Reference frame vs coordinate chart

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Discussion Overview

The discussion revolves around the concepts of 'reference frame' and 'coordinate chart' within the context of special relativity (SR). Participants explore the definitions, implications, and distinctions between these terms, particularly in relation to the use of rods and clocks for defining inertial frames and the mathematical representation of spacetime.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants propose that a 'frame of reference' can be understood as a 'rods & clocks latticework' which allows for the assignment of spatial positions in a grid.
  • Others argue that the concept of a 'reference frame' is not as flexible as suggested, emphasizing that it should adhere to specific conditions such as rigid rods and synchronized clocks, which define an inertial reference frame.
  • A distinction is made between a 'reference frame' and a 'coordinate chart', with some asserting that relaxing the conditions of synchronization and rigidity undermines the physical meaning of the reference frame.
  • Some participants identify three separate meanings for 'reference frame': (1) a physical system of clocks and rulers, (2) a coordinate chart, and (3) a tetrad, with varying preferences for which definition is most useful.
  • There is a suggestion that the term 'reference frame' should be avoided in favor of more precise terminology depending on the context, such as 'coordinates' or 'tetrad'.
  • Participants discuss the concept of a 'tetrad' as a set of four orthonormal vector fields, noting its utility in describing observers without establishing synchronization conventions.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of 'reference frame' and 'coordinate chart'. There is no consensus on a single definition, and multiple competing views remain regarding the appropriate usage of these terms.

Contextual Notes

Participants highlight the importance of context when discussing terms like 'tetrad' and the implications of using 'reference frame' in various scenarios. There are unresolved issues regarding the assumptions underlying the definitions and the physical realizations of these concepts.

  • #61
Dale said:
The standard inertial frame with Einstein synchronization convention where such and such body is at rest.
So that does mean: take a family of free bodies (zero proper acceleration) at rest w.r.t. the given (free/inertial) such and such body in a region surrounding it (just to fix ideas we can imagine a wristwatch attached to each of them).

Note that 'at rest' does actually mean that the round-trip time of 2-way light signals exchanged between those bodies does not change. Then, as pointed out in a recent PF thread, we can consistenly apply the Einstein synchronization convention to synchronize such wristwatches (the resulting one-way speed of light in the frame being defined is the universal constant value c).

Label every wristwatch (or body) with fixed different spatial coordinate values and take the proper time of each of them as the coordinate time of the frame being defined.

The map defined as above is the standard inertial frame you were talking about. Btw we're aware of we can do that just in a limited spacetime region in the context of GR. In flat spacetime instead (SR) there is no limit in principle to extend such standard inertial frame to the entire spacetime.

Make sense ? Thank you.
 
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  • #62
cianfa72 said:
Make sense ? Thank you
Yes, that makes sense.
 

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