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Pandres, Dave; Green, Edward L.

doi:10.1023/a:1026147725039

International Journal of Theoretical Physics

2003

DOI: 10.1023/a:1026147725039

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Dave Pandres¹,

Edward L. Green²

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Cited by 6 publications

References 22 publications

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Gravitational and electroweak unification by replacing diffeomorphisms with larger group

Pandres

2009

Gen Relativ Gravit

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The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers will agree whether any given quantity is conserved. Alternatively, and equivalently, it is defined by the assumption that all observers will agree that the general relativistic wave equation describes the propagation of light. Thus, the group replacement is analogous to the replacement of the Lorentz group by the diffeomorphisms that led Einstein from special relativity to general relativity, and is also consistent with the assumption of constant light velocity that led him to special relativity. The enlarged covariance group leads to a non-commutative geometry based not on a manifold, but on a nonlocal space in which paths, rather than points, are the most primitive invariant entities. This yields a theory which unifies the gravitational and electroweak interactions. The theory contains no adjustable parameters, such as those that are chosen arbitrarily in the standard model.

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Gravitational and electroweak unification by replacing diffeomorphisms with larger group

Pandres

2009

Gen Relativ Gravit

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Model of a solar system in the conservative geometry

Green

2020

Gen Relativ Gravit

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Pandres has shown that an enlargement of the covariance group to the group of conservative transformations leads to a richer geometry than that of general relativity. Using orthonormal tetrads as field variables, the fundamental geometric object is the curvature vector denoted by C µ. From an appropriate scalar Lagrangian field equations for both free-field and the field with sources have been developed. We first review models which use a free-field solution to model the Solar System and why these results are unacceptable. We also show that the standard Schwarzschild metric is also unacceptable in our theory. Finally we show that there are solutions which involve sources which agree with general relativity PPN parameters and thus approximate the Schwarzschild solution. The main difference is that the Einstein tensor is not identically zero but includes small values for the density, radial pressure and tangential pressure. Higher precision experiments should be able to determine the validity of these models. These results add further confirmation that the theory developed by Pandres is the fundamental theory of physics.

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Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Green

2008

Int J Theor Phys

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Pandres has developed a theory in which the geometrical structure of a real fourdimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres' theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres' theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.

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Cited by 6 publications

References 22 publications

Gravitational and electroweak unification by replacing diffeomorphisms with larger group

Gravitational and electroweak unification by replacing diffeomorphisms with larger group

Model of a solar system in the conservative geometry

Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

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