The Equivalence Principle, Special Relativity, and Newton’s Gravitational Law

2012 ◽  
pp. 51-66
Author(s):  
Constantinos G. Vayenas ◽  
Stamatios N.-A. Souentie
Keyword(s):  
Special Relativity ◽  
Equivalence Principle

The Equivalence Principle

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Time Dilation ◽  
Gravitational Redshift ◽  
Coordinate Systems ◽  
Spacetime Metric

The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.

Mass, Special Relativity and the Equivalence Principle

2012 ◽  
pp. 15-22
Author(s):  
Constantinos G. Vayenas ◽  
Stamatios N.-A. Souentie
Keyword(s):  
Special Relativity ◽  
Equivalence Principle

Gravitational “Doppler Boosting / De-boosting” Effect within the Framework of General Relativity

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Mark Zilberman ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Special Relativity ◽  
Spectral Index ◽  
Equivalence Principle ◽  
Relativistic Effect ◽  
Gravitational Redshift ◽  
Astronomical Observations ◽  
Complete Set ◽  
Einstein's Equivalence Principle

The “Doppler boosting / de-boosting” relativistic effect increases / decreases the apparent luminosity of approaching / receding sources of radiation. This effect was analyzed in detail within the Special Relativity framework and was confirmed in many astronomical observations. It is however not clear if “Doppler boosting / de-boosting” exists in the framework of General Relativity as well, and if it exists, which equations describe it. The “Einstein’s elevator” and Einstein’s “Equivalence principle” allow to obtain the formula for “Doppler boosting / de-boosting” for a uniform gravitational field within the vicinity of the emitter/receiver. Under these simplified conditions, the ratio ℳ between apparent (L) and intrinsic (Lo) luminosity can be conveniently represented using source’s spectral index α and gravitational redshift z as ℳ(z, α) ≡ L/Lo=(z+1)^(α-3). This is the first step towards the complete set of equations that describe the gravitational "Doppler boosting / de-boosting" effect within the General Relativity framework including radial gravitational field and arbitrary values of distance h between emitter and receiver.

scholarly journals A fundamental special-relativistic theory valid for all real-valued speeds

1984 ◽  
Vol 7 (3) ◽  
pp. 565-589
Author(s):  
Vedprakash Sewjathan
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relativistic Theory ◽  
Equivalence Principle ◽  
Rest Mass ◽  
Space Time ◽  
Twin Paradox ◽  
Relativistic Factor ◽  
Time Frames ◽  
Time Transformations

This paper constitutes a fundamental rederivation of special relativity based on thec-invariance postulate but independent of the assumptionds′2=±ds2(Einstein [1], Kittel et al [2], Recami [3]), the equivalence principle, homogeneity of space-time, isotropy of space, group properties and linearity of space-time transformations or the coincidence of the origins of inertial space-time frames. The mathematical formalism is simpler than Einstein's [4] and Recami's [3]. Whilst Einstein's subluminal and Recami's superluminal theories are rederived in this paper by further assuming the equivalence principle and “mathematical inverses” [4,3], this paper derives (independent of these assumptions) with physico-mathematical motivation an alternate singularity-free special-relativistic theory which replaces Einstein's factor[1/(1−V2/c2)]12and Recami's extended-relativistic factor[1/(V2/c2−1)]12by[(1−(V2/c2)n)/(1−V2/c2)]12, wherenequals the value of(m(V)/m0)2as|V|→c. In this theory both Newton's and Einstein's subluminal theories are experimentally valid on account of negligible terms. This theory implies that non-zero rest mass luxons will not be detected as ordinary non-zero rest mass bradyons because of spatial collapse, and non-zero rest mass tachyons are undetectable because they exist in another cosmos, resulting in a supercosmos of matter, with the possibility of infinitely many such supercosmoses, all moving forward in time. Furthermore this theory is not based on any assumption giving rise to the twin paradox controversy. The paper concludes with a discussion of the implications of this theory for general relativity.

