Enough of this! Einstein, .... -it is time we replaced GR

Astrophysics and Space Science Library, 2008

The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety years to describe gravitational phenomena on these various scales. We review the foundations of general relativity, discuss the recent progress in the tests of relativistic gravity, and present motivations for high-accuracy gravitational experiments in space. We also summarize the science objectives and technology needs for the laboratory experiments in space with laboratory being the entire solar system. We discuss the advances in our understanding of fundamental physics anticipated in the near future and evaluate discovery potential for the recently proposed gravitational experiments.

2018

A general theory of relativity is formulated without Einstein's equation. Einstein's tensor ties the space metric to the stress-energy tensor of a gravitational field. A homogeneous isotropic field metric is under consideration. In particular, the metric for a homogeneous isotropic universe possesses the anticipated density of our own universe. The speed of time progression at a distance from the observer slows according to an acceleration law asymptotically equal to Hubble's Law. A continuous field is homogeneous within the limits of small domains. This makes it possible to write a metric for a general continuous field and the single parameter given by the wave equation. The Schwarzschild problem has a continuous solution for r > 0. This solution approaches the Schwarzschild solution beyond the Schwarzschild radius and a second solution is obtained from the Schwarzschild problem-a stationary, expulsive, self-consistent field.

European Physical Journal H, 2017

Einstein’s 1915 theory of gravitation, also known as General Relativity, is now considered one of the pillars of modern physics. It contributes to our understanding of cosmology and of fundamental interactions between particles. But that was not always the case. Between the mid-1920s and the mid-1950s, General Relativity underwent a period of stagnation, during which the theory was mostly considered as a stepping-stone for a superior theory. In a special issue of EPJ H just published, historians of science and physicists actively working on General Relativity and closely related fields share their views on the process, during the post-World War II era, in particular, which saw the “Renaissance” of General Relativity, following progressive transformation of the theory into a bona fidae physics theory. In this special issue, new insights into the historical process leading to this renaissance point to the extension of the foundation of the original theory, ultimately leading to a global transformation in its character. Contributions from several experts reveals that the theory of 1915 was insufficient to reach firm conclusions without being complemented by intuitions drawn from the resources of pre-relativistic physics. Or, in the case of cosmology, the theory needed to be complemented by philosophical considerations that were hardly generalizable to help solve more mundane problems. As physicist Pascual Jordan puts it, there was a “mismatch between the simplicity of the physical and epistemological foundations and the annoying complexity of the corresponding thicket of formulae.” A number of contributions in this special issue also explain how the theory underwent a period of successive controversies, leading by the 1960s, to the renaissance of the theory. Subsequently, it became in the 1970s, an important, empirically well-tested branch of theoretical physics related to the new, successful sub-discipline of relativistic astrophysics.

2019

Annalen der Physik, 2005

General relativity in the Annalen and elsewhere Readers of this volume will notice that it contains only a few papers on general relativity. This is because most papers documenting the genesis and early development of general relativity were not published in Annalen der Physik. After Einstein took up his new prestigious position at the Prussian Academy of Sciences in the spring of 1914, the Sitzungsberichte of the Berlin academy almost by default became the main outlet for his scientific production. Two of the more important papers on general relativity, however, did find their way into the pages of the Annalen [35,41]. Although I shall discuss both papers in this essay, the main focus will be on [35], the first systematic exposition of general relativity, submitted in March 1916 and published in May of that year. Einstein's first paper on a metric theory of gravity, co-authored with his mathematician friend Marcel Grossmann, was published as a separatum in early 1913 and was reprinted the following year in Zeitschrift für Mathematik und Physik [50, 51]. Their second (and last) joint paper on the theory also appeared in this journal [52]. Most of the formalism of general relativity as we know it today was already in place in this Einstein-Grossmann theory. Still missing were the generally-covariant Einstein field equations. As is clear from research notes on gravitation from the winter of 1912-1913 preserved in the so-called "Zurich Notebook," 1 Einstein had considered candidate field equations of broad if not general covariance, but had found all such candidates wanting on physical grounds. In the end he had settled on equations constructed specifically to be compatible with energy-momentum conservation and with Newtonian theory in the limit of weak static fields, even though it remained unclear whether these equations would be invariant under any non-linear transformations. In view of this uncertainty, Einstein and Grossmann chose a fairly modest title for their paper: "Outline ("Entwurf") of a Generalized Theory of Relativity and of a Theory of Gravitation." The Einstein-Grossmann theory and its fields equations are therefore also known as the "Entwurf" theory and the "Entwurf" field equations. Much of Einstein's subsequent work on the "Entwurf" theory went into clarifying the covariance properties of its field equations. By the following year he had convinced himself of three things. First, generallycovariant field equations are physically inadmissible since they cannot determine the metric field uniquely. This was the upshot of the so-called "hole argument" ("Lochbetrachtung") first published in an appendix to [51]. 2 Second, the class of transformations leaving the "Entwurf" field equations invariant was as broad