The Beginning of General Relativity

2021 ◽  
Vol 30 (6) ◽  
pp. 30-35
Author(s):  
Dong-han YEOM
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Equations Of Motion ◽  
Absolute Space ◽  
Newtonian Mechanics ◽  
Coordinate Systems ◽  
Field Equations ◽  
Classical Physics ◽  
Space And Time ◽  
The Future

In this article, we briefly review the motivations behind general relativity. We first discuss the basics of classical physics, including the equations of motion and the field equations. Newtonian mechanics assumes absolute space and time, but this can be philosophically unnatural. Einstein constructed a general theory of classical physics with covariance for the general choice of coordinate systems. This theory is known as general relativity. Finally, we briefly mention how this theory is completed, how this theory is verified, and what can be the future of general relativity.

The mechanics of general relativity

1959 ◽  
Vol 251 (1264) ◽  
pp. 55-65 ◽  
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Equations Of Motion ◽  
Stress Singularity ◽  
Theory Of Relativity ◽  
General Theory Of Relativity

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.

scholarly journals R. DESCARTES IR I. NEWTONAS: GAMTOS FILOSOFIJOS SISTEMŲ PANAŠUMAI IR SKIRTUMAI (LAIKO IR ERDVĖS ASPEKTAI)

Problemos ◽  
2006 ◽  
Vol 69 ◽  
Author(s):  
Jonas Čiurlionis
Keyword(s):  
Natural Philosophy ◽  
Special Theory ◽  
The Other ◽  
Absolute Space ◽  
Newtonian Mechanics ◽  
Space And Time ◽  
History Of ◽  
Similarities And Differences ◽  
Laws Of Motion ◽  
In The Beginning

Erdvės ir laiko sampratų istorijoje I. Newtonas yra neabejotinai viena svarbiausių figūrų. Absoliučios erdvės ir laiko idėjos ilgą laiką buvo plačiai pripažintos ir realiai paneigtos tik XX a. pradžioje, atsiradus specialiajai reliatyvumo teorijai. Tačiau niutoniškajai mechanikai įsitvirtinti reikėjo nukonkuruoti R. Descartes’o gamtamokslines pažiūras. Kita vertus, ar gali būti, kad abiejų filosofų pažiūros yra ne tiek prieštaraujančios, kiek panašios? Ar gali būti, kad I. Newtonas pasinaudojo R. Descartes’o idėjomis, konstruodamas savo garsiuosius judėjimo dėsnius, kuriais konstatavo laiko ir erdvės absoliutumą? Šie probleminiai klausimai yra nagrinėjami straipsnyje.Reikšminiai žodžiai: erdvė, laikas, judėjimo dėsniai, reliatyvumas. R. DESCARTES AND I. NEWTON: SIMILARITIES AND DIFFERENCES BETWEEN THEIR SYSTEMS OF NATURAL PHILOSOPHYJonas Čiurlionis Summary Throughout the history of undertanding space and time, I. Newton is undoubtedly one of the most important figures. His ideas of absolute space and time were widely accepted and refused only in the beginning of the 20th century with the rise of special theory of reliativity. However, in order to be recognized, Newtonian mechanics had to win the competition against Cartesian natural philosophy. On the other hand, can it be that views of both philosophers are more similar than contradictory? Can it be that I. Newton used the ideas of R. Descartes while constructing his famous laws of motion – the foundation for the absolute space and time? These and similar problematic questions are discussed in the article.Keywords: space, time, laws of motion, relativity.

The Annotated Manuscript

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Equations Of Motion ◽  
Special Theory ◽  
Material Point ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
Theory Of Gravitation

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.

scholarly journals Ephemeris Astronomy Definitions and Constants in General Relativity

1997 ◽  
Vol 165 ◽  
pp. 439-446
Author(s):  
Victor A. Brumberg
Keyword(s):  
General Relativity ◽  
Time Scales ◽  
Absolute Space ◽  
Newtonian Mechanics ◽  
Reference Systems ◽  
Absolute Time ◽  
Astronomical Constants

AbstractCurrently employed definitions of ephemeris astronomy and the system of astronomical constants are based on Newtonian mechanics with its absolute time and absolute space. To avoid any relativistic ambiguities in applying new IAU (1991) resolutions on reference systems (RS) and time scales one should specify the astronomical constructions and definitions of constants to make them consistent with general relativity (GRT). Such an approach is developed with the aid of the existing relativisting hierarchy of relativistic reference systems and time scales.

ON EQUATIONS OF MOTION IN GENERAL RELATIVITY

1955 ◽  
Vol 33 (12) ◽  
pp. 824-827
Author(s):  
G. E. Tauber
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Charged Particle ◽  
Variational Principle ◽  
Classical Theory ◽  
Equations Of Motion ◽  
Field Equations

It has been shown that both the equations of motion of a charged particle in a gravitational field and the field equations can be obtained from one variational principle by suitably generalizing Dirac's classical theory of electrons.

scholarly journals Some minisuperspace model for the Faddeev formulation of gravity

2014 ◽  
Vol 29 (27) ◽  
pp. 1450141 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Distinctive Feature ◽  
Vector Fields ◽  
Measure Zero ◽  
Equations Of Motion ◽  
Zero Set ◽  
Constant Vector ◽  
Field Equations ◽  
Piecewise Constant ◽  
The Continuum

We consider Faddeev formulation of General Relativity (GR) in which the metric is composed of ten vector fields or a 4 ×10 tetrad. This formulation reduces to the usual GR upon partial use of the field equations. A distinctive feature of the Faddeev action is its finiteness on the discontinuous fields. This allows to introduce its minisuperspace formulation where the vector fields are constant everywhere on ℝ4 with exception of a measure zero set (the piecewise constant fields). The fields are parametrized by their constant values independently chosen in, e.g. the 4-simplices or, say, parallelepipeds into which ℝ4 can be decomposed. The form of the action for the vector fields of this type is found. We also consider the piecewise constant vector fields approximating the fixed smooth ones. We check that if the regions in which the vector fields are constant are made arbitrarily small, the minisuperspace action and equations of motion tend to the continuum Faddeev ones.

