[Paper Review] Einstein-Schrodinger theory in the presence of zero-point fluctuations

J. A. Shifflett|ArXiv.org|Oct 29, 2003

Cosmology and Gravitation Theories33 references3 citations

TL;DR

This paper proposes a modified Einstein-Schrödinger theory that incorporates zero-point fluctuations via a cosmological constant, which nearly cancels a 'bare' cosmological constant in the nonsymmetric tensor, yielding a physical cosmological constant consistent with observation. The theory reproduces Einstein-Maxwell electrodynamics to within $10^{-16}$ of standard terms, derives a Lorentz force via the EIH method, and avoids ghosts through a novel mechanism, with exact monopole solutions matching Reissner-Nordström to $10^{-66}$ precision.

ABSTRACT

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.

Motivation & Objective

• To resolve the historical failure of the Einstein-Schrödinger theory to reproduce the Lorentz force by incorporating quantum vacuum effects.
• To reconcile the theory with observed cosmological constant values through cancellation of zero-point fluctuation contributions with a bare cosmological constant.
• To demonstrate that the modified theory reproduces standard electro-vac Einstein-Maxwell physics to high precision, avoiding issues like pathological asymptotic behavior in solutions.
• To show that the theory avoids ghost states through a non-standard mechanism, unlike previous formulations.
• To establish that the EIH method yields consistent equations of motion matching known results, confirming the existence of a Lorentz force.

Proposed method

• Derive field equations from a Lagrangian density that includes both a symmetric metric and a nonsymmetric fundamental tensor with cosmological constant terms.
• Introduce a cosmological constant from zero-point fluctuations that multiplies the symmetric metric, while a 'bare' cosmological constant multiplies the nonsymmetric tensor, allowing near-cancellation to match measured values.
• Use the Christoffel connection from the symmetric metric to ensure the divergence of the Einstein equations vanishes, enabling consistent coupling to matter fields.
• Apply the Einstein-Infeld-Hoffmann (EIH) method to derive equations of motion for test particles, confirming the presence of a Lorentz force.
• Construct an exact electric monopole solution and compare it to the Reissner-Nordström solution, showing agreement to $\sim 10^{-66}$ precision.
• Take the limit as the zero-point fluctuation cosmological constant diverges to show the theory reduces exactly to electro-vac Einstein-Maxwell theory.

Experimental results

Research questions

• RQ1 Can the Einstein-Schrödinger theory be modified to reproduce the Lorentz force for charged particles, which it previously failed to do?
• RQ2 Can zero-point fluctuations be incorporated into the classical Einstein-Schrödinger framework to yield a physical cosmological constant consistent with observation?
• RQ3 Do the field equations of the modified theory reduce to the standard Einstein-Maxwell equations within measurable precision?
• RQ4 How does the theory avoid the ghost problem that plagues earlier versions of the Einstein-Schrödinger theory?
• RQ5 What is the behavior of the electric monopole solution in this modified theory, and how does it compare to the Reissner-Nordström solution?

Key findings

• The modified theory reproduces the electro-vac Einstein and Maxwell equations to within $< 10^{-16}$ of the standard terms for all measurable field strengths and rates of change.
• The EIH method yields equations of motion that match Einstein-Maxwell theory to Newtonian/Coulombian order, confirming the existence of a Lorentz force.
• An exact electric monopole solution is derived, differing from the Reissner-Nordström solution by terms of order $\sim 10^{-66}$ for all accessible radii.
• The theory avoids ghost states through a novel cancellation mechanism between the zero-point fluctuation cosmological constant and the bare cosmological constant.
• In the limit as the zero-point fluctuation cosmological constant tends to infinity, the theory reduces exactly to electro-vac Einstein-Maxwell theory.
• The field equations are consistent with energy-momentum conservation, as the divergence of the Einstein equations vanishes when using the Christoffel connection from the symmetric metric.