I don’t understand why a moving point charge would produce a magnetic field with directional asymmetry depending on the charge sign, i.e., why is there a right hand rule? That has to be explained at some point. Is it really true or merely an ontological convention?
Let’s ponder classical point charges and the right hand rule. Consider a system of two point charges. Science imagines that a moving point charge A produces a magnetic field that rotates around the line of travel according to the right hand rule. Then if point charge B is moving through that magnetic field we again apply the right hand rule. When determining action on point charges, we always apply the right hand rule twice. This causes me to wonder if there is an ontological error and that the two applications of the right hand rule are simply a technique that allows us to find the vector perpendicular to the gradient of A’s electric field at point charge B.
Is it possible that there is no right hand rule in nature and no corresponding directionally oriented magnetic field? In our two particle system, it really doesn’t matter what is happening in absolute time and space anywhere other than at the locations of our two point charges A and B. There is no ontological meaning to either electric field or magnetic field at locations in absolute time and space where there is no point charge present. However it is helpful from the perspective of understanding to imagine the vector E and B fields throught absolute time and space. The question becomes whether the imagination of science with respect to the B field is flawed.
What if the B field direction is simply the normal field to the gradient of the E field? What if two applications of the right hand rule simply helps us find that the direction of B, but that the science imagination of B as circling around a moving point charge is false?
It is said that a moving point charge will produce a magnetic field according to the right hand rule.
Now if we had a second point charge, to determine the action on the second point charge we apply the right hand rule again to the directional magnetic field imagined from the first point charge.
The right hand rule is an erroneous mental crutch that allows us to consistently apply a pair of cross product rotations to determine the action of the changing electric field from point charge A upon point charge B moving through the electric field of A.
Note that self action is allowed, so this is true even when A = B.
In a system of point charges in Euclidean space and time, there is no ontological purpose for the concept of electric field or magnetic field at any locations in R4 other than at the locations where point charges are located. That said, imagining the fields can be a useful cognitive technique. The question I am posing is whether such visualization has led us astray. In the end, we are applying a cross product twice, once when the field is generated at x1, y1, z1, t1 by charge A and again when the field takes action on charge B at x2, y2, z2, t2. We have imagined each cross product with a right hand rule and therefore we imagine a magnetic field throughout space and time with a directionality.
We need to remove the intermediate step that imagines an erroneous conception of a magnetic field. In a way it is kind of like relativity. If we imagine charge A moving, it creates a changing E field. Now imagine that E field shape as fixed in space, and charge B is moving through it.
J Mark Morris : Boston : Massachusetts