scholarly journals How to Be a Relativistic Spacetime State Realist

2020 ◽  
Vol 71 (3) ◽  
pp. 933-957 ◽  
Author(s):  
Noel Swanson
Keyword(s):  
Relativistic Spacetime

An axiomatic foundation of relativistic spacetime

Synthese ◽  
2013 ◽  
Vol 192 (7) ◽  
pp. 2009-2024
Author(s):  
Thomas Benda
Keyword(s):  
Axiomatic Foundation ◽  
Relativistic Spacetime

scholarly journals Relativistic spacetime crystals

2021 ◽  
Vol 77 (4) ◽  
Author(s):  
Venkatraman Gopalan
Keyword(s):  
Point Group ◽  
Minkowski Spacetime ◽  
The Other ◽  
Physical Sciences ◽  
Space Groups ◽  
Flat Spacetime ◽  
Inertial Frames ◽  
Relativistic Spacetime ◽  
Lorentz Boosts ◽  
Periodic Space

Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other hand need to account for the mixing of space and time in special relativity through Lorentz transformation, and have been listed only in 2D. This work shows that there exists a transformation between the conventional Minkowski spacetime (MS) and what is referred to here as renormalized blended spacetime (RBS); they are shown to be equivalent descriptions of relativistic physics in flat spacetime. There are two elements to this reformulation of MS, namely, blending and renormalization. When observers in two inertial frames adopt each other's clocks as their own, while retaining their original space coordinates, the observers become blended. This process reformulates the Lorentz boosts into Euclidean rotations while retaining the original spacetime hyperbola describing worldlines of constant spacetime length from the origin. By renormalizing the blended coordinates with an appropriate factor that is a function of the relative velocities between the various frames, the hyperbola is transformed into a Euclidean circle. With these two steps, one obtains the RBS coordinates complete with new light lines, but now with a Euclidean construction. One can now enumerate the RBS point and space groups in various dimensions with their mapping to the well known space crystal groups. The RBS point group for flat isotropic RBS spacetime is identified to be that of cylinders in various dimensions: mm2 which is that of a rectangle in 2D, (∞/ m ) m which is that of a cylinder in 3D, and that of a hypercylinder in 4D. An antisymmetry operation is introduced that can swap between space-like and time-like directions, leading to color spacetime groups. The formalism reveals RBS symmetries that are not readily apparent in the conventional MS formulation. Mathematica script is provided for plotting the MS and RBS geometries discussed in the work.

Tearing Spacetime Asunder

2017 ◽  
Author(s):  
Craig Callender
Keyword(s):  
Time And Space ◽  
Space And Time ◽  
Relativistic Spacetime

The physicist Hermann Minkowski famously claimed that relativity implies that space and time are doomed to fade away into mere shadows. It therefore may come as a surprise that relativistic spacetime is often decomposed into “time” and “space” in so-called “3 + 1” formulations of relativity. How should we regard these times? Are they hospitable to manifest time? This chapter adopts the perspective that relativity is still a “live” theory under development, so a distinguished time could emerge. However, such a time is unlikely to live up to what we want in manifest time.

scholarly journals Conformal Invariance of the Newtonian Weyl Tensor

2020 ◽  
Vol 50 (11) ◽  
pp. 1418-1425
Author(s):  
Neil Dewar ◽  
James Read
Keyword(s):  
Conformal Invariance ◽  
Weyl Tensor ◽  
Conformal Structure ◽  
Analogous Structure ◽  
Relativistic Spacetime

AbstractIt is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.

scholarly journals Unifying the Galilei Relativity and the Special Relativity

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Alexandre Lyra ◽  
Marcelo Carvalho
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
Lorentz Transformation ◽  
Dimensional Euclidean Space ◽  
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.

scholarly journals The Arithmetic of Uncertainty unifies Quantum Formalism and Relativistic Spacetime

2020 ◽  
Author(s):  
John Skilling ◽  
Kevin Knuth
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Three Dimensions ◽  
One Dimension ◽  
Lorentz Transformations ◽  
Mathematical Structures ◽  
Modern Physics ◽  
Relativistic Spacetime ◽  
The Universe ◽  
Dimensions Of Space

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary ``combining and sequencing'' symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies observation of quantity and imposes the use of pairs of numbers. The symmetries then lead directly to the use of complex \sqrt{-1} arithmetic, the standard calculus of quantum mechanics, and the Lorentz transformations of relativistic spacetime. One dimension of time and three dimensions of space are thus derived as the profound and inevitable framework of physics.

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