Accelerated frames

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.

Minkowski spacetime

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
Three Dimensional ◽  
Minkowski Spacetime ◽  
Dimensional Euclidean Space ◽  
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.

scholarly journals Time in the Special Theory of Relativity

2011 ◽  
Author(s):  
Steven Savitt
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Inertial Frame ◽  
Special Theory ◽  
Inertial Reference Frame ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Crucial Element ◽  
Most Significant Change ◽  
Conventionality Of Simultaneity

Restricted to special relativity, this chapter observes that the most significant change in the concept of time is certainly the relativity of simultaneity. What events are simultaneous with some event for one observer are different from those that are simultaneous with respect to an object traveling in a different inertial frame. Many believe that this relativity can play a role in an argument for eternalism. This chapter critically surveys these arguments before taking on the implications of relativity for the metaphysics of time. It also tackles the conventionality of simultaneity. Many philosophers of science, especially during the early days of relativity, felt that simultaneity is not only relative but also conventional—there is a crucial element of choice in deciding what events are simultaneous for any other in a given inertial reference frame, so that there is no fact of the matter about what is simultaneous.

scholarly journals The Space-evolution Frame as Alternative to Space-time

2021 ◽  
Author(s):  
Xiaonan Du
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
World Line ◽  
Minkowski Spacetime ◽  
Line Length ◽  
Dimensional Euclidean Space ◽  
Time Space ◽  
Coordinate Rotation ◽  
Self Consistent ◽  
New Perspective

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.

scholarly journals The Space-evolution Frame as Alternative to Space-time

2021 ◽  
Author(s):  
Xiaonan Du
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
World Line ◽  
Minkowski Spacetime ◽  
Line Length ◽  
Dimensional Euclidean Space ◽  
Time Space ◽  
Coordinate Rotation ◽  
Self Consistent ◽  
New Perspective

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.

scholarly journals Moving Unstable Particles and Special Relativity

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Eugene V. Stefanovich
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Unstable Particle ◽  
Internal Variables ◽  
Dirac Theory ◽  
Decay Probability ◽  
Unstable Particles ◽  
Interacting Systems

In Poincaré-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that, just like time translations, boost transformations have a nontrivial effect on internal variables of interacting systems. In this respect, boosts are different from space translations and rotations, whose actions are always universal, trivial, and interaction-independent. Applying this theory to unstable particles viewed from a moving reference frame, we prove that the decay probability cannot be invariant with respect to boosts. Different moving observers may see different internal compositions of the same unstable particle. Unfortunately, this effect is too small to be noticeable in modern experiments.

scholarly journals Group Structure and Geometric Interpretation of the Embedded Scator Space

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1504
Author(s):  
Jan L. Cieśliński ◽  
Artur Kobus
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
Group Structure ◽  
Geometric Interpretation ◽  
Commutative Group ◽  
Original Formulation ◽  
Extended Space

The set of scators was introduced by Fernández-Guasti and Zaldívar in the context of special relativity and the deformed Lorentz metric. In this paper, the scator space of dimension 1+n (for n=2 and n=3) is interpreted as an intersection of some quadrics in the pseudo-Euclidean space of dimension 2n with zero signature. The scator product, nondistributive and rather counterintuitive in its original formulation, is represented as a natural commutative product in this extended space. What is more, the set of invertible embedded scators is a commutative group. This group is isomorphic to the group of all symmetries of the embedded scator space, i.e., isometries (in the space of dimension 2n) preserving the scator quadrics.

On the total mean curvature of a compact space-like submanifold in Lorentz–Minkowski spacetime

2017 ◽  
Vol 148 (1) ◽  
pp. 199-210 ◽  
Author(s):  
Oscar Palmas ◽  
Francisco J. Palomo ◽  
Alfonso Romero
Keyword(s):  
Euclidean Space ◽  
Compact Space ◽  
Upper Bound ◽  
Mean Curvature ◽  
Light Cone ◽  
Minkowski Spacetime ◽  
Totally Umbilical ◽  
Total Mean Curvature ◽  
Lower Estimation ◽  
Compact Submanifold

By means of several counterexamples, the impossibility to obtain an analogue of the Chen lower estimation for the total mean curvature of any compact submanifold in Euclidean space for the case of compact space-like submanifolds in Lorentz–Minkowski spacetime is shown. However, a lower estimation for the total mean curvature of a four-dimensional compact space-like submanifold that factors through the light cone of six-dimensional Lorentz–Minkowski spacetime is proved by using a technique completely different from Chen's original one. Moreover, the equality characterizes the totally umbilical four-dimensional round spheres in Lorentz–Minkowski spacetime. Finally, three applications are given. Among them, an extrinsic upper bound for the first non-trivial eigenvalue of the Laplacian of the induced metric on a four-dimensional compact space-like submanifold that factors through the light cone is proved.

Accelerated frames and galactic rotation curves

2019 ◽  
Vol 34 (27) ◽  
pp. 1950218
Author(s):  
S. C. Ulhoa ◽  
F. L. Carneiro
Keyword(s):  
Experimental Data ◽  
General Relativity ◽  
Dark Matter ◽  
Reference Frame ◽  
Rotation Curve ◽  
Reference Frames ◽  
Galactic Rotation ◽  
Inertial Reference Frame ◽  
Galactic Rotation Curve ◽  
Accelerated Frames

In this paper, the galactic rotation curve is analyzed as an effect of an accelerated reference frame. Such a rotation curve was the first evidence for the so-called dark matter. We show another possibility for this experimental data: non-inertial reference frame can fit the experimental curve. We also show that general relativity is not enough to completely explain that which encouraged alternatives paths such as the MOND approach. The accelerated reference frames hypothesis is well-suited to deal with the rotation curve of galaxies and perhaps has some role to play concerning other evidences for dark matter.

scholarly journals DOUBLE SPECIAL RELATIVITY WITH A MINIMUM SPEED AND THE UNCERTAINTY PRINCIPLE

2012 ◽  
Vol 21 (02) ◽  
pp. 1250010 ◽  
Author(s):  
CLÁUDIO NASSIF
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Uncertainty Principle ◽  
Vacuum Energy ◽  
Background Field ◽  
Uncertainty Relations ◽  
Minimum Speed ◽  
Fundamental Understanding ◽  
Low Energies ◽  
Preferred Reference Frame

The present work aims to search for an implementation of a new symmetry in the spacetime by introducing the idea of an invariant minimum speed scale (V). Such a lowest limit V, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the spacetime at the subatomic level for very low energies close to the background frame (v ≈ V), providing a fundamental understanding for the uncertainty principle, i.e. the uncertainty relations should emerge from the spacetime with an invariant minimum speed.

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