but because it seems relevant to your thought experiment. As an aside, it seems to me that in such thought experiments a two-dimensional sheet of current is not sufficient to explain other experimental observations. I am of the impression that the current distribution that describes an electron orbital must be three dimensional, varying with the radius. Eric
