Easy, match up light field cameras with light field displays. Think polarized 3D screens, except a billion times better - they can project the light as if the objects literally are just behind the screen.

Add eye tracking and put the screens across every surface and you can make the views follow your field of vision.

Or you use AR glasses that essentially project images in front of you.

How do I shovel food into my maw when I'm wearing VR goggles? What happens when my spoon misses the bowl?

AR = augmented reality. You still see your own world and your own spoon and bowl. You can definitely have the view projected anchored in space above the physical things you interact with.

I can hear the complaints already: "Ouch! Dropbox Sync just kicked in and lagged my AR while I was eating dinner. Now I've got hot ramen all over me... fml."

There's transparent screen AR, like with HoloLens and Meta glasses from http://www.spaceglasses.com