3.2 The Three-Dimensional Nature of the Magnetic Field
It was Hermann Weyl, the philosopher of relativity as he has been called, in his beautiful book Symmetry who clearly emphasized faith in right-left equivalence as a central dogma of Western physical science, quite despite the fact that in his book he clearly shows the insurmountable difficulties in trying to frame the "asymmetry" of the behavior of the magnetic field, within an epistemological framework based on bilateral symmetry, whose real foundation is the same Aristotelian logic and whose character of faith derives from its predictive character, but which cannot account for the fact that the direction of the magnetic field is determined by the right-hand screw rule, which incidentally accounts for the formal definition of the vector product, so we can conclude that the magnetic field reflects the three-dimensional nature of space, from which its inherent capacity of energy storage could be derived.
It is significant that as soon as Weyl has stated that.
"The result is, in short, that nothing in Physics has indicated an intrinsic difference between left and right..."
that the violation of parity in weak interactions - where the invariant character of the spin direction of the magnetic field plays such a fundamental role - has indicated the opposite.
The parity-breaking experiment was performed by C.S.Wu, and for this: a sample of Co 60[2,418] was polarized in such a way that its nuclei had their magnetic fields or spins aligned:
the applied magnetic field configuration was set up as shown in Figure 3.3.a., which coincided with the polarization direction of Co 60.
"The system was inverted by rotating it 180° around the polarization line L, in such a way that the magnetic field and its spins were inverted and the experimental observation is shown in Figure 3.3.c: the result was that the direction of maximum electron emission intensity was inverted.
Actually based on the left-right equivalence it was theoretically thought to find something like the mirror image shown in Figure 3.3.b. but this was not what was observed experimentally. The experimental results are related to the fulfillment of the right-hand thread rule for the magnetic field and the indivisible unity of the magnetic poles.
All this we can interpret then, giving the magnetic field an ontological priority in relation to the electric field or the electric charge, and as an experimental proof of what Hermann Weyl did not want to recognize: that the physical structure of space contains a right-hand screw; that there is a fundamental asymmetry that leads us precisely to another type of symmetry whose starting point is not a line, but an ontological center that contains in itself a fundamental polarity, i.e., the same magnetic field.
One of the greatest drawback of special relativity as was presented by Einstein was that it was coinceived for lineat movements, as he used always real numbers, the Lorentz Transformation group showed how Maxwell's Equation remained invariant with it, but in fact for those equations, complex numbers must be used as has been done in electrical engineering, and its starting point is a rotating vector in the Complex Plane. See how, in my unpublished book Fisica, Semiotica y Ontologia, is showned a different framework for deducing the fundamental equations of physics, including that of the pendulum and the Schrödinger's wave equation.
As a matter of fact one of the greatest drawback of General Relativity was that Tensor Analisys was based on real numbers and as so, time was presented as a dimesions simillar to space dimension, something that make it totally incompatible with Quantum Mechanics.Furthermore Einstein wrote in his THE FOUNDATION OF THE GENERAL THEORY OF RELATIVITY:
..."Thus, according to the general theory of relativity, gravitation occupies an exceptional position with regard to other forces, particularly the electromagnectic forces, since the ten functions representing the gravitational field at the same time define the metrical properties of the space measured"
I just wonder if this incompabilty with other forces is not one of the reasons why the theory of big bang has been so widely accepted in spite that in that well documented book by Eric J. Lerner, The Big Bang Never Happened, is presented a new alternative based precisely on the electromagnetic field. the Plasma Cosmology.
You wrote:
"Complex numbers are only introduced because the area "under the curve" of a function is defined to be negative. Defining an area to be negative results in square roots of negative numbers being necessary to work with unknown values of x and y resulting in the "negative" area. Any physical representation using complex numbers can use other methods that are more physically specific for the representation by modifying the function that represents the system."
In electrical engineering, we use complex numbers, fundamentally because with them, the differential equations that result from Maxwell's equations, can be reduced to simple algebraic equations, which simplify the solution of those equations, and that is for the remarkable property of Euler's Equation, to remain the same, with those operations that represent change, I mean integration and differentiation, and in fact, sqr(-1) is just a symbol, for differention, as it were, two different order of reality such as active power and reactive power in IE, or time and space, in the case of QM, as is shown, with Schrödinger's wave equation based on complex numbers; here is in fact the great incompatibility, between QM and GR, because GR was coinceived by using a set of "real equations" in which time was a kind of variable of the same sort as space.
Einstein never thought of using complex numbers, and here lies in a certain sense of even the incompatibility between ER and GR...the one for linear systems, and the second for rotational systems.
When we treat both ER and GR with complex numbers, there is no incompatibility anymore as I have shown in various paper, including that one The Principle of Synergy and Isomorphic Units. Or in my unplished book in spanish, Física, Semiótica y Ontología.
Anyway this is the point of view of an IE, that had the opportunity, to text the use of complex numbers, for solving the state of a system of interconnected nodes of that network that constitute the most complex system built by man, I mean the Power System, from which we all depends daily. Solving with a real time state Estimator, a complex system of multiple interconected nodes, certainly is the best proof that complex numbers are for real... there is a real need, in my humble opinion of real paradigm shift regarding the unfortunate use of complex numbers, for considering sqr(-1), an imaginary unit as was named by Descartes... it is a symbol for separating two different orders of reality, that cannot be reduced the one to the other just as time and space.
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