I Rindler Coordinates & Quadrants: Resolving an Issue

[kent davidge]

Im reading a text where the author says that the Rindler coordinates cover the first quadrant of Minkowski space and thus can be used as coordinates there. He is considering only 1 spatial dimension.

I learned in high school that a quadrant is one quarter of an Euclidean plane. I looked up definitions on the web and the term may also refer to a 90° arc lengh of a circle.

But in the case of Rindler coordinates, considering only 1 space dimension, its clear that they cover only a part of Minkowski space that is bounded by two 45° lines, and this is not in agreement with the definitions of a quadrant.

On the other hand, I have so little knowledge about Relativity, so is this term used differently in Relativity?

 

[George Jones]

Im reading a text where the author says that the Rindler coordinates cover the first quadrant of Minkowski space and thus can be used as coordinates there. He is considering only 1 spatial dimension.

I learned in high school that a quadrant is one quarter of an Euclidean plane. I looked up for definitions on the web and the term may also refer to a 90° arc lengh of a circle.

But in the case of Rindler coordinates, considering only 1 space dimension, its clear that they cover only a part of Minkowski space that is bounded by two 45° lines, and this is not in agreement with the definitions of a quadrant.

On a spacetime diagram, the two lightlike lines ("lines at 45°") partition Minkowski spacetime (for one spatial dimension) into four regions. In this context, each of these regions is called a quadrant.

 

[Nugatory]

I learned in high school that a quadrant is one quarter of an Euclidean plane.

The Rindler wedge IS one-quarter of the plane. If it bothers you that the edges of the quadrant aren't vertical and horizontal, you can always turn your sheet of paper a quarter-turn counterclockwise.

 

[kent davidge]

The Rindler wedge IS one-quarter of the plane. If it bothers you that the edges of the quadrant aren't vertical and horizontal, you can always turn your sheet of paper a quarter-turn counterclockwise.

Oh I had actually considered this as a possibility but discarded later.

 

[Nugatory]

Oh I had actually considered this as a possibility but discarded later.

I should have said one-eighth of a turn and seriously, kidding aside, one of the early challenges for someone learning relativity is to break themselves of the habit of privileging their own viewpoint.