The Space-evolution Frame as Alternative to Space-time

Time Space ◽

Coordinate Rotation ◽

Self Consistent ◽

Abstract As a alternative to Minkowski spacetime frame, this paper propose a four dimensional Euclidean space that combine three spacial dimension with evolution instead of time. It is called space-evolution, in which time is considered as world line length and is absolute. The space-evolution frame provide a new perspective for understanding of time, space and special relativity. It is self-consistent without losing compatibility to special relativity, the Lorentz transform and its predictions could be derived geometrically by simple coordinate rotation.

The Space-evolution Frame as Alternative to Space-time

10.21203/rs.3.rs-528264/v2 ◽

2021 ◽

Author(s):

Xiaonan Du

Keyword(s):

Euclidean Space ◽

Special Relativity ◽

World Line ◽

Minkowski Spacetime ◽

Line Length ◽

Time Space ◽

Coordinate Rotation ◽

Self Consistent ◽

Abstract As a alternative to Minkowski spacetime frame, this paper propose a four dimensional Euclidean space that combine three spacial dimension with evolution instead of time. It is called space-evolution, in which time is considered as world line length and is absolute. The space-evolution frame provide a new perspective for understanding of time, space and special relativity. The new frame is self-consistent without losing compatibility to special relativity, the Lorentz transform and its predictions could be derived geometrically by simple coordinate rotation.

The Space-evolution Frame as Alternative to Space-time

10.21203/rs.3.rs-528264/v3 ◽

2021 ◽

Author(s):

Xiaonan Du

Keyword(s):

Special Relativity ◽

Proper Time ◽

World Line ◽

Minkowski Spacetime ◽

Spatial Dimension ◽

Line Length ◽

Absolute Space ◽

Time Space ◽

Abstract As an alternative to Minkowski spacetime frame, this paper propose a four-dimensional Euclidean space that combines three spatial dimension with proper time instead of time. We call it space-evolution, in which proper time is interpreted as evolutionary position, time is considered as world line length and is absolute. Space-evolution frame provide a new perspective for our understanding of time, space and special relativity. The new frame is self-consistent without losing compatibility to special relativity, the Lorentz transform and its predictions could be derived geometrically by simple coordinate rotation

The Space-Evolution Frame as an Alternative to Space-Time

10.21203/rs.3.rs-528264/v4 ◽

2021 ◽

Author(s):

Xiaonan Du

Keyword(s):

Proper Time ◽

World Line ◽

Time Frame ◽

Line Length ◽

Space Time ◽

Time Space ◽

Minkowski Space Time ◽

Spatial Dimensions ◽

Abstract As an alternative to the Minkowski space-time frame, this paper proposes a four-dimensional Euclidean space that combines three spatial dimensions with proper time instead of time. We call this space evolution, in which proper time is interpreted as an evolutionary position and time is considered world line length and absolute. The space-evolution frame provides a new perspective for our understanding of time, space and special relativity. The new frame is self-consistent and compatible to spacial relativity, the Lorentz transform and its predictions could be derived geometrically by simple coordinate rotation.

Minkowski spacetime

10.1093/oso/9780198786399.003.0019 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Euclidean Space ◽

Special Relativity ◽

Three Dimensional ◽

Minkowski Spacetime ◽

Fourth Dimension ◽

Relativistic Dynamics ◽

Newtonian Theory ◽

Space And Time ◽

Set Of Points

This chapter presents the main features of the Minkowski spacetime, which is the geometrical framework in which the laws of relativistic dynamics are formulated. It is a very simple mathematical extension of three-dimensional Euclidean space. In special relativity, ‘relative, apparent, and common’ (in the words of Newton) space and time are represented by a mathematical set of points called events, which constitute the Minkowski spacetime. This chapter also stresses the interpretation of the fourth dimension, which in special relativity is time. Here, time now loses the ‘universal’ and ‘absolute’ nature that it had in the Newtonian theory.

