Is it possible for there to be a generation ship that was completely self-sufficient? An airtight vessel that used plants to create food and oxygen, and reused everything with a tight hold on population control and other such factors. Maybe even taking apart molecules to create other molecules to get things like trace nutrients. Could it be done? Or would everything end up being soil (because of the plant waste turning into compost)?
TL/DR -- Yep, you sure can!
How do I know? Because we have tiny versions of same, available at amazon.com: https://www.amazon.com/dp/B005J0V33E/
Basically, it's a sealed glass jar with plants and little shrimp inside, like so:
Update -- some of the reviews claim that they have had this or similar ecosystems live for 9-10 years! That's pretty metal, and relevant to our purpose here.
Now, the bigger the population and the more you actually care about its survival -- shrimp are pretty expendable, right? -- the harder it is. You'll have "slippage", where some compounds accumulate which are hard to reprocess. These can be jettisoned, or used as extra ammunition for your mass-driver weapon. I can imagine your generation ship also needing a big warehouse full of "extras"; extra nitrogen perhaps, extra marshmallows, and so on.
Why all the extras? Well ... mistakes happen. Your calculations may be slightly off. You need margins. You also need extensive testing before you send the ship off; see the sad fate of Biosphere 2: https://en.wikipedia.org/wiki/Biosphere_2
Looks pretty, but it was like Mad Max inside. Privately, I think they tried to be too cute about it and model too many ecosystems inside, instead of optimizing for survival, but hey. I wasn't invited to the design meetings...
Update: Hey, what about a light source?
Thanks to Justin Thyme for pointing this out. We'll be a tolerable far way from the Sun for most of our journey, so we'll need to do something. Again, our own primitive technology is edging toward the answer. Check here: https://www.spectrumkingled.com/whats-different-about-spectrum-king-led-grow-lights/ . Specifically:
Spectrum King LED full spectrum LED grow lights consistently emit wavelengths in the range of 380 to 779nm. This includes those wavelengths visible to the human eye (what we perceive as color) and the invisible wavelengths, like ultraviolet and infrared. Our 400+ and SK600 LED grow lights truly mimic natural sunlight while matching intensities of traditional HPS lamps with over 100,000 Lux.
Now this product is aimed toward, um ... mitigating the scourge of glaucoma, but clearly these hobbyists are highly motivated to grow plants away from sunlight, low-flying DEA aircraft, and satellite photography. So, now that you have these lamps, any source of electricity will keep your farms in action!
Anyway -- the technology is there. What's missing is the art and the practicum.