Null coordinates in flat spacetime

In summary: Equation 2.12.In summary, there are several "standard" coordinate systems in flat spacetime that have at least one null coordinate, such as advanced/retarded coordinates, light cone coordinates, and the Light-cone Matrix. These coordinate systems include Minkowski (inertial), Rindler (uniform acceleration), and Born (rotation). The concept of Light-cone Coordinates is introduced in Section 2.3, page 20 of Barton Zwiebach's textbook "A First Course In String Theory."
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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.
 
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thanks Bill_K, is there a name for the advanced retarded coordinates (I mean a person's name)?
 
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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.
 
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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.)
 
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The basis vectors of u and v are null but not orthogonal.
 
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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
 
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FAQ: Null coordinates in flat spacetime

What are null coordinates in flat spacetime?

Null coordinates in flat spacetime refer to a coordinate system that is used to describe the geometry and motion of objects in a flat spacetime, as described by Einstein's theory of special relativity. These coordinates are based on the concept of light cones, where the paths of light rays are represented as straight lines at a 45-degree angle.

How are null coordinates related to the speed of light?

The speed of light plays a crucial role in defining null coordinates in flat spacetime. In this coordinate system, the speed of light is considered to be a fundamental constant and is used as a unit of measurement for both space and time. This means that the distance and duration of events can be measured in terms of the speed of light.

Why are null coordinates important in special relativity?

Null coordinates are important in special relativity because they provide a way to describe the effects of time and space dilation, as well as the phenomenon of length contraction, in a consistent and mathematically elegant manner. They also allow for the calculation of distances and durations in a way that is independent of the observer's reference frame.

How do null coordinates differ from other coordinate systems?

Unlike other coordinate systems, null coordinates are specifically designed to describe the geometry and motion of objects in a flat spacetime, as opposed to curved spacetimes. They also take into account the constant speed of light, which is not a factor in other coordinate systems such as Cartesian coordinates or polar coordinates.

Can null coordinates be used in non-flat spacetimes?

No, null coordinates are only applicable in flat spacetimes. In non-flat or curved spacetimes, other coordinate systems, such as general coordinates, are used to describe the geometry and motion of objects. This is because the concept of light cones and the constant speed of light do not hold true in these types of spacetimes.

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