scholarly journals Derivation of generalized Einstein's equations of gravitation based on a mechanical model of vacuum and a sink flow model of particles

2018 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Flow Model ◽  
Weak Field ◽  
Coordinate Systems ◽  
Previous Theory ◽  
Metric Tensor ◽  
Riemannian Spacetime ◽  
Einstein's Equation ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincaré have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, a generalized Einstein's equation is derived based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. Thus, this theory also explains all the experiments that support the theory of general relativity. There exists some fundamental differences between this theory and Einstein's theory of general relativity.

scholarly journals Derivation of generalized Einstein's equations of gravitation based on a mechanical model of vacuum and a sink flow model of particles

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Flow Model ◽  
Weak Field ◽  
Coordinate Systems ◽  
Previous Theory ◽  
Metric Tensor ◽  
Riemannian Spacetime ◽  
Einstein's Equation ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincaré have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, a generalized Einstein's equation in inertial systems is derived based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some fundamental differences between this theory and Einstein's theory of general relativity.

scholarly journals Derivation of a Generalized Einstein's Equation of Gravitation Based on a Mechanical Model of Vacuum and a Sink Flow Model of Particles

2018 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Flow Model ◽  
Weak Field ◽  
Coordinate Systems ◽  
Previous Theory ◽  
Metric Tensor ◽  
Riemannian Spacetime ◽  
Einstein's Equation ◽  
Theory Of Gravitation ◽  
Definition Of

There exist some puzzles and difficulties related to Einstein's theory of general relativity. We generalize our previous theory of gravitation by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. A generalized Einstein's equation is derived in inertial coordinate systems based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. There exists some differences between this theory and Einstein's theory of general relativity.

Derivation of Generalized Einstein's Equations of Gravitation Based on a Mechanical Model of Vacuum and a Sink Flow Model of Particles

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Reference Frames ◽  
Flow Model ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Previous Theory ◽  
Metric Tensor ◽  
Einstein's Equations ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. In some special non-inertial reference frames, generalized Einstein's equations are derived based on some assumptions. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some differences between this theory and Einstein's theory of general relativity.

scholarly journals Derivation of Generalized Einstein's Equations of Gravitation Based on a Mechanical Model of Vacuum and a Sink Flow Model of Particles

2019 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
General Relativity ◽  
Mechanical Model ◽  
Reference Frames ◽  
Flow Model ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Previous Theory ◽  
Metric Tensor ◽  
Einstein's Equations ◽  
Definition Of

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. In some special non-inertial reference frames, generalized Einstein's equations are derived based on some assumptions. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some differences between this theory and Einstein's theory of general relativity.

scholarly journals Derivation of Generalized Einstein's Equations of Gravitation in Inertial Systems Based on a Sink Flow Model of Particles

2021 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
Reference Frames ◽  
Flow Model ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Previous Theory ◽  
Metric Tensor ◽  
Einstein's Equations ◽  
Riemannian Spacetime ◽  
Definition Of ◽  
Inertial Systems

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. There exist some differences between this theory and Einstein's theory of general relativity.

NEW CLASS OF METRIC THEORIES OF GRAVITY NOT DESCRIBED BY THE PARAMETRIZED POST-NEWTONIAN (PPN) FORMALISM

1991 ◽  
Vol 06 (30) ◽  
pp. 5511-5532 ◽  
Author(s):  
IGNAZIO CIUFOLINI
Keyword(s):  
General Relativity ◽  
A Priori ◽  
Relativistic Effects ◽  
Weak Field ◽  
Metric Tensor ◽  
New Class ◽  
Theories Of Gravity ◽  
Experimental Values ◽  
Ppn Parameters ◽  
Infinite Set

After an introduction to theories of gravity alternative to general relativity, metric theories (Sec. 1) and the parametrized post-Newtonian (PPN) formalism (Sec. 2), we define a new class of metric theories of gravity (Sec. 3). It turns out that the post-Newtonian approximation of these new theories is not described by the PPN formalism (Sec. 4); in fact, in the limit of weak field and slow motions, the post-Newtonian expression of the metric tensor contains an, a priori, infinite set of new terms and correspondingly an, a priori, infinite set of new PPN parameters. As a consequence, the parametrized post-Newtonian formulas describing the classical relativistic tests should include these new parameters, and therefore the experimental values of the classical relativistic effects should not be used to put limits only on the standard ten PPN parameters. Finally, we note that a subset of this new class of theories has the same post-Newtonian limit and value of the PPN parameters as general relativity, and therefore is automatically in agreement with the classical general-relativistic tests (Sec. 4, theory III).

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

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.

scholarly journals Clock-dependent spacetime

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sung-Sik Lee
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Gravity ◽  
Hilbert Spaces ◽  
Coordinate Systems ◽  
Physical Laws

Abstract Einstein’s theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

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