Quantized Fields

No, I’m not going to talk about the Higgs boson.  Well, except to make one reference to it as far as my work is concerned:  it’s a new (but long predicted, and not yet shown to actually be the Higgs) particle and field to add to the particle zoo.  A step backwards, in a way–I think our understanding will advance when we find underlying connections between particles and fields, but adding more to the pile isn’t helpful to a deeper understanding.  Oh, and that the Higgs approach adds an inertial property to mass particles, a mechanism caused by a drag effect relative to the field.  That matters to my work because it appears to be a different mechanism than how I propose mass gets attached to particles.  Yes, it calls into question the validity of my work, but so do a whole bunch of other things.  I’m proceeding anyway.

I got some interesting results from some simulation efforts–a second stable state with three components.  It is particularly interesting because it appears to settle into a three way braid–and more importantly, seems to progress to faster and faster speeds–limited to the speed of light.  Not sure why it does that, more investigative work to determine if this is a model problem or real behavior of the three twist solution.  Does make me think of a neutrino, but that’s pure speculation.  Here’s some curious pics.  These sim has all three twists with equal momentum.  I’m going to set one or two twists to double momentum and see what happens.  I also need to fix the attraction/repulsion in these cases, currently these cannot represent reality because of three charge values instead of two in real life (+,-)–but you can see what a fertile ground the twist model shows.

This 3D simulation of a three twist interaction stabilizes into three way braid

This 3D projection of a three way twist array eventually stabilizes into a closely interacting stable entity

But the real work I’ve been doing lately is not these sims–instead, it’s my thinking about the continuous property of fields and quantization.  If the unitary twist field is continous, it is blocking–a twist bend cannot propagate through another twist bend if it is separated by a plane with background state orientation–another way of saying a continuous unitary field cannot be linear.  Real EM fields are linear.  Are they also continuous?  At first, I said no, they can’t be,  since real EM fields should be blocking as well.  But then I realized that unlike the unitary twist field, real EM fields are linear (effectively can pass through each other) because the field of one source can add on top of another field from another source.  In this case, the magnitude of the field at a given point is not constrained, so this is what makes the fields of QFT work, that is, be continuous and also linear.

Mathematically, that is possible–but now I believe that even the QFT model of fields such as the EM field cannot be continuous for a different reason, field quantization.  QFT says you cannot extract any energies from the field that don’t meet the quantization constraint.   Unitary twist fields will derive this quantization because only full twists from and to the background field direction are possible and topologically stable.  Any partial twist must return to the background state and will dissipate.  Here’s why I now think that any quantized field cannot be continuous.  Let’s talk unitary twist field first.  I had a groundbreaking discovery with unitary twist fields a month or so ago when I found that if this field is continuous, it is possible to create a situation where it blocks passage of field states.  If you put two oppositely charged particles separated by a distance r, symmetry requires that a plane separating the two particles must have zero twist, and thus one particle would see zero twist at distance r/2–the same thing it would see at an infinite distance.  The problem is, then there is a situation where there is no difference from the uncharged background state and the first particle cannot respond differently than if there were no nearby charged particles.  The bisecting plane with zero bend acts as a barrier preventing or blocking  the other particle from affecting the first.

OK, that was the unitary twist field case.  Now the QFT case doesn’t have this problem since the bisecting plane holds magnitudes, not the zero background state of the unitary twist field.  Therefore, the first particle can be subject to the effects of the second particle since the bisecting plane no longer blocks.

But, QFT fields have a different problem that still says it can’t be continuous.  A non-continuous field is the saving grace that might allow unitary twist fields to be a valid underlying solution–if the field is not continuous, but is granular.  If the QFT field has to be granular, then unitary twist field theory becomes a valid underlying architecture for QFT (of course, other constraints or problems might invalidate unitary twist theory, but right now granularity allows the unitary twist field to be non-blocking, otherwise there’s no way it could work).  In the granular case, a given epsilon neighborhood sees these passing components going from one particle to the other without blocking.  Thus, any quantized field such as QFT fields or unitary twist fields will be linear (and div and curl will be zero) if and only if the granular parts do not interact.

As I continued down this path of thinking, I began to realize that whether the QFT EM field or the unitary twist field are correct real world descriptions, neither of them can be continuous.   You could argue that the field itself is continuous but the particles that are extracted from the field are quantized, but this idea has serious fails if you create a field from a limited number of quanta.  Inductive reasoning is going to force either model of the field to be composed of granular components–it will not be possible to create a field from two quanta that is continuous because the information of the quanta is preserved.  Why do I say that?  Because a two quanta field that is continuous may only release a quantized particle from the energy of the field.  If the quanta information is preserved in the field, I cannot see any way that a definition of continuous could apply to this field.

Now, if the field is composed of quanta that do not interact, then linearity will result simply by the ability of packing more or less quanta into a set epsilon volume.  Linearity means that the quanta cannot interact (otherwise magnitudes at some points will not sum, a linearity requirement).  Therefore, the quantized field can be considered granular and infinitely sparse, that is, no constructive summation of fields can cause loss of total volume density of quanta.  In other less obtuse and verbose words, the quantized field must not be continuous and must consist of non-interacting quanta, regardless of whether we are talking unitary twist field or QFT EM fields.  If you buy this, then the twist field is not blocking and is still a potentially valid description of reality.  If this is true, then the geometrical basis for quantization comes from the twists returning to a background state, a conclusion that QFT currently does not provide, and thus  unitary twist field theory work is still a worthwhile effort.

Agemoz

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