Reference frame vs coordinate system

Click For Summary

Discussion Overview

The discussion centers on the distinction between reference frames and coordinate systems, exploring their definitions, implications in physics, and their relevance in classical mechanics and relativity. Participants examine the terminology and conceptual frameworks surrounding these ideas, particularly in the context of spacetime and vector fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that a reference frame has physical meaning related to physical laws, while a coordinate system is a mathematical tool for representing those frames numerically.
  • Others argue that the term "reference frame" can refer to multiple concepts, including coordinate charts, frame fields, and measurement apparatus, leading to ambiguity in discussions.
  • A participant questions how the concept of a frame field degenerates in classical mechanics and special relativity (SR), particularly regarding the need for a set of vectors and the implications for inertial and non-inertial frames.
  • It is noted that in classical mechanics, the concept of a frame field may not apply due to the absence of a spacetime metric, complicating the definitions of timelike and spacelike vectors.
  • Some participants clarify that a frame field does not assign coordinates to events but can represent an observer's perspective in spacetime.
  • There is a discussion about whether a tetrad field can serve as a basis for a coordinate chart, with some indicating that it can only serve as a non-coordinate basis in general.
  • A participant expresses a desire to understand the transition from classical mechanics to relativity and seeks resources that explain frame fields from that perspective.

Areas of Agreement / Disagreement

Participants generally agree that the terminology surrounding reference frames and coordinate systems is ambiguous and varies across literature. However, there is no consensus on the applicability of frame fields in classical mechanics, with differing opinions on how these concepts relate to inertial and non-inertial frames.

Contextual Notes

Limitations include the ambiguity of terms like "reference frame" and "frame field," which can refer to different concepts in different contexts. The discussion also highlights the challenges of defining orthonormal sets of vectors in classical mechanics due to the lack of a spacetime metric.

Who May Find This Useful

This discussion may be useful for those interested in the foundations of physics, particularly in understanding the differences between reference frames and coordinate systems, as well as their implications in classical mechanics and relativity.

  • #31
cianfa72 said:
I take it as if we assign fixed spatial coordinate values to observer's parts (i.e. to their worldlines in the worldtube) and define coordinate time such that the Pythagorean theorem holds for the proper distance of events at rest in the chart being defined that have the same coordinate time value (i.e. they are Einstein synchronized).
You can't do that if geodesic deviation is present. If geodesic deviation is present, one of the elements of your prescription must fail. It is impossible to meet all of your requirements in the presence of geodesic deviation.
 
  • Like
Likes   Reactions: cianfa72
Physics news on Phys.org
  • #32
I found some new reference on this. In book "Special Relativity in General Frame", the concept of "local frame" is defined, similarly the concept of observer, in section 3.4.

1637080067367.png


I wonder if this is a common definition, and does it generalise to GR well?
 
  • #33
lriuui0x0 said:
In book "Special Relativity in General Frame"
Can you give a link?
 
  • #34
lriuui0x0 said:
I wonder if this is a common definition, and does it generalise to GR well?
Yes and yes. The only thing missing from what you posted is that, to be a full frame field (i.e., tetrad field), the "local frame" needs to be defined, not just on the worldline, but in an open neighborhood around it. That enables the kinematic decomposition to be computed.
 
Last edited:

Similar threads

  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 23 ·
Replies
23
Views
2K
  • · Replies 87 ·
3
Replies
87
Views
5K
  • · Replies 61 ·
3
Replies
61
Views
6K
  • · Replies 78 ·
3
Replies
78
Views
8K
  • · Replies 52 ·
2
Replies
52
Views
4K
  • · Replies 27 ·
Replies
27
Views
2K
  • · Replies 34 ·
2
Replies
34
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 16 ·
Replies
16
Views
3K