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:

http://world.std.com/~sweetser/quaternions/gravity/unified_field/unified_field.html

Has Victor or Berkant looked at this?

Bill Hamilton

Executive Director

Skywatch International, Inc.

websites:

http://home.earthlink.net/~skywatcher22

http://home.earthlink.net/~skywatcher12

http://home.earthlink.net/~xplorerx

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