Right, so?

Where did the plants get the carbon from to build their organic structures?

(assuming the story is true), the amount of carbon in the bottle is unchanged. Life has to destroy old structure and recycle materials to build new structure. What certainly needs to be added is energy (from the sun) to power the cycles.

In this comment's grandparent referring to researching viable, man-made, self-sustaining biomes - which should then be robust to changes in external fauna/flora and conditions, I believe the idea is either to have the human become part of the biome (i.e. the carbon in your waste gets recycled) or to add materials when food is removed in some non-intrusive way.

I imagine that in some distant future we are going to have to have near perfect recycling. Human waste, and even our bodies will have to go back into these closed ecosystems.

I wonder if the energy from the sun is enough external input to sustain human life.

It's certainly possible, since earth doesn't need much external input other from sunlight to sustain life.

The question is, how scaled-down a self-sustaining ecosystem can we create and manage, which is capable of sustaining human life?