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?