Special Relativity - Which reference frame experiences which time?

[vela]

What I meant was that since we describe everything on Earth as one object, Earth, then, since the Earth and the dwarf planet have the same reference frame and velocity, why can't we describe them as one single object.

In this problem, you can treat the Earth and the dwarf planet as points in space because they're very small compared to the relevant length scale. The Earth's radius, for example, is about 6400 km, which is much smaller than the distance Lisa travels, which will be on the order of an astronomical unit, which is approximately 150,000,000 km.

 

[jbriggs444]

What I meant was that since we describe everything on Earth as one object, Earth, then, since the Earth and the dwarf planet have the same reference frame and velocity, why can't we describe them as one single object.

You can treat them as a single body. An body with a non-negligible spatial extent. An "extended body" if you will. As opposed to a "pointlike object".

As has been pointed out, you cannot treat them as a single event.

An extended body (such as a rocket, a meter stick or a pair of distant planets) will be length contracted when considered from the point of view of a frame of reference against which it is seen to be moving. That is, the length of the body as measured by third party observers will be shorter than the length of the body as measured by observers who are moving along with the body.

In the case at hand, length contraction can help reconcile traveler Lisa's account of events with an Earthbound observer's account of events.

A complete understanding of how the same object can be measured to have different lengths is more complicated. It can be approached by carefully defining what the "length of an object" actually means in terms of experimental procedures and then exploring the relativity of simultaneity. The explanation might include terms such as "world tube", "cross section", non-Euclidean interval measures and a Euclidean analogy with the width of a strip of paper.