My first (rather informal) attempt at germinating carrot seeds in bottles failed. I placed a few small stones at the bottom of each bottle, put a layer of activated charcoal on top, then put damp soil on top until each bottle was about half full. I put a single carrot seed in each bottle, covered over with some soil. I left the bottles in a reasonably well lit windowsill. The carrot seeds didn’t germinate. I noticed that a few weed seeds that had been in the soil did germinate, and produced rather spindly seedlings which died off after a few days. Now, six weeks later, there is nothing green growing in either bottle. What happened, and why did all of the weeds die? I’m not sure. One possibility is that because there is nothing to recycle the CO2 produced by the soil, it accumulates. Perhaps this makes the water in the bottle acidic. I can test this by measuring the pH of the water and comparing it to a sample of soil from the same place that I took the soil to fill the bottle. I could also try to quickly attach a CO2 meter to the top of one of the bottles without letting too much air escape to see what it reports.

UPDATE 22nd April 2018:
When a CO2 sensor was attached to one of these bottles it did indeed show that the CO2 level was high - over 5000ppm.