Understanding Reference Frames: Generality & Abstractions

In summary, the conversation discusses the generality of reference frames and the possibility of representing one frame in terms of another through spatial and rotational translations. It also mentions the concept of boosts in special relativity as a type of rotation that combines space and time.
  • #1
nanoWatt
88
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?
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 

1. What is a reference frame?

A reference frame is a set of coordinates used to describe the location and motion of an object in space. It serves as a point of reference for measuring and understanding the movement of objects in relation to it.

2. Why is understanding reference frames important?

Understanding reference frames is important because it allows us to accurately describe and predict the motion of objects in the physical world. It also helps us to understand the relationship between different objects and their movements.

3. What is the difference between generality and abstraction in reference frames?

Generality in reference frames refers to the idea that a reference frame can be used to describe the motion of a wide range of objects, regardless of their specific characteristics. Abstraction refers to the simplification of a reference frame by removing unnecessary details and focusing on the essential aspects of an object's motion.

4. How do scientists use reference frames in their research?

Scientists use reference frames in a variety of fields, such as physics, astronomy, and engineering. They use reference frames to accurately describe and measure the motion of objects, as well as to develop theories and models for predicting future motion.

5. Can reference frames be relative or absolute?

Yes, reference frames can be relative or absolute. Relative reference frames are defined in relation to another object or point of reference, while absolute reference frames are fixed in relation to the larger universe, such as the Earth's position in space.

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