Lorentz contraction vs different time coordinates?

Question

I am currently working my way through "Special Relativity and Classical Field Theory (The Theoretical Minimum)" by Susskind and Friedman, and I'm a little bit perplexed by the interpretation of this picture being used to describe Lorentz Contraction:

The idea is that an observer in the x', t' frame observes a 1-unit length OQ in the x, t frame as they move past. The author plugs the 1 into the Lorentz transformation equations and we see that OP is $\sqrt{1-v^2}$ where $v$ is in units of light-speeds. The authors say that the unit length therefore looks shorter.

It seems to me that an alternate interpretation is that the moving observer at point P is just witnessing the future of the end of the stationary meterstick at point Q. This is, I think, easy to see from the diagram, that P is in Q's future from the PoV of the stationary frame. Observing the future of Q, the moving observer does not see the end of the meterstick, but instead sees that they are somewhat past it (having passed it, since they are in a moving frame).

To illustrate, imagine that, to signal the measurement-taking, the moving observer flashes a light signal at both the origin and at point P simultaneously (for them) at time t'=0. They stop and come back to chat with the stationary observer and say "hey, I measured your meterstick to be less than 1." The stationary observer might reply "well no duh, I saw your signals and, even accounting for the speed of light I saw that you took your second measurement much later than the first."

Is this a valid alternate interpretation of the situation, or am I missing some crucial point here? Is length contraction just the manifestation of our divergent time axes?

Answer 1

The length of a stationary object is the distance between the positions of its endpoints. With moving objects, the distance between the two endpoints only gives the length if you pin them down at the same time. If I take the position of the front of a moving train and compare that with the position of the rear a few second later, the rear will have moved forward in the intervening few seconds, so the distance between the two points will be less than the true length of the train. That is essentially what is happening with length contraction. To measure the length of a moving object you have to determine the distance between its two endpoints simultaneously, and the problem is that two moments that are simultaneous in one frame are not simultaneous in another.

Answer 2

Your core concept is correct, but some of the specific details you state are not.

Any segment from the $x=0$ line to the $x=1$ which is parallel to OQ represents the length in the unprimed frame. And any segment parallel to OP represents the length in the primed frame. The fact that they are not parallel indeed stems from the divergent time axes, and also implies length contraction.

However, none of the comments hold regarding future or past. The distance is constant in each frame. It doesn’t change over time in either frame. So regardless which segment parallel to OP you choose, there are segments parallel to OQ which are entirely earlier, segments which are entirely later, and segments which “straddle” the chosen OP segment. None of those pairs of segments are priveliged over any other.