|Subject: RE: Electrostatic
Field lines and Magnetic field lines
Date: Wed, 6 Feb 2002 09:33:03 -0600
The concept of "field lines" originally came from Faraday, who visualized the "field" as basically a set of taut strings under tension. He visualized the perturbation of the field as "plucking" these strings. Hence the notion of the "transverse EM wave" in the "medium" consisting of those "taut strings" -- those field lines. Maxwell simply lifted the notion from Faraday, since he set about to basically mathematized Faraday's approach. For some situations the lines became tubes, etc. It's really just a way to visualize and represent something; it is not an "absolute" at all.
For simple situations, the field lines are perpendicular to the surfaces because the tangent of the surface is at right angles to the "radiation" of the field lines from a central source. In more complicated situations, in the "lines" model the lines are not necessarily perpendicular to the surface. E.g., where there is a nonlinear geometrical distribution of the internal sources, and where those sources are both negative and positive in the case of electrical sources, or both north and south poles in terms of magnetism.
The real problem with all of that is that it perpetuates the myth that the local spacetime is flat. It isn't. Whenever there is a field present in space, the energy density of that spacetime is changed by the field energy; hence the spacetime is curved a priori. As Wheeler says, "Mass (actually mass-energy) acts on spacetime to curve it, and curvature of spacetime acts on mass-energy to move it or change it.) This mutual interaction is missing in classical EM theory. Further, the local vacuum also is polarized and altered by the field. So for a "poor man's" cut at a full appreciation, I use the notion of the "supersystem", consisting of three parts: (1) the system and its dynamics, (2) the local active vacuum and its dynamics, and (3) the local curvatures of spacetime and their dynamics. All three components of the supersystem interact upon each other.
Classical EM theory kills the other two components -- which is simply killing the active environment of the system. In short, the Lorentz symmetry regauging of the Maxwell-Heaviside equations arbitrarily discards any NET exchange of work or energy between the system and its environment (the other two components).
Since any COP>1.0 EM system must be an open system far from disequilibrium with its environment, and freely receiving and using energy from that environment, then the Lorentz condition arbitrarily discarded all such systems by assuming a net equilibrium with the active environment.
That regauging made the equations much simpler (of course! It threw away the more complicated Maxwellian systems!), but it also selected only those Maxwellian systems which are in equilibrium and doomed to exhibit COP<1.0.
Put another way, Lorentz unwittingly selected that class of Maxwellian systems that rigorously obey classical equilibrium thermodynamics with its infamous second law. He arbitrarily discarded that class of Maxwellian systems that permissibly violate classical equilibrium thermodynamics, and comply with the thermodynamics of open systems far from equilibrium with their active environment. These latter systems are permitted (by the laws of physics and nonequilibrium thermodynamics), to perform five "magic" functions: (1) self-organize or self-order, which is actually an application of gauge freedom and the ability to freely change their potential energy, (2) self-oscillate or self-rotate, (3) output more energy than the operator himself arranges to input (the excess energy input is freely received from the external active environment via the broken symmetry), (4) power itself and its load simultaneously (all the energy is freely received from the external active environment via the broken symmetry, and (5) exhibit negentropy.
It is well-known, e.g., that the entropy of a system decreases when the system is in disequilibrium with its active environment, because equilibrium is the condition of maximum entropy. Indeed, the entropy of a system far from disequilibrium cannot even be calculated.
As you can see, the overwhelming majority of objections to COP>1.0 EM systems are simply na´ve, and based on the older classical equilibrium thermodynamics which does not even apply.
Your works on the new electromagnetism are doing us dreaming. Soon we will wake up in a better world.
For you or AIAS, what means the "field lines" in electrostatics or in magnetism.
Why this lines are always perpendicular to the surface they reach or they go out ?