Understanding Reference Frames: Generality & Abstractions

[nanoWatt]

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?

 

[pixel01]

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.

 

[nanoWatt]

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?

 

[Mentz114]

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.