Space-Time Structures in Classical Mechanics

1967 ◽  
pp. 28-34 ◽  
Author(s):  
Walter Noll
Keyword(s):  
Classical Mechanics ◽  
Space Time ◽  
Time Structures

Classical mechanics of special relativity in a Riemannian space‐time

1991 ◽  
Vol 32 (7) ◽  
pp. 1788-1795 ◽  
Author(s):  
Daniel Zerzion ◽  
L. P. Horwitz ◽  
R. I. Arshansky
Keyword(s):  
Special Relativity ◽  
Riemannian Space ◽  
Classical Mechanics ◽  
Space Time

scholarly journals Ordered space-time structures: Quantum carpets from Gaussian sum theory

2019 ◽  
Vol 62 (7) ◽  
Author(s):  
HuiXin Xiong ◽  
XueKe Song ◽  
HuaiYang Yuan ◽  
DaPeng Yu ◽  
ManHong Yung
Keyword(s):  
Space Time ◽  
Gaussian Sum ◽  
Ordered Space ◽  
Time Structures

scholarly journals The shape dynamics description of gravity

2015 ◽  
Vol 93 (9) ◽  
pp. 956-962 ◽  
Author(s):  
Tim Koslowski
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Small Scale ◽  
Shape Dynamics ◽  
Quantum Particles ◽  
Minkowski Space Time ◽  
Time Structures ◽  
Geometric Picture

Classical gravity can be described as a relational dynamical system without ever appealing to space–time or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than general relativity) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of space–time in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of space–time geometry, the role of local Minkowski space, universality of space–time geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincaré group. In this contribution I derive effective space–time structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an “experienced space–time geometry.” This leads (in an idealized approximation) to local Minkowski space and causal relations. The small-scale structure of the emergent geometric picture depends on the specific probes used to experience space–time, which limits the applicability of effective space–time to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski space–time emerges from the evolution of quantum particles.

A classification of space-time structures

1976 ◽  
Vol 10 (3) ◽  
pp. 297-310 ◽  
Author(s):  
Andrzej Trautman
Keyword(s):  
Space Time ◽  
Time Structures

scholarly journals Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

2014 ◽  
Vol 11 (10) ◽  
pp. 1450086 ◽  
Author(s):  
Horace W. Crater ◽  
Luca Lusanna
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Minkowski Space Time ◽  
Accelerated Observers ◽  
Inertial Frames ◽  
Locality Principle

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

Structure of the Madden–Julian Oscillation in the Superparameterized CAM

2009 ◽  
Vol 66 (11) ◽  
pp. 3277-3296 ◽  
Author(s):  
James J. Benedict ◽  
David A. Randall
Keyword(s):  
Boundary Layer ◽  
General Circulation ◽  
Deep Convection ◽  
Circulation Model ◽  
Grid Cell ◽  
Atmospheric Model ◽  
Space Time ◽  
Madden Julian Oscillation ◽  
Moist Convection ◽  
Time Structures

Abstract The detailed dynamic and thermodynamic space–time structures of the Madden–Julian oscillation (MJO) as simulated by the superparameterized Community Atmosphere Model version 3.0 (SP-CAM) are analyzed. Superparameterization involves substituting conventional boundary layer, moist convection, and cloud parameterizations with a configuration of cloud-resolving models (CRMs) embedded in each general circulation model (GCM) grid cell. Unlike most GCMs that implement conventional parameterizations, the SP-CAM displays robust atmospheric variability on intraseasonal space and time (30–60 days) scales. The authors examine a 19-yr SP-CAM simulation based on the Atmospheric Model Intercomparison Project protocol, forced by prescribed sea surface temperatures. Overall, the space–time structures of MJO convective disturbances are very well represented in the SP-CAM. Compared to observations, the model produces a similar vertical progression of increased moisture, warmth, and heating from the boundary layer to the upper troposphere as deep convection matures. Additionally, important advective and convective processes in the SP-CAM compare favorably with those in observations. A deficiency of the SP-CAM is that simulated convective intensity organized on intraseasonal space–time scales is overestimated, particularly in the west Pacific. These simulated convective biases are likely due to several factors including unrealistic boundary layer interactions, a lack of weakening of the simulated disturbance over the Maritime Continent, and mean state differences.

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