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Articles 1 - 2 of 2
Full-Text Articles in Physics
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Spacetime Algebra As A Powerful Tool For Electromagnetism, Justin Dressel, Konstantin Y. Bliokh, Franco Nori
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single …
Fundamental Mathematics Of Consciousness, Menas Kafatos
Fundamental Mathematics Of Consciousness, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We explore a mathematical formalism that ties together the observer with the observed in the view that Consciousness is primary, operating through three principles which apply at all levels, the essence of qualia of experience. The formalism is a simplified version of Hilbert space mathematics encountered in quantum mechanics. It does, however, go beyond specific interpretations of quantum mechanics and has strong philosophical foundations in Western philosophy as well as monistic systems of the East. The implications are explored and steps for the full development of this axiomatic mathematical approach to Consciousness are discussed.