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.

Inertia and inertial resistance in the Special Theory of Relativity

2021 ◽  
pp. 1-4
Author(s):  
Peter J. Riggs
Keyword(s):  
Special Relativity ◽  
Minkowski Spacetime ◽  
Special Theory ◽  
Classical Dynamics ◽  
Relativistic Motion ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Particle Inertia ◽  
Spacetime Structure

A broader concept of “resistance to acceleration” than used in classical dynamics, called “inertial resistance”, is quantified for both inertial and non-inertial relativistic motion. Special Relativity shows that inertial resistance is more than particle inertia and originates from Minkowski spacetime structure. Current mainstream explanations of inertia do not take inertial resistance into account and are, therefore, incomplete.

Taking Up Superspace

2021 ◽  
pp. 103-128
Author(s):  
Tushar Menon
Keyword(s):  
Field Theory ◽  
Special Relativity ◽  
Minkowski Spacetime ◽  
Field Theories ◽  
Spacetime Symmetries ◽  
Spacetime Structure ◽  
Standard Set ◽  
Supersymmetric Theories

Supersymmetry (SUSY) is a proposed symmetry between bosons and fermions. The structure of the space of SUSY generators is such that the distinction between internal and spacetime symmetries is blurred. As a result, there are two viable candidates for the spacetime setting for a flat supersymmetric field theory—Minkowski spacetime and superspace, an extension of Minkowski spacetime to include (at least) four new dimensions, coordinatized by ‘supernumbers’, i.e. numbers with nontrivial commutation properties. This chapter argues for two theses: first, that one standard set of arguments, related to universality of symmetry behaviour, that motivate a particular choice of spacetime structure in familiar spacetime theories motivates the choice of superspace as the appropriate spacetime for SUSY field theories; and second, that the metaphysical utility of the concept of spacetime requires more than just the satisfaction of this universality condition; in supersymmetric theories, the spacetime concept is not as useful as in special relativity.

Physics, Structure, and Reality

2021 ◽  
Author(s):  
Jill North
Keyword(s):  
Scientific Realism ◽  
Physical Theory ◽  
Scientific Explanation ◽  
Classical Mechanics ◽  
Careful Attention ◽  
Coordinate Systems ◽  
Spacetime Structure ◽  
The World ◽  
Background Assumption ◽  
And Mathematics

How do we figure out the nature of the world from a mathematically formulated physical theory? What do we infer about the world when a physical theory can be mathematically formulated in different ways? Physics, Structure, and Reality addresses these questions, questions that get to the heart of the project of interpreting physics—of figuring out what physics is telling us about the world. North argues that there is a certain notion of structure, implicit in physics and mathematics, that we should pay careful attention to, and that doing so sheds light on these questions concerning what physics is telling us about the nature of reality. Along the way, lessons are drawn for related topics such as the use of coordinate systems in physics, the differences among various formulations of classical mechanics, the nature of spacetime structure, the equivalence of physical theories, and the importance of scientific explanation. Although the book does not explicitly defend scientific realism, instead taking this to be a background assumption, the account provides an indirect case for realism toward our best theories of physics.

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 RELATIVITY GROUPOID INSTEAD OF RELATIVITY GROUP

2007 ◽  
Vol 04 (05) ◽  
pp. 739-749 ◽  
Author(s):  
ZBIGNIEW OZIEWICZ
Keyword(s):  
Velocity Field ◽  
Clifford Algebra ◽  
Special Relativity ◽  
Operator Algebra ◽  
Relative Velocity ◽  
Physical Theory ◽  
Loop Structure ◽  
Lorentz Covariance ◽  
Frobenius Operator ◽  
Nilpotent Endomorphism

