... So far no one talking about 3D pop has come up with an hypothesis. ...
... since you're having trouble explaining it. ...
Perhaps it's you who don't see nor hear them - just as you claim that I haven't provided evidence or definition although I have. Selective perception on your side, looks like. Or conscious manipulation attempts (trolling)?
I made an explanation, but now it seems that you have a hard time understanding it and keep claiming that I have trouble explaining it. You seem to want everything readily served on a golden plate right in front of you... come one are you so spoiled?
... Bring it on. Where are your pictures ? ...
Thanks for yours. I uploaded four of mine, downsized, and you should still be able to see how the contents pop out:
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At 50%-100% magnification (the original 50mp files), I can see that the objects really pop out, and that is probably further amplified by the crisp interfaces between the objects and their surroundings (great high-frequency MTF performance), as Lloyd Chambers describes in his Lenspire article. But that falls beyond the discussed question, so I don't provide crops of them here.
There are some logical prerequisites to seeing the pop though. Among other, your screen must be capable of displaying the tonality faithfully enough - if you use a poor screen (or a heavily miscalibrated one), there would be no wonder that you can't see it.
It's the subtle tonal transitions in the picture (e.g., a round pipe or anything with discernible 3D shape) - the low-frequency intertonal detail as in not from pixel to pixel, but across distances of several pixels to very many pixels (even all the way to across the entire frame if needed).
If the smoothness of the transition is lost or damaged - i.e. if the transitions begins very mildly and then there is a sudden shift to the other tone - then the 3D pop is negatively affected (or lost, put simply). That's my observation subjectively confirming what Yannick writes about on his blog.
For the addition, the 3D pop I am refering to is the function of both the image (sort of "hard data" in 2D) and human perception (highly intersubjective, but there are individuals who may have formed/trained the perception differently, or who might simply lack the ability to distinguish it, as in any other type of human perception).
Lastly, I have no pictures to compare that 3D rendering characteristic between different lenses so far (as e.g. Tony did in his video or Yannick does on his blog, both of which I linked to previously). In a follow-up to this I can try comparing Canon's EF 70-200 2.8 IS USM II with the Milvus 2/135 at 135mm... While I'm curious to see the difference when testing, I expect the Canon lens to retain the 3D pop better than e.g. the Sigma 135, but not as well as the Milvus. I'll be only able to verify the Canon vs. Milvus lens hypothesis, though.
EDIT:
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By the way, your pictures have an interesting artistic style, but because the contrast is so maxed out in them and the pictures are so heavily edited, they are not suitable to judge stuff like tonal transitions at all. Even if the tonal transitions were captured by your sensor into your RAW files, they would have been eliminated by such heavy editing.
By that I don't want to say that the pictures are anyhow faulty - they may be great pieces of art, but they are simply not suitable for this type of inquiry (3D pop), as far as I can see.