scholarly journals THERMODYNAMICS OF MODIFIED BLACK HOLES FROM GRAVITY'S RAINBOW

2007 ◽  
Vol 22 (36) ◽  
pp. 2749-2756 ◽  
Author(s):  
YI LING ◽  
XIANG LI ◽  
HONGBAO ZHANG
Keyword(s):  
Black Holes ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Dispersion Relations ◽  
Specific Class ◽  
Gravity’S Rainbow ◽  
Modified Dispersion Relations ◽  
Gravity's Rainbow

We study the thermodynamics of modified black holes proposed in the context of gravity's rainbow. A notion of intrinsic temperature and entropy for these black holes is introduced. In particular for a specific class of modified Schwarzschild solutions, their temperature and entropy are obtained and compared with those previously obtained from modified dispersion relations in deformed special relativity. It turns out that the results of these two different strategies coincide, and this may be viewed as a support for the proposal of deformed equivalence principle.

The equivalence principle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Reference Frames ◽  
Albert Einstein ◽  
Absolute Space ◽  
Inertial Forces ◽  
Theory Of Gravity

This chapter recalls several relevant aspects of Newton’s theory of gravity, as well as Maxwell’s theory of electromagnetism, to describe the conceptual path that Albert Einstein followed in going from the theory of special relativity to general relativity. Looking at 1907 and beyond, the chapter shows that the ambition of Einstein was to construct a theory in which all reference frames (and therefore none) were privileged. Moreover, there were no longer any inertial forces, no ordering of Newton’s absolute space. Therefore, Einstein’s theory was one in which the laws of physics had the same form in all frames, inertial or not, so that no frame could be regarded as being privileged. In brief, he sought a theory of general relativity.

scholarly journals Genesis of general relativity — A concise exposition

2016 ◽  
Vol 25 (14) ◽  
pp. 1630004
Author(s):  
Wei-Tou Ni
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Relativistic Fluids ◽  
Schwarzschild Solution ◽  
Stress Energy ◽  
Perihelion Advance ◽  
Theory Of Gravity

This short exposition starts with a brief discussion of situation before the completion of special relativity (Le Verrier’s discovery of the Mercury perihelion advance anomaly, Michelson–Morley experiment, Eötvös experiment, Newcomb’s improved observation of Mercury perihelion advance, the proposals of various new gravity theories and the development of tensor analysis and differential geometry) and accounts for the main conceptual developments leading to the completion of the general relativity (CGR): gravity has finite velocity of propagation; energy also gravitates; Einstein proposed his equivalence principle and deduced the gravitational redshift; Minkowski formulated the special relativity in four-dimentional spacetime and derived the four-dimensional electromagnetic stress–energy tensor; Einstein derived the gravitational deflection from his equivalence principle; Laue extended Minkowski’s method of constructing electromagnetic stress-energy tensor to stressed bodies, dust and relativistic fluids; Abraham, Einstein, and Nordström proposed their versions of scalar theories of gravity in 1911–13; Einstein and Grossmann first used metric as the basic gravitational entity and proposed a “tensor” theory of gravity (the “Entwurf” theory, 1913); Einstein proposed a theory of gravity with Ricci tensor proportional to stress–energy tensor (1915); Einstein, based on 1913 Besso–Einstein collaboration, correctly derived the relativistic perihelion advance formula of his new theory which agreed with observation (1915); Hilbert discovered the Lagrangian for electromagnetic stress–energy tensor and the Lagrangian for the gravitational field (1915), and stated the Hilbert variational principle; Einstein equation of GR was proposed (1915); Einstein published his foundation paper (1916). Subsequent developments and applications in the next two years included Schwarzschild solution (1916), gravitational waves and the quadrupole formula of gravitational radiation (1916, 1918), cosmology and the proposal of cosmological constant (1917), de Sitter solution (1917), Lense–Thirring effect (1918).

scholarly journals Test of special relativity and equivalence principle fromKphysics

1998 ◽  
Vol 58 (2) ◽  
Author(s):  
T. Hambye ◽  
R. B. Mann ◽  
U. Sarkar
Keyword(s):  
Special Relativity ◽  
Equivalence Principle
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