scholarly journals Generalized embedding variables for geometrodynamics and space‐time diffeomorphisms: Ultralocal coordinate conditions

1993 ◽  
Vol 34 (1) ◽  
pp. 115-129 ◽  
Author(s):  
Stephen P. Braham
Keyword(s):  
Space Time ◽  
Coordinate Conditions

Coordinate conditions in a Riemannian space for coordinates based on a subspace

1971 ◽  
Vol 323 (1552) ◽  
pp. 1-10 ◽  
Keyword(s):  
General Relativity ◽  
Coordinate System ◽  
Riemannian Space ◽  
Line Element ◽  
Linear Part ◽  
Riemann Tensor ◽  
Space Time ◽  
Metric Tensor ◽  
Single Argument ◽  
Coordinate Conditions

It is customary to specify the geometry of a Riemannian N -space by writing down a quadratic line-element, the coefficients being ½ N ( N + 1) functions of the coordinates. But since there is an N -fold arbitrariness in the choice of coordinates, there is an N -fold arbitrariness in the metric tensor, and one expresses this by saying that the metric tensor satisfies N coordinate conditions, so that there are essentially only ½ N ( N - 1) components. If the coordinate system is made definite by constructing it according to some geometrical plan, the coordinate conditions may be made explict; their form is well known for Riemannian coordinates (based on geodesics drawn out from a point) and for Gaussian coordinates (based on geodesics drawn orthogonal to an ( N - 1)-space), and in some other cases. Our purpose is to present in a single argument the coordinate conditions for coordinates based on geodesics drawn orthogonal to a subspace of M dimensions ( M = 0, 1, ..., N - 1). These conditions are very simple in form. They are used to express the metric tensor in terms of integrals of the linear part L ijkm of the covariant Riemann tensor. If in these integrals L ijkm is replaced by any other set of functions E ijkm having the same symmetries as L ijkm , then L ijkm and E ijkm differ only by terms evaluated on the subspace. All the results are applicable to the space-time of general relativity if one puts N = 4.

Space, Time and Einstein

2002 ◽  
Author(s):  
J. B. Kennedy
Keyword(s):  
Space Time

Spinors and Space-Time

1984 ◽  
Author(s):  
Roger Penrose ◽  
Wolfgang Rindler
Keyword(s):  
Space Time

Do Writing Directions Influence How People Map Space onto Time?

2018 ◽  
Vol 77 (4) ◽  
pp. 173-184
Author(s):  
Wenxing Yang ◽  
Ying Sun
Keyword(s):  
Mental Representations ◽  
Space Time ◽  
Horizontal Axis ◽  
Causal Role ◽  
Writing Systems ◽  
Temporal Cognition ◽  
Japanese Speakers ◽  
Psychological Experiments ◽  
Vertical Up

Abstract. The causal role of a unidirectional orthography in shaping speakers’ mental representations of time seems to be well established by many psychological experiments. However, the question of whether bidirectional writing systems in some languages can also produce such an impact on temporal cognition remains unresolved. To address this issue, the present study focused on Japanese and Taiwanese, both of which have a similar mix of texts written horizontally from left to right (HLR) and vertically from top to bottom (VTB). Two experiments were performed which recruited Japanese and Taiwanese speakers as participants. Experiment 1 used an explicit temporal arrangement design, and Experiment 2 measured implicit space-time associations in participants along the horizontal (left/right) and the vertical (up/down) axis. Converging evidence gathered from the two experiments demonstrate that neither Japanese speakers nor Taiwanese speakers aligned their vertical representations of time with the VTB writing orientation. Along the horizontal axis, only Japanese speakers encoded elapsing time into a left-to-right linear layout, which was commensurate with the HLR writing direction. Therefore, two distinct writing orientations of a language could not bring about two coexisting mental time lines. Possible theoretical implications underlying the findings are discussed.

Sign in / Sign up

Export Citation Format

Share Document