Lambda-Renormalized Einstein-Schrodinger Theory

The Einstein-Schrodinger theory without a cosmological constant was originally proposed by Einstein and Straus in 1946. In this form it is also known as "Einstein's Unified Field Theory", or the "Einstein-Straus Theory", or the "Hermitian Theory of Relativity", or the "Nonsymmetric Gravitational Theory", or the "Generalized Theory of Gravitation", or the "Relativistic Theory of the Non-symmetric Field". Schrodinger made an important contribution to the theory in 1947 by generalizing it to include a cosmological constant, and by showing that the theory can be derived from a very simple Lagrangian density if this cosmological constant is assumed to be non-zero. This more general theory is usually called "Schrodinger's Affine Field Theory" or the "Einstein-Schrodinger Theory".



Here are a few of Einstein's and Schrodinger's original papers on this topic.

The Einstein-Schrodinger theory is a generalization of ordinary general relativity which allows a non-symmetric fundamental tensor. When Einstein and Schrodinger developed the theory they suspected that this fundamental tensor might contain both the metric and electromagnetic field, and they hoped that the theory would unify gravitation and electromagnetism. However, using the EIH method it was shown way back in 1953 that the original theory apparently does not predict a Lorentz force between charged particles. Since then there has been some interest in the theory by a few researchers who dispute the proof of the missing Lorentz force. Other researchers have assumed that the theory is correct but represents something other than gravity and electromagnetism. Still others have investigated theories which are significantly modified versions of the original theory. In general though, there has not been much interest in the Einstein-Schrodinger theory for 50 years.

Lambda-renormalized Einstein-Schrodinger theory:
Recently it has been shown that a well motivated modification of the Einstein-Schrodinger theory does indeed closely approximate ordinary general relativity and electromagnetism (Einstein-Maxwell theory), the modification being the addition of a cosmological constant caused by zero-point fluctuations. It is reasonable to assume that the Einstein-Schrodinger theory must eventually be quantized to accurately predict reality, and this cosmological constant can be viewed as a kind of zeroth order quantization effect. 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, resulting in a total "physical" cosmological constant which matches measurement. The fact that these two cosmological constants multiply different fields has the effect of creating a Lorentz force, and also fixes some other problems with the original theory. The fine-tuning of cosmological constants is less objectionable when one considers that it is similar to renormalization methods which are commonplace in quantum field theory. For example, to cancel self energy, ``bare'' particle masses become large (infinite if the cutoff wavenumber goes to infinity), but the total ``physical'' mass remains small. In a similar manner in the present theory, Schrodinger's ``bare'' cosmological constant becomes large, but the total ``physical'' cosmological constant remains small. This is essentially a vacuum energy renormalization of the original Einstein-Schrodinger theory to account for zero-point fluctuations. With this quantum mechanical effect included, the theory closely approximates Einstein-Maxwell theory when the cosmological constant from zero-point fluctuations is limited by a cutoff frequency of 1/(Planck length), and it becomes exactly Einstein-Maxwell theory in the limit as this cosmological constant goes to infinity. For the details, see my papers.

"A modification of Einstein-Schrodinger theory that contains both general relativity and electrodynamics (Gen. Rel. Grav. version)",
"A modification of Einstein-Schrodinger theory that contains both general relativity and electrodynamics (arxiv.org version)",
"A modification of Einstein-Schrodinger theory that contains Einstein-Weinberg-Salam theory",
"Einstein-Schrodinger theory in the presence of zero-point fluctuations",
"Einstein-Schrodinger theory using Newman-Penrose tetrad formalism",
"Lambda-Renormalized Einstein-Schrodinger theory with spin-0 and spin-1/2 sources",

Here are some of my presentations on this topic:
Shifflett_Dissertation_Presentation.ppt - given 22 April 2008 at Washington University.
Non-Abelian_LRES.pdf - given 13 April 2008 at the April APS meeting.
Einstein_Schrodinger.pdf - given 15 April 2007 at the April APS meeting.
GradSeminar16Feb2007.ppt - given 16 Feb 2007 at the Washington University Graduate Student Seminar.
shifflett_james_win.pdf - given 17 Nov 2006 at the 16th Midwest Relativity Meeting.

Here are some MAPLE programs associated with this theory.

Here is my dissertation, Shifflett_James_A_Dissertation.pdf.

My name is James Shifflett.
I did my PhD work at the Physics Department of Washington University, St. Louis, MO under Clifford Will.
I can be contacted HERE.

Go back to my home page.