Understanding Reference Frames: Generality & Abstractions

Click For Summary

Discussion Overview

The discussion revolves around the concept of reference frames in physics, exploring their generality and the nature of their relationships. Participants examine whether vectors can exist differently across frames and the implications of transformations between them, including spatial and rotational translations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether a vector in one reference frame can not exist in another frame, suggesting a need for a relationship between frames.
  • Another participant proposes that a vector can be zero in a different frame, using the example of a free fall frame where the gravity vector is nearly zero.
  • A participant seeks clarification on whether reference frame A can always be represented in terms of reference frame B through spatial and rotational translations.
  • A later reply discusses special relativity, indicating that transformations between inertial frames involve translations, spatial rotations, and boosts, which mix space and time.

Areas of Agreement / Disagreement

Participants express varying views on the nature of reference frames and their transformations, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

There are unresolved assumptions regarding the definitions of reference frames and the conditions under which vectors may or may not exist across them. The discussion also touches on the complexity of transformations in special relativity, which may not be fully explored.

nanoWatt
Messages
85
Reaction score
2
I am wondering about the generality of reference frames, and how abstract they can be.

Is it possible for a vector in one reference frame to not exist in another frame? Or is there always a relation between two reference frames?

Also, are two reference frames like two different sets of coordinate axes? I mean can you always get from one reference frame to another just by knowing the position and or rotation values?
 
Last edited:
Physics news on Phys.org
I think one vector in one frame can be zero in another frame. For example, in a free fall frame, the gravity vector is juxt zero.
 
Ok, I think what I meant to say is,

Can a reference frame A always be represented in terms of reference frame B only by having a spatial and a rotational translation?
 
nanoWatt said:
Ok, I think what I meant to say is,

Can a reference frame A always be represented in terms of reference frame B only by having a spatial and a rotational translation?

In special relativity the transformations between inertial frames are translation, spatial rotation and boosts. Boosts are rotations that mix space and time and represent a frame that is moving wrt the base frame.
 

Similar threads

Undergrad Reference frames, center of rotation, etc
  • · Replies 88 ·
3
Replies
88
Views
4K
Graduate Reference frame in collision problems
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Are vectors independent of reference frames?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Reference frames in terms of homogenity/isotropy
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Velocity transformation between frames rotating relative to one another
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Which inertial frame is used when resolving toward the centre
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Using reference frames for derivation of Lagrangian
  • · Replies 25 ·
Replies
25
Views
3K
Undergrad Energy and reference frames
  • · Replies 87 ·
3
Replies
87
Views
5K
High School Thoughts about Galilean transformations
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Law of inertia (inertial observer and inertial frames of reference)
  • · Replies 2 ·
Replies
2
Views
2K