scholarly journals How Does Spacetime “Tell an Electron How to Move”?

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2283
Author(s):  
Garnet Ord
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Continuum Limit ◽  
Minkowski Spacetime ◽  
Discrete Space ◽  
Kinematics And Dynamics ◽  
Uniform Motion ◽  
Classical Particles

Minkowski spacetime provides a background framework for the kinematics and dynamics of classical particles. How the framework implements the motion of matter is not specified within special relativity. In this paper we specify how Minkowski space can implement motion in such a way that ’quantum’ propagation occurs on appropriate scales. This is done by starting in a discrete space and explicitly taking a continuum limit. The argument is direct and illuminates the special tension between ’rest’ and ’uniform motion’ found in Minkowski space, showing how the formal analytic continuations involved in Minkowski space and quantum propagation arise from the same source.

scholarly journals FROM QUANTUM DEFORMATIONS OF RELATIVISTIC SYMMETRIES TO MODIFIED KINEMATICS AND DYNAMICS

2011 ◽  
Vol 20 (10) ◽  
pp. 1961-1967 ◽  
Author(s):  
JERZY LUKIERSKI
Keyword(s):  
Field Theory ◽  
Special Relativity ◽  
Minkowski Space ◽  
Star Product ◽  
Einstein Gravity ◽  
Kinematics And Dynamics ◽  
Noncommutative Field Theory ◽  
Quantum Deformations ◽  
Theory Framework

Starting from noncommutative generalization of Minkowski space we consider quantum deformed relativistic symmetries which lead to the modification of kinematics of special relativity. The noncommutative field theory framework described by means of the star product formalism is briefly described. We briefly present the quantum modifications of Einstein gravity.

RELATIVITY AND THE SPEED OF LIGHT – A 100 YEAR OLD MISUNDERSTANDING

2006 ◽  
Vol 15 (02) ◽  
pp. 275-283 ◽  
Author(s):  
W. J. ŚWIATECKI
Keyword(s):  
Quantum Mechanics ◽  
Special Relativity ◽  
Thought Experiment ◽  
Minkowski Spacetime ◽  
Speed Of Light ◽  
The Past ◽  
Mistaken Belief

I point out a conceptual misunderstanding in the exposition of relativity, namely the mistaken belief that light has something to do with the essence of relativity. This misunderstanding can be clarified by stressing that the content of Special Relativity is simply that "we live in a Minkowski spacetime", together with a thought experiment that illustrates how one could discover this fact without ever mentioning even the existence of light. I also note a recently uncovered implication of living in Minkowski spacetime, namely the Copenhagen reinterpretation of Quantum Mechanics, developed in the past decade.

scholarly journals DOUBLY SPECIAL RELATIVITY VERSUS κ-DEFORMATION OF RELATIVISTIC KINEMATICS

2003 ◽  
Vol 18 (01) ◽  
pp. 7-18 ◽  
Author(s):  
JERZY LUKIERSKI ◽  
ANATOL NOWICKI
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Noncommutative Space ◽  
Relativistic Kinematics ◽  
Large Classes ◽  
Doubly Special Relativity ◽  
Deformed Minkowski Space ◽  
Composition Law ◽  
Poincaré Algebra ◽  
The One

We argue that the so-called doubly special relativity (DSR), recently proposed by Amelino-Camelia et al.1,2 with deformed boost transformations identical with the formulae for κ-deformed kinematics in bicrossproduct basis is classical special relativity in nonlinear disguise. The choice of symmetric composition law for deformed four-momenta as advocated in Refs. 1 and 2 implies that DSR is obtained by considering the nonlinear four-momenta basis of classical Poincaré algebra and it does not lead to noncommutative space–time. We also show how to construct two large classes of doubly special relativity theories — generalizing the choice in Refs. 1 and 2 and the one presented by Magueijo and Smolin.3 The older version of deformed relativistic kinematics, differing essentially from classical theory in the coalgebra sector and leading to noncommutative κ-deformed Minkowski space is provided by quantum κ-deformation of Poincaré symmetries.

scholarly journals How to be a realist about Minkowski spacetime without believing in magical explanations

2020 ◽  
Vol 35 (2) ◽  
pp. 175
Author(s):  
Adan Sus
Keyword(s):  
Special Relativity ◽  
Physical Theory ◽  
Minkowski Spacetime ◽  
General Assumption ◽  
Recent Discussion ◽  
Spacetime Structure ◽  
The Status ◽  
Ontological Dimension

The question about the relation between spacetime structure and the symmetries of laws has received renewed attention in a recent discussion about the status of Minkowski spacetime in Special Relativity. In that context we find two extreme positions (either spacetime explains symmetries of laws or vice-versa) and a general assumption about the debate being mainly about explanation. The aim of this paper is twofold: first, to argue that the ontological dimension of the debate cannot be ignored; second, to claim that taking ontology into account involves considering a third perspective on the relation between spacetime and symmetries of laws; one in which both terms would be somehow derived from common assumptions on the formulation of a given physical theory.

scholarly journals Affine Symmetry Tensors in Minkowski Space

2016 ◽  
Vol 13 (3) ◽  
Author(s):  
Isaac Ahern ◽  
Sam Cook
Keyword(s):  
Minkowski Space ◽  
Computational Algorithm ◽  
Minkowski Spacetime ◽  
Lie Derivative ◽  
Killing Tensor ◽  
Spacetime Dimension ◽  
Killing Vectors ◽  
Killing Tensors ◽  
Affine Symmetry

Killing vectors are generators of symmetries in a spacetime. This article defines certain generalizations of Killing vectors, called affine symmetry tensors, or simply affine tensors. While the affine vectors of the Minkowski spacetime are well known, and partial results for valence n = 2 have been discussed, affine tensors of valence n > 2 have never been exhibited. In this article, we discuss a computational algorithm to compute affine tensors in Minkowski spacetime, and discuss the results for affine tensors of valence 2 ≤ n ≤ 7. After comparison with analogous results concerning Killing tensors, we make several conjectures about the spaces of affine tensors in Minkowski spacetime. KEYWORDS: Affine Symmetry Tensors; Affine Vectors; Killing Tensors; Killing Vectors; Minkowski Spacetime; Dimension; Maple CAS; Lie Derivative; Generalized Killing Tensor

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.

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