arXiv subjects

J. A. Shifflett

Publications and source records attributed to J. A. Shifflett.

5 recordsLinked to original sources

arXiv2009

A modification of Einstein-Schrodinger theory that contains Einstein-Maxwell-Yang-Mills theory

The Lambda-renormalized Einstein-Schrodinger theory is a modification of the original Einstein-Schrodinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein-Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of dxd Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein-Maxwell-Yang-Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein-Maxwell-Yang-Mills theory in that the extra terms in the field equations are 10^-13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg-Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.

gr-qc↗

arXiv2008

A modification of Einstein-Schrodinger theory that contains both general relativity and electrodynamics

We modify the Einstein-Schrodinger theory to include a cosmological constant $Λ_z$ which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant $Λ_z$ is assumed to be nearly cancelled by Schrodinger's cosmological constant $Λ_b$ which multiplies the nonsymmetric fundamental tensor, such that the total $Λ=Λ_z+Λ_b$ matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as $|Λ_z|\to\infty$. For $|Λ_z|\sim 1/(Planck length)^2$ the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are $<10^{-16}$ of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrodinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordstrom solution except for additional terms which are $\sim 10^{-66}$ of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

gr-qc↗

arXiv2007

Einstein-Schrodinger theory in the presence of zero-point fluctuations

The Einstein-Schrodinger theory is modified by adding a cosmological constant contribution caused by zero-point fluctuations. This cosmological constant which multiplies the symmetric metric is assumed to be nearly cancelled by Schrodinger's ``bare'' cosmological constant which multiplies the nonsymmetric fundamental tensor, such that the total ``physical'' cosmological constant matches measurement. We first derive the field equations of the theory from a Lagrangian density. We show that the divergence of the Einstein equations vanishes using the Christoffel connection formed from the symmetric metric, allowing additional fields to be included in the same manner as with ordinary general relativity. We show that the field equations match the ordinary electro-vac Einstein and Maxwell equations except for additional terms which are $<10^{-16}$ of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. We also show that the theory avoids ghosts in an unusual way. We show that the Einstein-Infeld-Hoffmann (EIH) equations of motion for this theory match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force. We derive an exact electric monopole solution, and show that it matches the Reissner-Nordstrom solution except for additional terms which are $\sim10^{-66}$ of the usual terms for worst-case radii accessible to measurement. Finally, we show that the theory becomes exactly electro-vac Einstein-Maxwell theory in the limit as the cosmological constant from zero-point fluctuations goes to infinity.

gr-qc↗

arXiv2007

Lambda-renormalized Einstein-Schrodinger theory with spin-0 and spin-1/2 sources

The Einstein-Schrodinger theory is extended to include spin-0 and spin-1/2 sources, and the theory is derived from a Lagrangian density which allows other fields to be easily added. The original theory is also modified by including a cosmological constant caused by zero-point fluctuations. This cosmological constant which multiplies the symmetric metric is assumed to be nearly cancelled by Schrodinger's ``bare'' cosmological constant which multiplies the nonsymmetric fundamental tensor, such that the total ``physical'' cosmological matches measurement. We show that the resulting Lambda-renormalized Einstein-Schrodinger theory closely approximates ordinary Einstein-Maxwell theory and one-particle quantum mechanics. In particular, the field equations match the ordinary Einstein and Maxwell equations except for additional terms which are $<10^{-16}$ of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. We also show that the theory predicts the exact Lorentz force equation and the exact Klein-Gordon and Dirac equations. And the theory becomes exactly Einstein-Maxwell theory and one-particle quantum mechanics in the limit as the cosmological constant from zero-point fluctuations goes to infinity. Lastly, we discuss the merits of our Lagrangian density compared to the Einstein-Maxwell Lagrangian density.

gr-qc↗

arXiv2005

Einstein-Schrodinger theory using Newman-Penrose tetrad formalism

The Einstein-Schrodinger theory is modified to include a large cosmological constant caused by zero-point fluctuations. This ``extrinsic'' cosmological constant which multiplies the symmetric metric is assumed to be nearly cancelled by Schrodinger's ``bare'' cosmological constant which multiplies the nonsymmetric fundamental tensor, such that the total cosmological constant is consistent with measurement. This modified Einstein-Schrodinger theory is expressed in Newman-Penrose form, and tetrad methods are used to confirm that it closely approximates ordinary general relativity and electromagnetism. A solution for the connections in terms of the fundamental tensor is derived in the tetrad frame. The tetrad form of an exact electric monopole solution is shown to approximate the Reissner-Nordstrom solution and to be of Petrov type-D.

gr-qc↗