The Theory of Relativity: Coordinate System
by Eduardo Prachedes
Based on the perception of distance as a branch of physics, it is necessary to have a way to measure these distances. Einstein proposes the idea of creating a measuring rod “S” as a unit of measurement in his physical interpretation of distance. Therefore, let’s consider Einstein’s examples for now.
Basis of any length measurement
Considering A and B as two points on a rigid body, the straight line segment between them, constructed with the laws of geometry, one can start from A and subtract the segment “S” from it to reach B. Then the number of times this subtraction is repeated is the distance from A to B.
How is it in everyday life?
If I analyze the specification of the location ‘at Potsdam Square in Berlin,’ it means the following: the Earth is the rigid body to which the specification refers, and on it, there is a marked point with a name, ‘Potsdam Square in Berlin,’ with which the event spatially coincides.
This way of specifying locations is considered primitive and applicable only to the surface of rigid bodies and distinguishable points.
Getting rid of restrictions
a) A rigid body is related to a specific location (point) and extended to reach the object.
b) Instead of giving the point a name, such as A or B, it is given a number representing the size of the rod. Measured with a ruler.
c) The height of the object does not need to be measured by a material object like a rod or a pole. Height can be deduced from calculations taking into account angles from various points of view and how light propagates in the atmosphere.
To emancipate ourselves from “named points,” the use of numerical measurements in a Cartesian coordinate system will be necessary.
The system
The system consists of three flat, rigid walls, perpendicular and connected to a rigid body. Any event positioned in this system is described by specifying a length of three plumb lines or coordinates (x, y, z) extending from the event’s location to these three walls.
In this case, to calculate the length of these three lines, Euclidean Geometry will be necessary.
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//This text was translated from Portuguese to English, therefore it is subject to grammatical and translation mistakes. Report any mistake