Accelerated frames

10.1093/oso/9780198786399.003.0023 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Euclidean Space ◽

Special Relativity ◽

Reference Frame ◽

Inertial Frame ◽

Physical Space ◽

Minkowski Spacetime ◽

Curvilinear Coordinates ◽

Accelerated Frames

This chapter shows how, within the framework of special relativity, Newtonian inertial accelerations turn into mere geometrical quantities. In addition, the chapter states that labeling the points of Minkowski spacetime using curvilinear coordinates rather than Minkowski coordinates is mathematically just as simple as in Euclidean space. However, the interpretation of such a change of coordinates as passage from an inertial frame to an accelerated frame is more subtle. Hence, the chapter studies some examples of this phenomenon. Finally, it addresses the problem of understanding what the curvilinear coordinates actually represent. Or, similarly, it considers the question of how to realize them by a reference frame in actual, ‘relative, apparent, and common’ physical space.

Unifying the Galilei Relativity and the Special Relativity

ISRN Mathematical Physics ◽

10.1155/2013/156857 ◽

2013 ◽

Vol 2013 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Alexandre Lyra ◽

Marcelo Carvalho

Keyword(s):

Euclidean Space ◽

Special Relativity ◽

Lorentz Transformation ◽

Low Velocity ◽

3 Dimensional ◽

Absolute Time ◽

Starting Point ◽

Relativistic Spacetime ◽

The Absolute

We present two models combining some aspects of the Galilei and the Special relativities that lead to a unification of both relativities. This unification is founded on a reinterpretation of the absolute time of the Galilei relativity that is considered as a quantity in its own and not as mere reinterpretation of the time of the Special relativity in the limit of low velocity. In the first model, the Galilei relativity plays a prominent role in the sense that the basic kinematical laws of Special relativity, for example, the Lorentz transformation and the velocity law, follow from the corresponding Galilei transformations for the position and velocity. This first model also provides a new way of conceiving the nature of relativistic spacetime where the Lorentz transformation is induced by the Galilei transformation through an embedding of 3-dimensional Euclidean space into hyperplanes of 4-dimensional Euclidean space. This idea provides the starting point for the development of a second model that leads to a generalization of the Lorentz transformation, which includes, as particular cases, the standard Lorentz transformation and transformations that apply to the case of superluminal frames.

The Emergence and Formation of the Theory of Optimal Set Partitioning for Sets of the n Dimensional Euclidean Space. Theory and Application

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v50.i9.10 ◽

2018 ◽

Vol 50 (9) ◽

pp. 1-24 ◽

Cited By ~ 4

Author(s):

Elena M. Kiseleva

Keyword(s):

Euclidean Space ◽

Set Partitioning ◽

Space Theory ◽

Optimal Set

On Vitali's Theorem for Groups of Motions of Euclidean Space

Georgian Mathematical Journal ◽

10.1515/gmj.1999.323 ◽

1999 ◽

Vol 6 (4) ◽

pp. 323-334

Author(s):

A. Kharazishvili

Keyword(s):

Euclidean Space ◽

Finite Dimensional

Abstract We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [Sul problema della misura dei gruppi di punti di una retta, 1905] holds true. This characterization is formulated in purely geometrical terms.

Some properties of Wigner coefficients and hyperspherical harmonics

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410003142x ◽

1956 ◽

Vol 52 (3) ◽

pp. 424-430 ◽

Cited By ~ 25

Author(s):

A. P. Stone

Keyword(s):

Angular Momentum ◽

Euclidean Space ◽

Rotation Group ◽

Hyperspherical Harmonics ◽

Shift Operators ◽

Analytical Relations

ABSTRACTGeneral shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

On inequalities of the Tchebychev type

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100002085 ◽

1963 ◽

Vol 59 (1) ◽

pp. 135-146 ◽

Cited By ~ 11

Author(s):

J. F. C. Kingman

Keyword(s):

Probability Theory ◽

Euclidean Space ◽

Random Variable ◽

Real Random Variable ◽

Finite Dimensional

1. A type of problem which frequently occurs in probability theory and statistics can be formulated in the following way. We are given real-valued functions f(x), gi(x) (i = 1, 2, …, k) on a space (typically finite-dimensional Euclidean space). Then the problem is to set bounds for Ef(X), where X is a random variable taking values in , about which all we know is the values of Egi(X). For example, we might wish to set bounds for P(X > a), where X is a real random variable with some of its moments given.