English | 2020 | ISBN: N/A | ASIN: B08L9KQCG1 | 328 pages | PDF | 4.93 Mb
Applied mathematics algebra without positive actual infinity - Maxwell's Equations unite with the Dirac Equation to combine electron dynamics with photon dynamics because, by use of the algebra, an electron projects itself as a photon. Electron/photon double existence derives from Schrцdinger's Cat because each place-value digit of a real number beyond a finite maximum in count is unknown and unknowable, analogous to the cat being both alive and dead inside its unopened box. The algebra is derived from a proposed axiom that replaces Cantor's Continuum Hypothesis. - Empirically derived energy density and the Poynting Vector unite in the force density invariant as one mathematical model. That unity suggests quantities in our geometric world actually do have finite imprecision, and that the new algebra applies to more modern theories of physics. - Visualizations and exercises help comprehension. - The mathematics is simple enough to be understood by a high school student who has taken first year level college math and physics classes (and is familiar with trigonometry and logarithms, complex numbers, matrix multiplication, geometric-unit-vectors, and partial differential equations). - One particle at two places violates a preconceived notion that that isn't possible. The one particle is material (fermion electron) and, its opposite, force (boson photon). Take this radical notion further by supposing perceived reality results from numbers, alone from objects, interacting by becoming more precise with respect to each other, to form patterns we see as the Dirac Equation and other mathematical models of physics. The universe is fundamentally numbers. - Preface - The first four chapters of Special Algebra for Special Relativity present an all-number mathematical structure for Special Relativity. The fifth chapter restricts a measurable quantity to finite precision by limiting place-value digits to a maximum count before and after the decimal point. - For example, each side of a unit square has small magnitude finite imprecision added to it. The finite imprecision adder is a non-finite type of number because it isn't knowable. - Finite imprecision larger than a measurable quantity is the division reciprocal of small magnitude imprecision. In Special Relativity large magnitude imprecision is added to time-space hyperbolic angle "alpha" (that relates to speed by "v = c*tanh(alpha)") using a Lorentz Transformation. Large magnitude imprecision models electromagnetism by uniting Maxwell's Equations with the Dirac Equation. Precision improves with time to cause measurable dynamics. - Electromagnetic field force density components are calculated using the same process by which electric current density components are calculated. Included are energy density and Poynting Vector components. - Uniting those three empirically derived electromagnetic phenomena into one mathematical model is new and that success suggests quantities in our geometric world actually do have finite imprecision and suggests finite imprecision numbers should also apply to more modern theories of physics.
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