Continuous Fields Cannot be Linear

A shocking revelation for me, in all my years both as a professional electrical engineer and as an amateur physicist.  I realize I have zero credibility out there with anyone, but at least for myself, I have discovered something fundamental about fields that I did not know.  Perhaps if I were a mathematician I would have worked this out.  Nevertheless, it is quite provable in my mind, and has enormous impact on how I must model the two particle interaction, whether by QFT or unitary twist field theory.

The concept of linear central force fields means that multiple potential sources create the field by means of linear superposition.  If you have two sources of potential, the effect on the field at any point is the sum of the effect due to either one.  There are potential corner cases such as if the potential is infinite at the point source, but in every finite potential situation, the field is the sum of all sources at that point.  Electrostatic fields are supposedly both continuous and linear, but this cannot be at the quantum scale.

I have been discussing in previous posts the concept of a median plane between two charged sources, and particularly enlightening was the attraction case of a positive and negatively charged particle.  Between these two particles will be a median plane whose normal runs through both particles.  This median plane can have no absolute potential (relative to the electrostatic field potential at infinite distance).  This field cannot pass any information, even about the existence of, one charged particle through this median plane.  In fact, it is well known in electrostatics that if you put a metal plane between two particles and ground it, you will get the same charge field distribution as if the second particle wasn’t there–it cannot be determined if the second particle actually exists or not.

The only way a field can pass information across this median plane is if the field is not continuous.  If the field  is created by a spaced array of quantized particles, such that they never, or almost never, interact, then the effect of the field can be made linear.  Indeed, shooting real photons at each other could collide, but that is exceeding rare, and modeling the field by photons, virtual or real, in either QFT or unitary twist field theory,  would produce a linear superposition of fields.  But there is no question now in my mind that if I simulate this, I cannot assume a continuous electrostatic field, such a thing cannot exist.  This field has to be almost entirely empty, with only very sporadic quantized particles, then I can see how linearity would be possible.  Every quantized particle that interacts with a quantized particle from the other source will distort the appearance of linearity, so the fact that deviations from linearity are experimentally unmeasurable strongly points to a extremely sparse field component density.

I had thought that QFT virtual particles could construct a continuous field in a Taylor or Fourier series type of composition, but it is clear that it cannot.  The QFT virtual particles must be exceedingly sparse, just like the twists in unitary twist field theory.  It also suggests that QFT virtual particles would have to clump in some way in order for localized neighborhoods in the field to obey conservation.

Now I see a workable model for twists.  The median plane problem cannot exist if the field is not continous.


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