I know one is not allowed to reap plants on Shabbat, but does this apply to hydroponics on shabbos? I know for instance one can cultivate hydroponics on shmita (sabbatical) year. Does this mean that in a hydroponics system one can reap from it on Shabbat?
Star-K address this concept here
Nurturing plants is one of the 39 melachos, prohibited categories of work on Shabbos and Yom Tov. Therefore, on those days the seeds may not be placed in their base, nor may nutrients or water be added. (Shulchan Aruch O.C. 336:11. See Minchas Chinuch 32 and Teshuvos Har Tzvi (Zeraim 2:31))
This is an excellent question, and a pet peeve of mine :)
To frame the question in another way: how can pulling some plants out of water be harvesting - harvesting should require an action of cutting from the ground? [It's important to note that many types of hydroponics are grown in some nutrient containing medium and this would appear to be classic harvesting. The discussion that follows is for hydroponics grown solely in a liquid.)
As others pointed out, the mainstream halachic approach is that it is forbidden. Rav Falk, in the Machzeh Eliyahu @dov linked to above is an excellent approach to the sugya. That being said, it's clearly not classic harvesting. What follows are some highlights from the sugya.
The gemara in Shabbos appears to address this question, and provides a unique source for a prohibition on harvesting from liquid: Abaya taught (Shabbos 108a) that pulling a mushroom from a moist surface is prohibited because he is being עוֹקֵר דָּבָר מִגִּידּוּלוֹ. (Uprooting something from its place of growth). The continuation of the gemara makes clear that this is only a problem because mushrooms naturally grow on moist surfaces (הַיְינוּ רְבִיתֵיהּ ) The gemara there juxtaposes three types of actions and includes them under the same category of עוֹקֵר דָּבָר מִגִּידּוּלוֹ. First, aborting a cow fetus, Second, harvesting hops (a parasitic plant) and finally harvesting mushrooms. The Ramban in shabbos has an explantion of the gemara that explains these are all not "classic harvesting" but forbidden under the broader category of "uprooting." [But see the Meiri there who understands this as a broad definition of "classic harvesting"]. If I recall correctly, based on this Ramban, Rav Shlomo Miller has a teshuva limiting the prohibition to plants that naturally grow in damp (like mushrooms or sprouts). That being said, most poskim take this prohibition so far as to prohibit pulling flowers out of a vase. They argue that the water/plant food is nurturing the flowers and pulling them out is harvesting (See e.g. Nishmas Shabbos 241). In summary, harvesting hydroponics is forbidden. However (according to the Ramban and most others), it's never classic harvesting "kotzer", it's a sub-prohibition of kotzer called עוֹקֵר דָּבָר מִגִּידּוּלוֹ which has different rules. The only heter that I would rely on is that if you have plants in a nutrient bath, and the flow of the water is stopped before shabbos and the water drains by itself, picking up the plants would not be a prohibited act.