Dynamics of proper time in the theory of gravitation and conformal unification of interactions

Astrophysics ◽  
1999 ◽  
Vol 42 (1) ◽  
pp. 101-113
Author(s):  
M. Pavlovski ◽  
V. V. Papoyan ◽  
V. N. Pervushin ◽  
V. I. Smirichinskii
Keyword(s):  
Proper Time ◽  
Theory Of Gravitation ◽  
Unification Of Interactions

scholarly journals MATHEMATICAL EXPANSION OF SPECIAL THEORY OF RELATIVITY ONTO ACCELERATIONS

2021 ◽  
Vol 4 (1) ◽  
pp. 69-89
Author(s):  
Jakub Czajko
Keyword(s):  
Proper Time ◽  
Special Theory ◽  
Lorentz Factor ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Accelerator Pedal ◽  
Earth Gravity ◽  
Time Differential ◽  
Theory Of Gravitation

The special theory of relativity (STR) is operationally expanded onto orthogonal accelerations: normal  and binormal  that complement the instantaneous tangential speed  and thus can be structurally extended into operationally complete 4D spacetime without defying the STR. Thus the former classic Lorentz factor, which defines proper time differential  can be expanded onto  within a trihedron moving in the Frenet frame (T,N,B). Since the tangential speed  which was formerly assumed as being always constant, expands onto effective normal and binormal speeds ensuing from the normal and binormal accelerations, the expanded formula conforms to the former Lorentz factor. The obvious though previously overlooked fact that in order to change an initial speed one must apply accelerations (or decelerations, which are reverse accelerations), made the Einstein’s STR incomplete for it did not apply to nongravitational selfpropelled motion. Like a toy car lacking accelerator pedal, the STR could drive nowhere. Yet some scientists were teaching for over 115 years that the incomplete STR is just fine by pretending that gravity should take care of the absent accelerator. But gravity could not drive cars along even surface of earth. Gravity could only pull the car down along with the physics that peddled the nonsense while suppressing attempts at its rectification. The expanded formula neither defies the STR nor the general theory of relativity (GTR) which is just radial theory of gravitation. In fact, the expanded formula complements the STR and thus it supplements the GTR too. The famous Hafele-Keating experiments virtually confirmed the validity of the expanded formula proposed here.

scholarly journals Weyl geometry and gauge-invariant gravitation

2014 ◽  
Vol 23 (11) ◽  
pp. 1450091 ◽  
Author(s):  
F. P. Poulis ◽  
J. M. Salim
Keyword(s):  
General Relativity ◽  
Gauge Symmetry ◽  
Proper Time ◽  
Gauge Invariant ◽  
Weyl Geometry ◽  
Test Particles ◽  
Constant Solution ◽  
Intimate Relation ◽  
Theory Of Gravitation ◽  
Particles Trajectories

In this paper, we provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Spacetimes. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with spacetime description. As a consequence of this relation and the theory's gauge symmetry we recover all predictions of general relativity. This feature is made even clearer by a new exact solution we provide which reveals the importance of a well defined proper-time. The thermodynamical description of the source fields is given and we observe that each of the geometric fields have a certain physical significance, despite the gauge-invariance. This is shown by two examples, where one of them consists of a new cosmological constant solution. Our conclusions highlight the intimate relation among test particles trajectories, proper-time and spacetime description which can also be applied in any other situation, whether or not it recovers general relativity results and also in the absence of a gauge symmetry.

On the degree of sharpness in solutions of Einstein’s field equations

1971 ◽  
Vol 321 (1546) ◽  
pp. 397-408 ◽  
Keyword(s):  
Proper Time ◽  
Empty Space ◽  
Relative Importance ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Wave Space ◽  
Theory Of Gravitation ◽  
Huygens Principle ◽  
Weak Fields

Einstein’s theory of gravitation predicts that small changes in the gravitational field will propagate both sharply along the light cone and diffusively through its interior. In this paper the relative importance of sharp and diffusive propagation is linked to an invariant which arises in Sciama, Waylen & Gilman’s integral formulation of Einstein’s field equations. The invariant can be evaluated as an expansion in proper time, and the leading terms used to estimate the extent of diffusion. It is shown that, on a general empty space-time, the onset of diffusion is governed by a scalar related to the Bel-Robinson tensor. For some weak fields and all null fields this scalar may be equated to the covariant d’Alembertian of a gravitational density. On flat and plane wave space-times this quantity vanishes and the field equations satisfy a Huygens principle.

Proper-time gauge in the quantum theory of gravitation

1983 ◽  
Vol 28 (2) ◽  
pp. 297-309 ◽  
Author(s):  
Claudio Teitelboim
Keyword(s):  
Quantum Theory ◽  
Proper Time ◽  
Quantum Theory Of Gravitation ◽  
Theory Of Gravitation

Clinical Update: Assessing Maximum Medical Improvement in Carpal Tunnel Syndrome

2003 ◽  
Vol 8 (4) ◽  
pp. 4-5
Author(s):  
Christopher R. Brigham ◽  
James B. Talmage
Keyword(s):  
Carpal Tunnel Syndrome ◽  
Carpal Tunnel ◽  
Proper Time ◽  
Carpal Tunnel Release ◽  
Hand Function ◽  
Factors Affecting ◽  
Early Results ◽  
Medical Evaluation ◽  
Nerve Recovery ◽  
Tunnel Syndrome

Abstract Permanent impairment cannot be assessed until the patient is at maximum medical improvement (MMI), but the proper time to test following carpal tunnel release often is not clear. The AMA Guides to the Evaluation of Permanent Impairment (AMA Guides) states: “Factors affecting nerve recovery in compression lesions include nerve fiber pathology, level of injury, duration of injury, and status of end organs,” but age is not prognostic. The AMA Guides clarifies: “High axonotmesis lesions may take 1 to 2 years for maximum recovery, whereas even lesions at the wrist may take 6 to 9 months for maximal recovery of nerve function.” The authors review 3 studies that followed patients’ long-term recovery of hand function after open carpal tunnel release surgery and found that estimates of MMI ranged from 25 weeks to 24 months (for “significant improvement”) to 18 to 24 months. The authors suggest that if the early results of surgery suggest a patient's improvement in the activities of daily living (ADL) and an examination shows few or no symptoms, the result can be assessed early. If major symptoms and ADL problems persist, the examiner should wait at least 6 to 12 months, until symptoms appear to stop improving. A patient with carpal tunnel syndrome who declines a release can be rated for impairment, and, as appropriate, the physician may wish to make a written note of this in the medical evaluation report.

The researches of A. A. Fridman on the Einstein theory of gravitation

1963 ◽  
Vol 80 (7) ◽  
pp. 353-356 ◽  
Author(s):  
V.A. Fok
Keyword(s):  
Einstein Theory ◽  
Theory Of Gravitation

: The Proper Time . Tom Laughlin, Business Administration Co..

1960 ◽  
Vol 13 (3) ◽  
pp. 54-55
Author(s):  
Joseph Kostolefsky
Keyword(s):  
Proper Time ◽  
Business Administration

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

Spacetime Geometry

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Coordinate System ◽  
Special Relativity ◽  
Displacement Vector ◽  
Proper Time ◽  
Plane Geometry ◽  
Spatial Displacement ◽  
Spacetime Geometry ◽  
Space And Time ◽  
Displacement Vectors

This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.

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