Reference Frames

What we see depends on where we stand...

Reference frames are immaterial things conjured up to enable folks to specify the location of objects in space relative to some observer. If we are working in a one-dimensional space a single real number line marked with numbers from negative infinity, through zero to positive infinity, representing units of length, is sufficient to identify the location of all the points in that space. Adding a second such real number line perpendicular to the first such that their zeros coincide enables us to identify the location of all the points in a two-dimensional space. A third such real number line through the intersection of the first two and perpendicular to both with its zero coincident with theirs completes a three-dimensional reference frame.

The real number lines are ordinarily labeled with the letters x, y and z, and called the x-axis, y-axis and z-axis. Sometimes the dimensions of the space spanned by the lines are identified with the labels on the axes so we speak of the x dimension, y dimension or z dimension. This arrangement allows us to identify any point in space by a set of three numbers (x,y,z). When we picture objects in the reference frame, each may be associated with a point in space called its location.

Each observer may be thought to have her own reference frame and witness events in that frame, as well as be aware of other reference frames and their observers. Being immaterial structures, frames may overlap and pass through one another without interference. Reference frames may have any speed and direction (velocity) of motion relative to one another. Often it is convenient to have a reference frame attached to an object so that that object is at rest in the frame. In the case of objects interacting, it is sometimes convenient to associate the reference frame with the center of mass of the objects. Since we are making these things up we have a lot of latitude in choosing location, velocity and inhabitants of our reference frames.