Relativistic Dynamics

Author(s):  
David D. Nolte

The invariance of the speed of light with respect to any inertial observational frame leads to a surprisingly large number of unusual results that defy common intuition. Chief among these are time dilation, length contraction, and loss of simultaneity. The Lorentz transformation intermixes space and time, but an overarching structure is provided by the metric tensor of Minkowski space-time. The pseudo-Riemannian metric supports 4-vectors whose norms are invariants, independent of any observational frame. These invariants constitute the proper objects of reality to study in the special theory of relativity. Relativistic dynamics defines the equivalence of mass and energy, which has many applications in nuclear energy and particle physics. Forces have transformation properties between relatively moving frames that set the stage for a more general theory of relativity that describes physical phenomena in noninertial frames.

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.


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.


1962 ◽  
Vol 14 ◽  
pp. 87-112 ◽  
Author(s):  
J. R. Vanstone

Modern differential geometry may be said to date from Riemann's famous lecture of 1854 (9), in which a distance function of the form F(xi, dxi) = (γij(x)dxidxj½ was proposed. The applications of the consequent geometry were many and varied. Examples are Synge's geometrization of mechanics (15), Riesz’ approach to linear elliptic partial differential equations (10), and the well-known general theory of relativity of Einstein.Meanwhile the results of Caratheodory (4) in the calculus of variations led Finsler in 1918 to introduce a generalization of the Riemannian metric function (6). The geometry which arose was more fully developed by Berwald (2) and Synge (14) about 1925 and later by Cartan (5), Busemann, and Rund. It was then possible to extend the applications of Riemannian geometry.


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.


2016 ◽  
Vol 25 (13) ◽  
pp. 1645014 ◽  
Author(s):  
John Ellis

Cosmology and particle physics have long been dominated by theoretical paradigms: Einstein’s general theory of relativity in cosmology and the standard model of particle physics. The time may have come for paradigm shifts. Does cosmological inflation require a modification of Einstein’s gravity? Have experiments at the LHC discovered a new particle beyond the Standard Model? It is premature to answer these questions, but we theorists can dream about the possibilities.


2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Ali Rıza ŞAHİN ◽  

The general theory of relativity is based on expressing gravity by means of the metric tensor and its elements instead of some fields as in electrodynamics. This work starts with by defining some vector fields for metric or metric tensor. After metric and metric tensor are expressed in terms of these fields, the geodesic equations and Einstein equations are derived for these fields. Finally, perihelion precession and light deflection are recalculated, as two different applications of the introduced fields.


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.


2018 ◽  
Vol 10 (4) ◽  
pp. 38
Author(s):  
Koshun Suto

In the thought experiment in this paper, we consider inertial frames M and A moving at constant velocity relative to each other. First, a light signal is emitted from inertial frame M toward inertial frame A when the time on a clock in inertial frame M is 1 (s). In the scenario of this paper, that light arrives at inertial frame A when time on the clock in A is 2 (s). Next, the situation is reversed, and a light signal is emitted from inertial frame A toward inertial frame M when the time in inertial frame A is 1 (s). That light arrives at inertial frame M when the time in M is 2 (s). According to the special theory of relativity (STR), the two inertial frames are equivalent, and thus it is not surprising that symmetric experiment results are obtained. However, it has already been pointed out that, among the coordinate systems regarded by Einstein as inertial frames, there are “classically stationary frames” where light propagates isotropically, and “classically moving frames” where light propagates anisotropically. If a classically stationary frame is incorporated into a thought experiment, it becomes easier to predict the experiment results. This paper elucidates a system whereby symmetrical experiment results can be obtained, even if the two coordinate systems are not equivalent. If one attempts to explain such experiment results from the standpoint of the STR, it ironically requires the use of logic that is unacceptable under the STR. Thus, this paper explains those experiment results by using logic different from the STR, and demonstrates the breakdown in the STR.


2020 ◽  
Vol 25 (2) ◽  
pp. 151-168
Author(s):  
Anatoliy Pypych

The author proceeds from the traditional consideration of the specifics of the social from the views of the Neo-Kantians and Dilthey on the distinction between "humanities" and "science". First of all, this difference is overcome by the synthesis of knowledge of human and nature, sociobiology being an example of that. Within non-classical and post-non-classical varieties of scientific knowledge, the tendency for theoretical synthesis is being increased. Cybernetics and synergetics are mentioned as oriented towards a new type of rationality and being essentially synthetic already in their origins. The author argues that the social knowledge, performative in its nature, obtains particular importance in the holistic world-picture. Its theoretical synthesis is difficult to achieve due to the large number of different concepts of the social, which has been designated as its multiparadigmality. According to the author, the approach to systematization proposed by sources does not contribute to solving the problem. Especially when taking into account within the world-picture the impact on the synthesis process caused not only by the knowledge of human and nature, but by technical knowledge as well. It is suggested to return to the origins of the very concept of paradigm by T. Kuhn, it's not only historical (paradigms change over time) but logical aspect as well (they are internally related). An example provided is A. Einstein's theory of relativity, where this connection of the two paradigms (both Galileo-Newton’s and Einstein's principles of relativity) constitutes a unity through the interconnection of general and special relativity. On this ground the author proposes to take the mentioned structure as a model for constructing a synthetic theory of the social, in which a special and general theory of the social would constitute a certain integrity. The first part (the special theory) would have a direct relation to human, and the second part would deal with human relations in the light of the knowledge of nature and technology (general theory of the social).


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