Hermann Weyl's Analysis of the “Problem of Space” and the Origin of Gauge Structures

2004 ◽  
Vol 17 (1-2) ◽  
pp. 165-197 ◽  
Author(s):  
Erhard Scholz
Keyword(s):  
General Relativity ◽  
Dirac Equation ◽  
A Priori ◽  
Group Extension ◽  
Central Idea ◽  
German Word ◽  
General Relativistic ◽  
Empirical Turn ◽  
Relativistic Framework ◽  
Internal Symmetries

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.

scholarly journals Shear-free conditions of a Chaplygin-gas-dominated universe

2021 ◽  
pp. 2150192
Author(s):  
Amare Abebe ◽  
Mudhahir Al Ajmi ◽  
Maye Elmardi ◽  
Hemwati Nandan ◽  
Noor ul Sabah
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Chaplygin Gas ◽  
Current Investigation ◽  
Free Condition ◽  
General Relativistic ◽  
Relativistic Framework ◽  
Fluid Spacetimes

In this work, we revisit the shear-free conjecture of general relativity and study the well-known shear-free condition in the context of the Chaplygin-gas cosmology. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin-gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe in what follows, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.

The Dirac equation and spinning particles in general relativity

1981 ◽  
Vol 377 (1771) ◽  
pp. 417-424 ◽  
Keyword(s):  
General Relativity ◽  
Dirac Equation ◽  
Spinning Particles ◽  
First Order ◽  
General Relativistic

By means of a systematic first-order W.K.B. approximation, the equations of Mathisson and Papapetrou are derived from the general relativistic Dirac equation.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

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.

scholarly journals About the Use of Entropy Production for the Landau–Fermi–Dirac Equation

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
R. Alonso ◽  
V. Bagland ◽  
L. Desvillettes ◽  
B. Lods
Keyword(s):  
Dirac Equation ◽  
Classical Limit ◽  
Large Time ◽  
A Priori Estimates ◽  
Landau Equation ◽  
A Priori ◽  
Time Behaviour ◽  
Entropy Dissipation ◽  
Priori Estimates ◽  
Potential Case

AbstractIn this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

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.

All classical predictions of general relativity from special relativistic Hamiltonian dynamics

2018 ◽  
Vol 33 (29) ◽  
pp. 1850169
Author(s):  
J. H. Field
Keyword(s):  
General Relativity ◽  
Euclidean Space ◽  
Hamiltonian Dynamics ◽  
Gravitational Redshift ◽  
Newtonian Mechanics ◽  
Light Deflection ◽  
Schwarzschild Metric ◽  
Related Literature ◽  
General Relativistic ◽  
Relativistic Hamiltonian Dynamics

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.

scholarly journals CONSTRAINING THE PREFERRED-FRAME α1, α2 PARAMETERS FROM SOLAR SYSTEM PLANETARY PRECESSIONS

2014 ◽  
Vol 23 (01) ◽  
pp. 1450006 ◽  
Author(s):  
L. IORIO
Keyword(s):  
Binary System ◽  
Solar System ◽  
Relative Motion ◽  
A Priori ◽  
The Other ◽  
Preferred Frame ◽  
General Relativistic ◽  
Ppn Parameters ◽  
Invariable Plane ◽  
Analytical Expressions

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the Parametrized Post-Newtonian (PPN) parameters α1, α2. Preliminary constraints on α1, α2 are inferred from the latest determinations of the observationally admitted ranges [Formula: see text] for any anomalous Solar System planetary perihelion precessions. Other bounds existing in the literature are critically reviewed, with particular emphasis on the constraint [Formula: see text] based on an interpretation of the current close alignment of the Sun's equator with the invariable plane of the Solar System in terms of the action of a α2-induced torque throughout the entire Solar System's existence. Taken individually, the supplementary precessions [Formula: see text] of Earth and Mercury, recently determined with the INPOP10a ephemerides without modeling PFE, yield α1 = (0.8±4) × 10-6 and α2 = (4±6) × 10-6, respectively. A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a priori bias of unmodeled/mismodeled standard effects such as the general relativistic Lense–Thirring precessions and the classical rates due to the Sun's oblateness J2, allows to infer α1 = (-1 ± 6) × 10-6, α2 = (-0.9 ± 3.5) × 10-5. Such figures are obtained by assuming that the ranges of values for the anomalous perihelion precessions are entirely due to the unmodeled effects of α1 and α2. Our bounds should be improved in the near-mid future with the MESSENGER and, especially, BepiColombo spacecrafts. Nonetheless, it is worthwhile noticing that our constraints are close to those predicted for BepiColombo in two independent studies. In further dedicated planetary analyses, PFE may be explicitly modeled to estimate α1, α2 simultaneously with the other PPN parameters as well.

STRANGE MATTER STARS AND GENERAL RELATIVITY

1998 ◽  
Vol 13 (16) ◽  
pp. 1253-1264 ◽  
Author(s):  
LUIS P. NEIRA CERVILLERA ◽  
ROBERTO O. AQUILANO ◽  
HECTOR VUCETICH
Keyword(s):  
General Relativity ◽  
Supernova Remnant ◽  
Strange Matter ◽  
Relativistic Star ◽  
Young Supernova Remnant ◽  
General Relativistic

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.

scholarly journals Astronomical Units and Constants in a Relativistic Framework

1995 ◽  
Vol 10 ◽  
pp. 201-201
Author(s):  
N. Capitaine ◽  
B. Guinot
Keyword(s):  
General Relativity ◽  
Minimum Degree ◽  
Degree Of Approximation ◽  
Theoretical Background ◽  
Point Of View ◽  
Astronomical Unit ◽  
Dynamical Astronomy ◽  
Unit Of Length ◽  
Relativistic Framework ◽  
Astronomical Constants

In 1991, IAU Resolution A4 introduced General Relativity as the theoretical background for defining celestial space-time reference sytems. It is now essential that units and constants used in dynamical astronomy be defined in the same framework, at least in a manner which is compatible with the minimum degree of approximation of the metrics given in Resolution A4.This resolution states that astronomical constants and quantities should be expressed in SI units, but does not consider the use of astronomical units. We should first evaluate the usefulness of maintaining the system of astronomical units. If this system is kept, it must be defined in the spirit of Resolution A4. According to Huang T.-Y., Han C.-H., Yi Z.-H., Xu B.-X. (What is the astronomical unit of length?, to be published in Asttron. Astrophys.), the astronomical units for time and length are units for proper quantities and are therefore proper quantities. We fully concur with this point of view. Astronomical units are used to establish the system of graduation of coordinates which appear in ephemerides: the graduation units are not, properly speaking astronomical units. Astronomical constants, expressed in SI or astronomical units, are also proper quantities.

scholarly journals On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 443
Author(s):  
Lorenzo Iorio
Keyword(s):  
General Relativity ◽  
Present Author ◽  
Moment Of Inertia ◽  
The Other ◽  
Orbital Elements ◽  
Binary Pulsars ◽  
Orbital Phase ◽  
Order Of Magnitude ◽  
General Relativistic ◽  
The Moment

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.

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