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A classical Unified Field Theory using Riemanian Quarternions

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  • Bill Hamilton
    Here is the Abstract: Abstract The equations governing gravity and electromagnetism show both profound similarities and unambiguous differences. Albert
    Message 1 of 1 , Jul 26, 2001
      Here is the Abstract:

      The equations governing gravity and electromagnetism show both profound
      similarities and unambiguous differences. Albert Einstein worked to unify
      gravity and electromagnetism, mainly by trying to generalize Riemannian
      geometry. Hamilton's quaternions are a 4-dimensional topological algebraic
      field related to the real and complex numbers equipped with a static
      Euclidean 4-basis. Riemannian quaternions as defined herein explicitly allow
      for dynamic changes in the basis vectors. The equivalence principle of
      general relativity which applies only to mass is generalized because for any
      Riemannian quaternion differential equation, the chain rule means a change
      could be caused by the potential and/or the basis vectors. The Maxwell
      equations are generated using a quaternion potential and operators.
      Unfortunately, the algebra is complicated. The unified force field proposed
      is modeled on a simplification of the electromagnetic field strength tensor,
      being formed by a quaternion differential operator acting on a potential,
      Box* A* . This generates an even, antisymmetric-matrix force field for
      electricity and an odd, antisymmetric-matrix force field for magnetism,
      where the even field conserves its sign if the order of the differential and
      the potential are reversed unlike the odd field. Gauge symmetry is broken
      for massive particles by the even, symmetric-matrix term, which is
      interpreted as being due to gravity. In tensor analysis, a differential
      operator acting on the field strength tensor creates the Maxwell equations.
      The unified field equations for an isolated source are generated by acting
      on the unified force field with an additional differential operator, Box*
      Box* A* = 4 pi J*. This contains a quaternion representation of the Maxwell
      equations, a classical link to the quantum Aharonov-Bohm effect, and dynamic
      field equations for gravity. Vacuum solutions to the unified field equations
      are discussed. The field equations conserve both electric charge density and
      mass density. Under a Lorentz transformation, the gravitational and
      electromagnetic fields are Lorentz invariant and Lorentz covariant
      respectively, but there are residual terms whose meaning is not clear
      presently. An additional constraint is required for gauge transformations of
      a massive field.

      Einstein's vision using quaternions

      Here is the link:

      Has Victor or Berkant looked at this?

      Bill Hamilton
      Executive Director
      Skywatch International, Inc.

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