The minimum length for a lulav is four hand-breadths, one more than that of the myrtle and the willow, and this is so that it will be “long enough to wave.” There is a special link between the lulav and waving:

  • The spiritual service of the soul in this world elevates it to the level of “motion,” i.e. true progress without limit, in which the highest level is incomparably higher than the lowest. This progress is expressed in the Jewish custom of swaying while learning Torah and praying. Unlimited progress is possible only through attachment to G‑dliness, the truly infinite. Since true attachment flows specifically from involvement in Torah, waving also pertains specifically to the lulav, which represents learning Torah.
  • The motion of waving represents constant addition in the learning of Torah. As our sages say: “to labor in the Torah and be involved in it, and add to it every day.”
  • To truly understand an opinion in Torah requires argument and reasoning: at the beginning it seems to us that the reason is such-and-such, afterwards we decide that it is different, and thus we bring the opinion “back and forth” and “wave” it from one side to the other until we reach the true conclusion.

(Likkutei Sichot, vol. 4, p. 1162)