The Annotated Manuscript

Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn

This section presents annotations of the manuscript of Albert Einstein's canonical 1916 paper on the general theory of relativity. It begins with a discussion of the foundation of the general theory of relativity, taking into account Einstein's fundamental considerations on the postulate of relativity, and more specifically why he went beyond the special theory of relativity. It then considers the spacetime continuum, explaining the role of coordinates in the new theory of gravitation. It also describes tensors of the second and higher ranks, multiplication of tensors, the equation of the geodetic line, the formation of tensors by differentiation, equations of motion of a material point in the gravitational field, the general form of the field equations of gravitation, and the laws of conservation in the general case. Finally, the behavior of rods and clocks in the static gravitational field is examined.

Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn

This section discusses the development of Albert Einstein's ideas and attitudes as he struggled for eight years to come up with a general theory of relativity that would meet the physical and mathematical requirements laid down at the outset. It first considers Einstein's work on gravitation in Prague before analyzing three documents that played a significant role in his search for a theory of general relativity: the Zurich Notebook, the Einstein–Grossmann Entwurf paper, and the Einstein–Besso manuscript. It then looks at Einstein's completion of his general theory of relativity in Berlin in November 1915, along with his development of a new theory of gravitation within the framework of the special theory of relativity. It also examines the formulation of the basic idea that Einstein termed the “equivalence principle,” his Entwurf theory vs. David Hilbert's theory, and the 1916 manuscript of Einstein's work on the general theory of relativity.


2015 ◽  
Vol 93 (11) ◽  
pp. 1335-1342 ◽  
Author(s):  
Sergey G. Fedosin

The difference of equations of motion in the covariant theory of gravitation and in the general theory of relativity is used to explain the Pioneer anomaly. Calculation shows that the velocities of a spacecraft in both theories at equal distances can differ by several centimetres per second. This leads also to a possible explanation of the flyby anomaly and comet disturbances, which are not taken into account by the general theory of relativity.


2004 ◽  
Vol 59 (10) ◽  
pp. 715-719 ◽  
Author(s):  
F. Winterberg

In a paper, published in 1997 by L. Corry, J. Renn, and J. Stachel, it is claimed that the recently discovered printer’s proofs of Hilbert’s 1915 paper on the general theory of relativity prove that Hilbert did not anticipate Einstein in arriving at the correct form of the gravitational field equations, as it is widely believed, but that only after having seen Einstein’s final paper did Hilbert amend his published version with the correct form of the gravitational field equations. However, because a crucial part of the printer’s proofs of Hilbert’s paper had been cut off by someone, a fact not mentioned in the paper by Corry, Renn, and Stachel, the conclusion drawn by Corry, Renn, and Stachel is untenable and has no probative value. I rather will show that the cut off part of the proofs suggests a crude attempt by some unknown individual to falsify the historical record.


2021 ◽  
Vol 58 (4) ◽  
pp. 175-195
Author(s):  
Vladimir P. Vizgin ◽  

The article is based on the concepts of epistemic virtues and epistemic vices and explores A. Einstein’s contribution to the creation of fundamental physical theories, namely the special theory of relativity and general theory of relativity, as well as to the development of a unified field theory on the basis of the geometric field program, which never led to success. Among the main epistemic virtues that led Einstein to success in the construction of the special theory of relativity are the following: a unique physical intuition based on the method of thought experiment and the need for an experimental justification of space-time concepts; striving for simplicity and elegance of theory; scientific courage, rebelliousness, signifying the readiness to engage in confrontation with scientific conventional dogmas and authorities. In the creation of general theory of relativity, another intellectual virtue was added to these virtues: the belief in the heuristic power of the mathematical aspect of physics. At the same time, he had to overcome his initial underestimation of the H. Minkowski’s four-dimensional concept of space and time, which has manifested in a distinctive flexibility of thinking typical for Einstein in his early years. The creative role of Einstein’s mistakes on the way to general relativity was emphasized. These mistakes were mostly related to the difficulties of harmonizing the mathematical and physical aspects of theory, less so to epistemic vices. The ambivalence of the concept of epistemic virtues, which can be transformed into epistemic vices, is noted. This transformation happened in the second half of Einstein’s life, when he for more than thirty years unsuccessfully tried to build a unified geometric field theory and to find an alternative to quantum mechanics with their probabilistic and Copenhagen interpretation In this case, we can talk about the following epistemic vices: the revaluation of mathematical aspect and underestimation of experimentally – empirical aspect of the theory; adopting the concepts general relativity is based on (continualism, classical causality, geometric nature of fundamental interactions) as fundamental; unprecedented persistence in defending the GFP (geometrical field program), despite its failures, and a certain loss of the flexibility of thinking. A cosmological history that is associated both with the application of GTR (general theory of relativity) to the structure of the Universe, and with the missed possibility of discovering the theory of the expanding Universe is intermediate in relation to Einstein’s epistemic virtues and vices. This opportunity was realized by A.A. Friedmann, who defeated Einstein in the dispute about if the Universe was stationary or nonstationary. In this dispute some of Einstein’s vices were revealed, which Friedman did not have. The connection between epistemic virtues and the methodological principles of physics and also with the “fallibilist” concept of scientific knowledge development has been noted.


It is shown how to obtain, within the general theory of relativity, equations of motion for two oscillating masses at the ends of a spring of given law of force. The method of Einstein, Infeld & Hoffmann is used, and the force in the spring is represented by a stress singularity. The detailed calculations are taken to the Newtonian order.


Author(s):  
Geoff Cottrell

By the beginning of the twentieth century, our understanding of matter was completely transformed by the great discoveries of electromagnetism and relativity. ‘Energy, mass, and light’ outlines Einstein’s special theory of relativity of 1905, which describes what happens when objects move at speeds close to the speed of light. The theory transformed our understanding of the nature of space and time, and matter through the equivalence of mass and energy. In 1916, Einstein extended the theory to include gravity in the general theory of relativity, which revealed that matter affects space by curving space around it.


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