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So in this vid I discuss a conversation I had with the neighbor about science.
One of the questions I asked him - when he mentioned Tesla - I pointed out that Steinmetz had converted Tesla's inventions into mathematics and I asked if Steinmetz had used quaternions - I said I think Steinmetz had used quaternions but I was not sure.
So I just looked this up and this is what I discovered!!! https://www.researchgate.net/publication/269468849_A_geometric_algebra_reformulation_and_interpretation_of_Steinmetz's_symbolic_method_and_his_power_expression_in_alternating_current_electrical_circuits
A geometric algebra reformulation and interpretation of Steinmetz's symbolic method and his power expression in alternating current electrical circuits.
Developed more than a century ago, Steinmetz’s symbolic method is still puzzling us. It puzzles us because, in spite of its theoretical inconsistencies, it is heuristically efficient. However, it remains the dominant method in design, analysis, and operation of electrical power networks. The paper shows that Steinmetz’s mathematical expression for electrical power is based on assumptions inconsistent with the algebra of complex numbers. The paper argues that, although the numbers are correct, the mathematical interpretation of these numbers is not. Steinmetz got empirical right results for wrong conceptual reasons; the success of the symbolic method is based on the fact that, unwittingly, Steinmetz rediscovered Grassmann–Clifford geometric algebra. The paper challenges the dominant paradigm in power theory which represents voltage, current, active, reactive and apparent power as complex numbers and/or vectors (phasors). The author proposes a new paradigm in which these entities are represented as an algebraic group; the group is composed of a scalar, two vectors and a bivector which are residing in a four-dimensional algebraic space and in a two-dimensional Euclidean geometric space. The paper claims that Steinmetz’s symbolic method is the oldest engineering application of Clifford Algebra. The paper provides a strong motivation for a new didactic of power theory based on Geometric Algebra as Physics’ unifying language.
So this is so amazing since Basil J. Hiley also uses clifford geometry as noncommutative phase quantum algebra for the fifth force. This is what Steinmetz had called "Wattless Power."
The paper examines mathematical representations of electrical magnitudes in a.c. Circuit theory. It gives an historical and technical perspective of the development of the power concept and its geometrical and algebraic interpretations. The paper criticises the existing mathematical model of electrical power for being an entanglement of two mutually inconsistent, algebras: 1) standard vector algebra (Gibbs-Heaviside) and 2) complex algebra. The paper examines the ubiquitous expressions for power: S = P + jQ Ṡ = ṾI∗ The paper analyzes Steinmetz's symbolic method and exposes its inconsistencies. The paper proves that Steinmetz hypothesis, of a new and noncommutative algebra for power theory, represents a rediscovery of Grassmann-Clifford Algebra. The paper proposes a new didactic of power theory that should include Geometric Algebra.
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