Basic Question about Relativity Reference Frame Shifts

[tesla111]

Homework Statement

I'm using Shankar's Introductory Physics course and I can't get a question out of my head regarding his setup of Relativity.

There are two observers, S and S'. Observer S is stationary, while Observer S' is sliding past S (to the right) with velocity u. They agree to set their origin of t=0 at the moment when Observer S' passes Observer S. Shankar states that while the two observers will agree on their time origin, the x origin of Observer S' will be shifted to the right relative to the x origin of Observer S, by virtue of the fact that Observer S' is moving.

My question is a very simple conceptual question. Why does the x origin of Observer S' experience a point shift due to its velocity? Wouldn't it make more sense for Observer S' to experience something more like a stretch, in which Observers S and S' agree on the starting point of the x origin (the x origin of S), but due to the velocity of S', the x origin of S' covers a stretch of distance in that span of time versus just a point?

For example, if I were on a train and someone were on the ground, and we agreed to press a stopwatch the moment we passed each other, intuitively I can't figure out why that would simply mean that I pressed my stopwatch at a distance 3 feet (just as an example) from where he pressed his stopwatch.

Homework Equations

The Attempt at a Solution

 

[phyzguy]

The x origin of observer S' is moving relative to the x origin of observer S. While they align at time t=0, the x-origin of observer S' moves further and further to the right as time passes.

 

[tesla111]

The x origin of observer S' is moving relative to the x origin of observer S. While they align at time t=0, the x-origin of observer S' moves further and further to the right as time passes.

Now I get it. I misunderstood how he presented the problem. Thank you!