*This comfortable circumstance ceases immediately once we begin to consider frames of reference in nonuniform motion even within special relativity.…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.*An observer O, situated at the origin of a local set of coordinates – a frame of reference F.

*This comfortable circumstance ceases immediately once we begin to consider frames of reference in nonuniform motion even within special relativity.…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.*An observer O, situated at the origin of a local set of coordinates – a frame of reference F.

[…] 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.

The situation thus differs from Galilean relativity, where all possible coordinate times are essentially equivalent.

The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms.

We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below: We first introduce the notion of reference frame, itself related to the idea of observer: the reference frame is, in some sense, the "Euclidean space carried by the observer". The frame, denoted , coordinates are changed from R to R′ by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.

As noted by Brillouin, a distinction between mathematical sets of coordinates and physical frames of reference must be made.

On the other hand, a coordinate system may be employed for many purposes where the state of motion is not the primary concern.

For example, a coordinate system may be adopted to take advantage of the symmetry of a system.

So frames correspond at best to classes of coordinate systems.

In traditional developments of special and general relativity it has been customary not to distinguish between two quite distinct ideas.

## Comments Reference Diagrams In Essays

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