Einstein tensor

The golden ring to which most physicists aspire is a unified field theory that incorporates all of modern and classical physics. Some scientists and others call this a TOE or ‘theory of everything’, but it is no more than false hubris to believe that humans could possibly know and explain everything about the universe at this time. Einstein chased this goal for the last three decades of his life, basing his theoretical research on his general theory of relativity. Meanwhile, the vast majority of scientists supporting the other major accomplishment of the Second Scientific Revolution were investing all of their time and efforts to advancing the quantum theory and their quest has been extremely successful. They originally had no interest in a unified field theory. After Einstein died in 1955, his efforts were all but abandoned because of his philosophical stance against the prevalent Copenhagen Interpretation of quantum theory even though he had been one of quantum theory’s founders. During the 1970s the tables started to turn and quantum theorists became interested in unifying physics, although not from the foundational principles of relativity theory. They claimed that quantum theory was more fundamental than relativity so they began the same quest from a totally different direction despite their claims to be continuing Einstein’s quest.  Throughout the development of the ensuing standard quantum model, superstring theory and many other theoretical schemes, quantum theorists have remained resolute in their conviction that the quantum and relativity are mutually incompatible so the quantum must completely do away with and replace relativity once and for all. However, the quantum theory and relativity are not actually incompatible and, in fact, say the some of the same things about the nature of physical reality. When the similarities are fully defined and studied and the basic assumptions behind each of the theories are altered to reflect the similarities instead of the incompatibilities, only then can the point of their compatibility be determined and act as a unifying principle resulting in a completed unified field theory of the type that Einstein once sought. The development of this physical model of reality is not without irony. Not only is the quantum theory incomplete as Einstein argued in EPR, but Einstein’s general relativity is also seriously incomplete and true unification cannot be rendered complete at any level of reality until all the theoretical models being unified are themselves complete.

Science is a work in progress, although the progress that science has made over the past few decades has been vastly limited by the narrow, limited and dogmatic worldviews representing the major paradigms of physics. It is not hard or even overwhelmingly original to conclude that science has followed the wrong direction at a fork in the road and led itself into a corner with little to no room for escape. Both the quantum theory and general relativity have made spectacularly accurate predictions, nearly all of which have been verified, but these two paradigms remain mutually incompatible while the standard model of particles used within the quantum paradigm keeps predicting the existence of particles that are not falsifiable and completely beyond verification. Newer physical models such as the superstring and brane theories have not lived up to their promise and show no signs of settling the problems of unification for which they were designed. This book takes a different route and tells the story of a new form of unified field theory that combines or merges the best parts of the quantum theory and relativity together within a single field theory structure. It covers four primary areas of scientific inquiry: the macrocosm, the microcosm, the everyday world of life, mind and experience, and the abstract world of theoretical and philosophical mathematics and science. In so doing, this book offers the best chance for an alternative physics worldview that is nothing less than the science of our future, a preview of the science that will carry us into a brave new world of being and becoming our own future.

Keywords: Future physics, theory of everything, unified field theory, quantized space-time, consciousness, evolution, paraphysics

Modern physics is based on two paradigms that emerged from the Second Scientific Revolution - relativity and the quantum. Since their inception these two theoretical giants have advanced science and society far beyond anything that their originators could have even dreamed up, but in a sense they seem to be progressing in different directions and are regarded mutually incompatible. Yet they come to a point in history where the next step in their own advancement would be to unify into a single overwhelming physical paradigm. The concept of unification is well known in relativity theory with many attempts dating from just a few short years after Einstein first developed relativity. But the hyperspace unification that seems to have originated with Kaluza in 1921 and was modified by Klein a few years later has become the best known attempt. This book has two parts. The first, Hyperspace, deals with the original Kaluza theory in all of its aspects and incarnations up until the 1960s. After the 1960s the idea of unification was adopted by quantum theoreticians based on their belief that the quantum is more fundamental than relative space-time. However, since the 1980s Klein’s adaptation of Kaluza’s theory has been used to unify physics under the quantum banner as has the purely quantum theory Standard Model. Yet both of these quantum attempts have fundamental problems that can only be solved by returning to Kaluza’s original theory as modified by Einstein and Bergmann in the 1930s. So the second part of the book, Continuum, tells the rest of the story and offers a new theory, a five-dimensional single field theory, the merges the best of both paradigms together. By merging the two paradigms instead of replacing one by the other, single field theory preserves all of the many successes of both theories. This is the book that every physicist, physical scientist and non-professional science advocate should read and every theoretical physicist and physics students must read.

I discuss Einstein's path-breaking November 1915 General Relativity papers. I show that Einstein's field equations of November 25, 1915 with an additional term on the right hand side involving the trace of the energy-momentum tensor appear to have sprung from his first November 1915 paper: the November 4, 1915 equations. Second paper among three papers.

I discuss Albert Einstein's 1916 General Theory of Relativity. I show that in Einstein's 1916 review paper, "the Foundation of the General Theory of Relativity", he derived his November 25, 1915 field equations with an additional term on the right hand side involving the trace of the energy-momentum tensor (he posed the condition square root -g=1) using the equations he presented on November 4, 1915. Series of papers: Final paper.

Before developing his 1915 General Theory of Relativity, Einstein held the "Entwurf" theory. Tullio Levi-Civita from Padua, one of the founders of tensor calculus, objected to a major problematic element in this theory, which reflected its global problem: its field equations were restricted to an adapted coordinate system. Einstein proved that his gravitational tensor was a covariant tensor for adapted coordinate systems. In an exchange of letters and postcards that began in March 1915 and ended in May 1915, Levi-Civita presented his objections to Einstein's above proof. Einstein tried to find ways to save his proof, and found it hard to give it up. Finally Levi-Civita convinced Einstein about a fault in his arguments. However, only in spring 1916, long after Einstein had abandoned the 1914 theory, did he finally understand the main problem with his 1914 gravitational tensor. In autumn 1915 the G\"ottingen brilliant mathematician David Hilbert found the central flaw in Einstein's 1914 derivation. On March 30, 1916, Einstein sent to Hilbert a letter admitting, "The error you found in my paper of 1914 has now become completely clear to me".

Since the 1970s, an ever growing number of theoretical physicists have become interested in unifying the quantum and relativity upon a quantum basis. Before the 1970s, only Einstein and a select few sought unification, but their theoretical work was based upon the continuity of relativity rather than quantum’s discrete nature of reality. To date neither paradigm has developed anything that would appear to unify physics, except for the work of one physicist and a few of his colleagues. H.T. Flint published more than thirty-five articles in well-known peer-reviewed journals over a period of four decades, extending relativity to include electromagnetism and the quantum. Yet his work and that of his close associates is almost completely unknown today. Flint published his complete unified field theory in the 1960s, well before most quantum theorists even began thinking along the lines of unification.  Strangely enough, Flint’s unification theory has been completely forgotten by a scientific community that has become enamored enough with the idea of unification that it would accept the most outrageous and non-intuitive ideas as long as they are based on the quantum, but then Kaluza’s five-dimensional unification of relativity and electromagnetism supposedly was not known until it was rediscovered by the superstring theorists, or so they claim. In reality, these ideas were lost in plain sight for decades simply because the physics community was unwilling to recognize accomplishments based on relativity theory.

The equations were first published by Einstein in 1915 in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor)