# Rindler Coordinates & Quadrants: Resolving an Issue

• I
• kent davidge
In summary, the author says that the Rindler coordinates cover the first quadrant of Minkowski space and can be used as coordinates there. However, this is not in agreement with the definitions of a quadrant.
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?

kent davidge said:
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.

kent davidge
kent davidge said:
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.

PeterDonis and kent davidge
Nugatory said:
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.

kent davidge said:
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.

Ibix and kent davidge

## 1. What are Rindler Coordinates?

Rindler Coordinates are a set of coordinates used in the study of relativity, specifically in the context of accelerating frames of reference. They are named after physicist Wolfgang Rindler and are used to describe the motion of an observer in a constantly accelerating reference frame.

## 2. How are Rindler Coordinates different from other coordinate systems?

Rindler Coordinates are different from other coordinate systems, such as Cartesian or polar coordinates, because they are specifically designed to describe the motion of an observer in an accelerating reference frame. They take into account the effects of acceleration on time and space measurements.

## 3. What is the issue with Rindler Coordinates and Quadrants?

The issue with Rindler Coordinates and Quadrants arises when trying to define and label the quadrants in the coordinate system. There is no universally agreed upon convention for labeling the quadrants, leading to confusion and inconsistency in the literature.

## 4. How can the issue with Rindler Coordinates and Quadrants be resolved?

One proposed solution to the issue with Rindler Coordinates and Quadrants is to use a consistent labeling convention, such as the one proposed by physicist John Wheeler. This convention labels the quadrants in the same way as Cartesian coordinates, with the positive x-axis pointing to the right and the positive y-axis pointing upwards.

## 5. Why are Rindler Coordinates and Quadrants important in relativity?

Rindler Coordinates and Quadrants are important in relativity because they allow us to describe the effects of acceleration on time and space measurements. They are also useful in understanding the concept of spacetime curvature and the effects of gravity on the motion of objects in the universe.

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