The Two-Dimensional Electrostatic Solutions of Born's new Field Equations

1935 ◽  
Vol 31 (1) ◽  
pp. 50-68 ◽  
Author(s):  
M. H. L. Pryce
Keyword(s):  
General Solution ◽  
General Theory ◽  
Singular Solution ◽  
Equations Of Motion ◽  
Constant Field ◽  
Two Dimensional ◽  
Field Equations ◽  
Special Cases

The general solution of Born's new field equations is found for the two-dimensional electrostatic case, by which the coordinates are expressed as functions of the field vectors, Conditions for inversion are discussed. Special cases are worked out, namely: singnle charge, two charges, charge in a constant field. Expressions are given for forces acting on the charges. A singular solution is also discussed, with reference to the neutron. The implication of the solutions on the general theory and the equations of motion is discussed in the conclusion.

Newton To Maxwell: The Principia and British Physics

1988 ◽  
Vol 42 (1) ◽  
pp. 75-96 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Absolute Space ◽  
Theory Of Relativity ◽  
Quantum Theories ◽  
Classical Physics ◽  
Newtonian Physics ◽  
World Picture ◽  
Space And Time ◽  
The World ◽  
Modern Physics

It is conventional to denote the physics of the period 1700-1900, from A the Principia to the advent of the relativity and quantum theories, as ‘classical’ or ‘Newtonian’ physics. These terms are not, however, very satisfactory as historical categories. The contrast between classical and ‘modern’ physics is perceived in terms that highlight the innovatory features of physics after 1900: the abandonment of the concepts of absolute space and time in Einstein’s theory of relativity, and of causality and determinism in quantum mechanics. ‘ Classical ’ physics is thus defined by ‘non-classical’ physics. The definitions and axioms of Principia , Newton’s exposition of the concepts of absolute space and time, and his statement of the Newtonian laws of motion, are rightly seen as fundamental to the 17th-century mechanization of the world picture.

The Development of Machian Themes in the Twentieth Century

2006 ◽  
Author(s):  
Julian Barbour
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
Quantum Gravity ◽  
Space Time ◽  
Field Theories ◽  
Absolute Space ◽  
Rates Of Change ◽  
Space And Time

This chapter charts the complicated legacy of Mach's critique of absolute space and time. In 1902, Poincaré achieved a clear formulation of what a truly Machian mechanics should accomplish: it should permit a unique prediction of future motion on the basis of just the relative separations of bodies, and these separations' rates of change. However, this work made no impact on Einstein, despite his admiration for Mach. The discussion explains how several independent ideas that dominated Einstein's thinking about space, time and matter led him to a quite different interpretation (or misinterpretation) of Mach. This chapter also argues that, despite the misinterpretation, general relativity is perfectly Machian (in a sense that is the analogue for field theories of Poincaré's criterion), and that this shows general relativity to be ‘timeless’ in a certain sense, which is suggestive of quantum gravity.

Modeling the dynamics of black holes through balanced equations of motion in the null gauge

2019 ◽  
Vol 16 (09) ◽  
pp. 1950131
Author(s):  
Emanuel Gallo ◽  
Osvaldo M. Moreschi
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Field Equation ◽  
General Framework ◽  
Gravitational Constant ◽  
Equations Of Motion ◽  
Field Equations ◽  
Asymptotic Structure ◽  
Strong Connection ◽  
The Past

We develop further the general framework for modeling the dynamics of the motion of black holes, presented in [E. Gallo and O. M. Moreschi, Modeling the dynamics of black holes through balanced equations of motion, Int. J. Geom. Meth. Mod. Phys. 16(3) (2019) 1950034], by employing a convenient null gauge, in general relativity, for the construction of the balanced equations of motion. This null gauge has the property that the asymptotic structure is intimately related to the interior one; in particular there is a strong connection between the field equations and the balanced equations of motion. Our work is very related to what we have called “Robinson–Trautman (RT) geometries” [S. Dain, O. M. Moreschi and R. J. Gleiser, Photon rockets and the Robinson–Trautman geometries, Class. Quantum Grav. 13(5) (1996) 1155–1160] in the past. These geometries are used in the sense of the general framework, we have presented in [E. Gallo and O. M. Moreschi, Modeling the dynamics of black holes through balanced equations of motion, Int. J. Geom. Meth. Mod. Phys. 16(3) (2019) 1950034]. We present the balanced equations of motion in second order of the acceleration. We solve the required components of the field equation at their respective required orders, [Formula: see text] and [Formula: see text], in terms of the gravitational constant. We indicate how this approach can be extended to higher orders.

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