In 1908, Minkowski [13] used space-like binary velocity-field of a medium, relative to an observer. In 1974, Hestenes introduced, within a Clifford algebra, an axiomatic binary relative velocity as a Minkowski bivector [7, 8]. We propose to consider binary relative velocity as a traceless nilpotent endomorphism in an operator algebra. Any concept of a binary axiomatic relative velocity made possible the replacement of the Lorentz relativity group by the relativity groupoid. The relativity groupoid is a category of massive bodies in mutual relative motions, where a binary relative velocity is interpreted as a categorical morphism with the associative addition. This associative addition is to be contrasted with non-associative addition of (ternary) relative velocities in isometric special relativity (loop structure). We consider an algebra of many time-plus-space splits, as an operator algebra generated by idempotents. The kinematics of relativity groupoid is ruled by associative Frobenius operator algebra, whereas the dynamics of categorical relativity needs the non-associative Frölicher–Richardson operator algebra. The Lorentz covariance is the cornerstone of physical theory. Observer-dependence within relativity groupoid, and the Lorentz-covariance within the Lorentz relativity group, are different concepts. Laws of Physics could be observer-free, rather than Lorentz-invariant.

scholarly journals What do light clocks say to us regarding the so-called clock hypothesis?

2018 ◽  
Vol 33 (3) ◽  
pp. 435
Author(s):  
Mario Bacelar Valente
Keyword(s):  
Special Relativity ◽  
Physical System ◽  
Proper Time ◽  
Arbitrary Degree ◽  
The Status ◽  
Time Reading ◽  
Clock Hypothesis

The clock hypothesis is taken to be an assumption independent of special relativity necessary to describe accelerated clocks. This enables to equate the time read off by a clock to the proper time. Here, it is considered a physical system–the light clock–proposed by Marzke and Wheeler. Recently, Fletcher proved a theorem that shows that a sufficiently small light clock has a time reading that approximates to an arbitrary degree the proper time. The clock hypothesis is not necessary to arrive at this result. Here, one explores the consequences of this regarding the status of the clock hypothesis.

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.

The Limits of Historical Explanations

Philosophy ◽  
1966 ◽  
Vol 41 (157) ◽  
pp. 199-215 ◽  
Author(s):  
Quentin Skinner
Keyword(s):  
Recent Trend ◽  
Recent Discussion ◽  
The Past ◽  
The Status

Although the literature on the logic of historical enquiry is already vast and still growing, it continues to polarise overwhelmingly around a single disputed point—whether historical explanations have their own logic, or whether every successful explanation must conform to the same deductive model. Recent discussion, moreover, has shown an increasing element of agreement—there has been a marked trend away from accepting any strictly positivist view of the matter. It will be argued here that both the traditional polarity and the recent trend in this debate have tended to be misleading. The positiviste (it will be conceded) have been damagingly criticised. But their opponents (it will be suggested) have produced no satisfying alternative. They have tended instead to accept as proper historical explanations whatever has been offered by the historians themselves in the course of trying to explain the past. But a further type of analysis must be required (and will be attempted here) if some account is to be given of the status, and not merely the function, of the language in which these explanations are offered. Such an analysis, moreover (it will finally be suggested) has implications of some importance in considering the appropriate strategy for historical enquiries.

scholarly journals CONFORMAL STRUCTURES AND TWISTORS IN THE PARAVECTOR MODEL OF SPACETIME

2007 ◽  
Vol 04 (04) ◽  
pp. 547-576 ◽  
Author(s):  
R. DA ROCHA ◽  
J. VAZ
Keyword(s):  
Clifford Algebra ◽  
Clifford Algebras ◽  
Isometry Group ◽  
Twistor Space ◽  
Minkowski Spacetime ◽  
Adjoint Representation ◽  
Inner Product ◽  
Spacetime Dimension ◽  
Conformal Maps ◽  
Spacetime Structure

Some properties of the Clifford algebras [Formula: see text] and [Formula: see text] are presented, and three isomorphisms between the Dirac–Clifford algebra [Formula: see text] and [Formula: see text] are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU(2,2) and the group $pin+(2,4) is also investigated, in the light of a suitable isomorphism between [Formula: see text] and [Formula: see text]. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $pin+(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian ℝ4,1 spacetime. We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac–Clifford algebra [Formula: see text] using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over ℝ4,1 is also used to describe conformal maps, instead of ℝ2,4. Our formalism sheds some new light on the use of the paravector model and generalizations.

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