I was studying the history of relativity and invariance and using the new Wikipedia wikisources for Lorentz and Fitzgerald contractions from the 1890's to consider some aspects of Maxwell's equations and get a new perspective on time and space. I personally have a different view of how to consider space and time which has no effect on the computations, but it is the way that I see it as real. I was using blender with three cones to represent the "world lines" in 2D space and 1 of time for the action of what is considered magnetic and I simply see as some aspect of how space and time interact. I am not a person who denies that these relativistic effects occur, on the contrary I was required to deal with speed of light delay and transforms in my profession. Using GPS satellites also require a knowledge of these things.I simply disagree on the existential grouping of particles having the same velocity or with in a logical space that even by its own definition does not exist. The space between particles is not being dragged in a group and this all only applies to particles , and by anthropomorphizing the physics, it detracts from the science IMHO. I watched a PTV show about "M Brane string theory" and it was disturbing to see conjecture on things that can't be done and perhaps will never be done included to make it more entertaining. I don't think science is enhanced by draping it in clever art. I enjoy it for itself and pointless snappy graphics just make me irritated.
The image is a boolean intersection of two cones which would be a positive charge world line and a negative charge world line. The third is the interacting world line that exhibits magnetic effects. The intersect volume is the force and vector direction. It is very difficult to represent 4 space and an extra dimension of time with vector addition and I don't think there is a medium that could really show that effectively, though imagination does work to deal with n-dimensional things. I also used key frames for location of the third
sphere cone and then hid all unselected objects to show the shape of the field in simulated 5 space.
This is the beginning intersect and would represent a steady state where no magnetic influence would be observed. It is only the Σ of the vectors in this state and as it proceeds closer or further away. It makes no difference in this case if A and B move or if C moves, as it is the same sum and only requires a coordinate transform, as in that case C would be a static charge being accelerated.
So the Σ or sum of effect in time upon time is what I view as magnetic effect. I can use the handed rule and consider poles of magnets, but it seems that this is just some anachronistic perspective and there really are no poles in a physical sense. It is the fact that the direction of action is defined in that way. It isn't confusing to me to use it either way, but I prefer seeing it as an effect of time within time. It just seems clumsy to me to do vector cross products, unless that is a short hand in a specific situation in the same way as E=IR is a situational approximation. It can be a real mind f2ker to deal with the first time. Conventional experience suggests a pattern to actions and observations that is certainly true in common practice and unless you deal with electricity or physics, it is unlikely that it is ever an issue. It is absolutely necessary to understand if a person wants to actually understand what is taking place in the universe. I often wonder about how concepts are represented and one of those is Planck's constant. I get that it is a solution to total energy and that higher frequency requires higher energy. This is true of any waves. What I don't get is why it is presented with such flourish, as if it were a monumental leap of intelligence to associate it in that way or to measure it. Perhaps I am missing something that I will understand later.
It is just my opinion that lumping two of any number of particles into a system is where it all goes to hell. It looks like a cross between philosophy and physics that leads to all sorts of problems and logical conflict. If a circuit board is duplicated for a phone and they are identical, I do not see them as having any existential conflict with each other and I feel the same way about any collection of parts. So perhaps I just have a different philosophical viewpoint and in the end it makes little difference as the equations are solved exactly the same if I wear a wizard's hat or nothing at all. The cross between two associated temporal space axes and two others seems to add a complexity that though it can be computed, can be easily knotted in thought. It makes a situation which is 4! ( 4 factorial = 24 ) complex. I think it is just arbitrarily more complex and provides no extra insight.
ADDED: After some thought I could use the length of the conic boolean intersection as a kind of line integral and the normals to that line pointing at their origin as vectors and represent 2 more dimensions with optical intensity and shades of color from red to blue. With animation, it would give me 6 different dimensions of representation, but would require a lot of explanation as to what those dimension represented, though red could be positive field and green negative as well as intensity as the field strength based on inverse square potentiality. Perhaps I will get that enthusiastic the next time I visit the subject.