Understanding Reference Frames: Generality & Abstractions

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The discussion focuses on the generality and abstraction of reference frames in physics, questioning whether vectors in one frame can exist in another and the relationship between different frames. It explores the idea that reference frames can be likened to different sets of coordinate axes, suggesting that transitions between them may involve spatial and rotational translations. The concept of a vector being zero in one frame, such as the gravity vector in a free-fall frame, is highlighted. Additionally, it mentions that in special relativity, transformations between inertial frames include translations, spatial rotations, and boosts, which account for motion relative to a base frame. The conversation emphasizes the complexity and interconnectivity of reference frames in understanding physical phenomena.
nanoWatt
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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?
 
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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.
 

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