scholarly journals Affine sphere spacetimes which satisfy the relativity principle

2017 ◽  
Vol 95 (2) ◽  
Author(s):  
E. Minguzzi
Keyword(s):  
Affine Sphere ◽  
Relativity Principle

scholarly journals Relative locality: a deepening of the relativity principle

2011 ◽  
Vol 43 (10) ◽  
pp. 2547-2553 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Laurent Freidel ◽  
Jerzy Kowalski-Glikman ◽  
Lee Smolin
Keyword(s):  
Relativity Principle

scholarly journals Characterization of affine ruled surfaces

1997 ◽  
Vol 39 (1) ◽  
pp. 17-20 ◽  
Author(s):  
Włodzimierz Jelonek
Keyword(s):  
Shape Operator ◽  
Ruled Surfaces ◽  
Affine Sphere ◽  
Affine Surface ◽  
Codazzi Tensor ◽  
Difference Tensor ◽  
The Difference ◽  
In The Beginning ◽  
Affine Metric

The aim of this paper is to give certain conditions characterizing ruled affine surfaces in terms of the Blaschke structure (∇, h, S) induced on a surface (M, f) in ℝ3. The investigation of affine ruled surfaces was started by W. Blaschke in the beginning of our century (see [1]). The description of affine ruled surfaces can be also found in the book [11], [3] and [7]. Ruled extremal surfaces are described in [9]. We show in the present paper that a shape operator S is a Codazzi tensor with respect to the Levi-Civita connection ∇ of affine metric h if and only if (M, f) is an affine sphere or a ruled surface. Affine surfaces with ∇S = 0 are described in [2] (see also [4]). We also show that a surface which is not an affine sphere is ruled iff im(S - HI) =ker(S - HI) and ket(S - HI) ⊂ ker dH. Finally we prove that an affine surface with indefinite affine metric is a ruled affine sphere if and only if the difference tensor K is a Codazzi tensor with respect to ∇.

The General Theory of Relativity

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
General Theory ◽  
Reference Frames ◽  
Mathematical Formulation ◽  
Rotating Disk ◽  
Theory Of Relativity ◽  
Relativity Principle ◽  
Non Euclidean Geometry ◽  
Physical Laws

This chapter shows how Einstein has developed and described the mathematical apparatus that is necessary to formulate the physical contents of the general theory of gravity. It first discusses the transition from the special to the general relativity principle. According to Einstein's understanding of such a general relativity principle, physical laws are independent of the state of motion of the reference space in which they are described. The chapter argues that such a generalization of the relativity principle to include accelerated reference frames is possible because all inertial effects caused by acceleration can be alternatively attributed to the presence of a gravitational field. The model of a rotating disk is then used to show that general relativity implies non-Euclidean geometry and that the gravitational field is represented by curved spacetime. After the introduction of these basic concepts and principles, the chapter presents the mathematical formulation of the theory.

The Relativity Principle

2019 ◽  
pp. 23-35
Author(s):  
Helmut Günther ◽  
Volker Müller
Keyword(s):  
Relativity Principle

Timekeeping evidence refutes the relativity principle

2016 ◽  
Vol 29 (1) ◽  
pp. 62-64 ◽  
Author(s):  
Thomas E. Phipps
Keyword(s):  
Relativity Principle

Time dilation in the GPS invalidates the relativity principle

2020 ◽  
Vol 33 (3) ◽  
pp. 302-305 ◽  
Author(s):  
Stephan J. G. Gift
Keyword(s):  
Special Relativity ◽  
Global Positioning System ◽  
Time Dilation ◽  
Positioning System ◽  
Relativity Principle ◽  
Preferred Frame ◽  
Global Positioning

Asymmetrical time dilation in the Global Positioning System (GPS) invalidates the relativity principle of special relativity since it confirms the existence of a preferred frame that is prohibited by the principle. It also contradicts symmetrical time dilation predicted by special relativity.

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