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Well, I actually thought this was going to be about phased array optics, so I guess there is some distinction here.

This is quite close to phased array optics actually.

I think on sites like HN - even with non-controversial subjects - you have to say "improbable" instead of "impossible" and stay away from absolutes.

Maybe "zoomable lens with no conventional moving parts", or "non-mechanical zooming" or solid-state zoom lens or...

It's a valid observation. A lens that could somehow do that without moving at all would be pretty magical, and the headline plays on this to get your attention. The headline could have been "MIT Creates Zoomable Lens That Works Using Heat" which is still cool, but not as sensational.

Or better yet, "MIT Creates Zoomable Lens That Works by Moving More or Less".

By this definition of movement absolutely nothing would do anything. If there was electric current you could say, "but the electrons are moving in the material". It's like saying your stove moves when you cook.

By any reasonable definition without moving parts means without any macroscopic (mechanical) parts that move.