In general, when a forbidden food becomes mixed with a permitted food, it is batel be-shishim (rendered insignificant if the forbidden food constitutes less than one sixtieth of the mixture); in such small quantities, it does not contribute flavor. At the level of Torah law, ĥametz is also batel be-shishim. The Sages, however, ordained that even a drop of ĥametz render a permitted food forbidden when mixed with it. Even if the quantity of permitted food is a thousand or ten thousand times greater than the ĥametz, the entire mixture becomes forbidden.
The Sages added this stringency because the Torah itself is more stringent about ĥametz than other forbidden foods. This is true in two respects: 1) generally, if one consumes a Torah-forbidden food, the punishment is malkot (lashes), but one who eats ĥametz incurs the more severe punishment of karet (extirpation); 2) whereas all other forbidden foods may be kept in one’s home, ĥametz can neither be seen nor be found in our homes throughout Pesaĥ. The Sages therefore continued in this direction by establishing a safeguard: even if a drop of ĥametz falls into a food, it is forbidden to consume or derive benefit from it. Another reason for this stringency is that all other forbidden foods are prohibited throughout the year, and we are therefore accustomed to distancing ourselves from them, but since we eat ĥametz all year long, we are liable to forget that it is forbidden on Pesaĥ. The Sages, therefore, are more stringent about ĥametz, so that everybody remembers to be careful about it.
This law, that even a drop of ĥametz renders a mixture forbidden, goes into effect with the onset of Pesaĥ. Before Pesaĥ, ĥametz is batel be-shishim like all other forbidden foods. Although the prohibition against eating ĥametz and the mitzva to dispose of ĥametz go into effect at midday on the fourteenth of Nisan, the law that ĥametz is not batel be-shishim does not take effect until Pesaĥ begins. This is because one who consumes ĥametz incurs karet only once Pesaĥ has begun, when the prohibitions of bal yera’eh and bal yimatzei take effect (SA 447:2).
. According to She’iltot, Rabbeinu Tam, and Raz, ĥametz is similar to other forbidden foods and is batel be-shishim. All other poskim (including Rif, Rosh, and Rambam) maintain that ĥametz is not batel even in a thousand-to-one ratio, as per the opinion of Rava, following Rav, in Pesaĥim 30a. Even Rabbeinu Tam and Raz refrained from acting leniently (see Birur Halakha ad loc.). However, MB 447:2 states, citing Aĥaronim, that in a case where there are other factors that support a lenient ruling, She’iltot and Rabbeinu Tam can also be taken into consideration.
The aforementioned reasons for the strict nature of ĥametz are from Rashi, Rosh, Smak, Rabbeinu Yona, and many others. The first reason is the principal one, and therefore ĥametz becomes forbidden in the most minuscule quantities only once Pesaĥ begins. However, Rambam and Ramban explain that the reason a tiny amount of ĥametz is forbidden is that after Pesaĥ it will again become permitted, since on the Torah level ĥametz she-avar alav ha-Pesaĥ is permissible, and anything that will become permissible in the future (davar she-yesh lo matirin) is not batel in any mixture. According to this opinion, the tiniest amounts of ĥametz are forbidden as early as midday of the fourteenth, and this is indeed what Magid Mishneh claims is Rambam’s opinion. This is also the opinion of several Rishonim and Aĥaronim. It is possible, however, that according to this, ĥametz is not batel after midday on the fourteenth unless it is mixed with the same sort of food item (min be-mino). Kaf Ha-ĥayim 447:46 and Hilkhot Ĥag Be-ĥag 9:23 quote those who adopt this opinion. Nonetheless, even based on the rationale that we are used to eating ĥametz, there are still grounds to forbid even the tiniest amounts of ĥametz starting from midday of the fourteenth, as Ran writes.
SA adopts the opinion that tiny amounts of ĥametz only become forbidden once Pesaĥ begins, and most Aĥaronim accept this view.