I'm not sure I agree.
Going off of your own link, in my scenario the Grebe is the blue bottle in the distance, not the pink bottle in the foreground. That blue bottle DEFINITELY changes in each frame, as does its relationship with its surroundings. The apparent distance between the pink bottle and the blue bottle is the kind of change I am talking about.
You can disagree, but you'd be wrong. Please read the linked post again, in its entirety. The blue and pink water bottles are not my example, they're wikipedia's, and they are confusing because while the focal lengths are prominently labeled, distances aren't stated - and the distance is a covariant.
Scroll down to the beer bottles - those are my examples. Look just at the left column - those images have decreasing focal lengths but the same distance, and thus the perspective is identical. The 100mm shot could be 600mm for the grebe, and the 50mm shot analogous to a 300mm lens - if you're the same distance from the grebe, the perspective will be the same, whether the foreground is a loon or open water. To change the perspective as you see in the right column of beer bottle images, you'd need to be wading out into that 10' deep water. Bring your A1400 if you want, or your 600mm lens - in either case, it'll be the changing distance that's altering the perspective of the shot, not the camera/lens you're holding while treading water.
Ok, yeah, I agree with that. That also wouldn't really be what I was referring to, but that is my fault. If I use the 100-400mm lens as an example....if I change the focal length from 100 to 400, the background, and the relationship between whatever I'm focused on and the background, does change...when the exact same aperture is used for both focal lengths. Perhaps that is not "perspective"...maybe the correct terminology is simply "background compression." Whatever the correct term is...the relationship between the focused subject and its background does change. I'll see if I can get some examples, including crops.
This is the difference that I'm talking about. Maybe this can only be called "Depth Compression" or "Background Compression"...but to me, the relationship
between the subject (the brick...or a Grebe...) and its background CHANGED...that is perspective, no? I guess one could say that only if the relative positions
of elements change, do you have a change in perspective. I would be willing to agree with that, however I have a number of friends who are wedding photographers who use the term "perspective" to refer to both changes in relationship...both change in relative positions of near/far elements, as well as the change in blur and apparent depth between a subject and it's background. I'm willing to accept that the latter definition is not accepted. I can just call it background compression from now on.
Same aperture, f/6.3, used at both 100mm and 400mm. Camera was set up at a fixed point, subject distance did NOT change. The 100mm shot was scaled and cropped in Photoshop to match the 400mm shot. The relationship of the brick to its background changes considerably between the two (sorry, the lens is not parfocal, so the focal plane shifted forward by a couple millimeters in the 400mm shot):