Reference Frames – Difference Between Reference Frame and Coordinate System Explained

coordinate systemsdefinitionreference frames

In wikipedia, regarding this topic, different examples are given as to why a reference frame and coordinate system are NOT the same thing (https://en.wikipedia.org/wiki/Frame_of_reference).
Example from J.D Norton:

More recently, to negotiate the obvious ambiguities of Einstein’s
treatment, the notion of frame of reference has reappeared as a
structure distinct from a coordinate system.

I am trying to understand the different definition and I have come up with the following understanding, for which I want to know whether is correct or faulty.

First off all I consider that a difference between the two exists. For once a coordinate system is a mathematical/abstract concept while the reference frame is something grounded in physics/or physical.

I would consider a coordinate system of whatever kind as "tool" (for lack of better words), which assigns a set of numbers to each point in space.

The reference frame is an "entity" (for lack of better words again), which is correlated or related to a physical location/body etc, to which a coordinate system of whatever kind is attached to, giving to the observer, in this physical location (one can say the observer is at rest in this reference frame) the possibility to assign a location and a time to an event E.

Best Answer

First off all I consider that a difference between the two exists. For once a coordinate system is a mathematical/abstract concept while the reference frame is something grounded in physics/or physical

It is very important to recognize that different authors may use the same term differently. I have seen at least three different meanings of the term “reference frame” in different sources:

  1. some authors treat the term “reference frame” as a synonym for “coordinate system”, sometimes with the implication that it is restricted to coordinate systems with one timelike coordinate three spacelike coordinates.

  2. other authors use the term “reference frame” to refer to a tetrad. Again usually that is restricted to a tetrad with one timelike vector field and three spacelike vector fields, and often with the further requirement that the vector fields be orthogonal and normalized.

  3. yet other authors use the term “reference frame” to refer to a collection of rods and clocks or other physical devices used for measuring time and position. These are automatically timelike and spacelike respectively, and often orthogonal.

I would not try to take a very rigid stance on the meaning of the term. Simply find out how an individual author is using it. Also, if there is any ambiguity, then simply clarify how you are using it. It is simply a choice of definition, so there is no particular right or wrong answer. But when people don’t clarify their usage it can lead to confusion

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