All classical predictions of general relativity from special relativistic Hamiltonian dynamics

2018 ◽  
Vol 33 (29) ◽  
pp. 1850169
Author(s):  
J. H. Field

Previous special relativistic calculations of gravitational redshift, light deflection and Shapiro delay are extended to include perigee advance. The three classical, order G, post-Newtonian predictions of general relativity as well as general relativistic light-speed-variation are therefore shown to be also consequences of special relativistic Newtonian mechanics in Euclidean space. The calculations are compared to general relativistic ones based on the Schwarzschild metric equation, and related literature is critically reviewed.

Open Physics ◽  
2004 ◽  
Vol 2 (4) ◽  
Author(s):  
Abhijit Biswas ◽  
Krishnan Mani

AbstractThe time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.


R. d’E. Atkinson has shown that the path of a test particle, the light rays and the gravitational red shift predicted by general relativity for the case of the Schwarzschild metric may all be interpreted in terms of Euclidean space. By introducing the concept of a background space it is shown that Atkinson’s interpretation may be extended for the case of any finite static gravitating system. It is pointed out that the interpretation is applicable to any theory of gravitation in which the path of a test particle and the light rays are geodesics of the space-time metric.


Author(s):  
David M. Wittman

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.


Author(s):  
David M. Wittman

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.


Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.


2004 ◽  
Vol 17 (1-2) ◽  
pp. 165-197 ◽  
Author(s):  
Erhard Scholz

Hermann Weyl (1885–1955) was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben (in all senses of the German word) in the general relativistic framework for the Dirac equation. He preserved the central idea of gauge as a “purely infinitesimal” aspect of (internal) symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations.


1998 ◽  
Vol 13 (16) ◽  
pp. 1253-1264 ◽  
Author(s):  
LUIS P. NEIRA CERVILLERA ◽  
ROBERTO O. AQUILANO ◽  
HECTOR VUCETICH

In this letter we present a general relativistic star with strange matter to explain in a young supernova remnant the radial millisecond oscillations. The results confirm previous conclusions.


Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 443
Author(s):  
Lorenzo Iorio

One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit kPK. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession ω˙PK. It was recently remarked that the periastron ω of PSR J0737–3039A/B may be used to measure/constrain the moment of inertia of A through the extraction of the general relativistic Lense–Thirring precession ω˙LT,A≃−0.00060∘yr−1 from the experimentally determined periastron rate ω˙obs provided that the other post-Newtonian (PN) contributions to ω˙exp can be accurately modeled. Among them, the 2PN seems to be of the same order of magnitude of ω˙LT,A. An analytical expression of the total 2PN periastron precession ω˙2PN in terms of the osculating Keplerian orbital elements, valid not only for binary pulsars, is provided, thereby elucidating the subtleties implied in correctly calculating it from k1PN+k2PN and correcting some past errors by the present author. The formula for ω˙2PN is demonstrated to be equivalent to that obtainable from k1PN+k2PN by Damour and Schäfer expressed in the Damour–Deruelle (DD) parameterization. ω˙2PN actually depends on the initial orbital phase, hidden in the DD picture, so that −0.00080∘yr−1≤ω˙2PN≤−0.00045∘yr−1. A recently released prediction of ω˙2PN for PSR J0737–3039A/B is discussed.


Author(s):  
Jin Tong Wang ◽  
Jiangdi Fan ◽  
Aaron X. Kan

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.


Sign in / Sign up

Export Citation Format

Share Document