Null coordinates in flat spacetime

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Discussion Overview

The discussion centers on the existence of "standard" coordinate systems in flat spacetime that incorporate at least one null coordinate. Participants explore various coordinate systems, their properties, and naming conventions, focusing on theoretical aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants identify standard coordinate systems in flat spacetime, including Minkowski, Rindler, and Born coordinates.
  • Advanced and retarded coordinates are proposed as examples of systems with null coordinates, defined as u = t+x and v = t-x.
  • A participant mentions a more complex coordinate system based on null cones, specifically u = t-r.
  • There is a query regarding the attribution of advanced and retarded coordinates to a specific individual, with responses suggesting Brinkmann as a possible name.
  • Another participant notes that advanced and retarded coordinates are also referred to as "light cone coordinates" or "radar coordinates," explaining the latter's connection to radar detection.
  • A point is made about the basis vectors of the null coordinates being null but not orthogonal.
  • Barton Zwiebach's textbook is referenced for the introduction of light-cone coordinates, specifically in the context of string theory.

Areas of Agreement / Disagreement

Participants present multiple viewpoints regarding the naming and properties of coordinate systems with null coordinates, indicating that no consensus has been reached on a singular "standard" coordinate system.

Contextual Notes

Some discussions involve varying definitions and interpretations of coordinate systems, and the relationship between different types of coordinates remains unresolved.

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There are some "standard" coordinate systems in flat spacetime, such as Minkowski (inertial), Rindler (uniform acceleration), and Born (rotation).

Is there a "standard" coordinate system in flat spacetime which has at least one null coordinate?
 
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Sure, there are several. Take advanced/retarded coordinates, u = t+x, v = t-x. If you want something fancier, the coordinate system based on the null cones whose vertices lie on a straight line: u = t-r.
 
thanks Bill_K, is there a name for the advanced retarded coordinates (I mean a person's name)?
 
DaleSpam said:
thanks Bill_K, is there a name for the advanced retarded coordinates (I mean a person's name)?
I've seen them attributed to Brinkmann.
 
Not somebody's name, but I've also heard them called "light cone coordinates" or "radar coordinates". (The latter because if you imagine the observer detecting objects using radar, he transmits a pulse at time v and receives an echo at time u, in the notation of post #2.)
 
The basis vectors of u and v are null but not orthogonal.
 
DaleSpam said:
There are some "standard" coordinate systems in flat spacetime, such as Minkowski (inertial), Rindler (uniform acceleration), and Born (rotation).

Is there a "standard" coordinate system in flat spacetime which has at least one null coordinate?

Barton Zwiebach uses Light-cone Coordinates in his textbook, "A First Course In String Theory." The concept is introduced in Section 2.3, page 20. The Light-cone Matrix is
LightCone_Matrix2.jpg
 
Last edited:

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