Reference Diagrams In Essays
[…] Of special importance for our purposes is that each frame of reference has a definite state of motion at each event of spacetime.
[…] Within the context of special relativity and as long as we restrict ourselves to frames of reference in inertial motion, then little of importance depends on the difference between an inertial frame of reference and the inertial coordinate system it induces.
For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference.
Sometimes the state of motion is emphasized, as in rotating frame of reference.
The first is the notion of a coordinate system, understood simply as the smooth, invertible assignment of four numbers to events in spacetime neighborhoods.
The second, the frame of reference, refers to an idealized system used to assign such numbers […] To avoid unnecessary restrictions, we can divorce this arrangement from metrical notions.
In a physical problem, they could be spacetime coordinates or normal mode amplitudes.
The idea of a reference frame is really quite different from that of a coordinate system.
Frames differ just when they define different spaces (sets of rest points) or times (sets of simultaneous events).
In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements.
In n dimensions, reference points are sufficient to fully define a reference frame.