Yesterday, we noted the famous rule of “chatzi shiur” which the Gemara (Yoma 74a) infers from a verse in Parashat Tzav (7:23), and which extends Torah prohibitions to all quantities. One who eats forbidden food is liable to court-administered punishment only if he consumes a certain minimum quantity (generally, a ke-zayit), but the law of chatzi shiur establishes that it is nevertheless forbidden to eat even smaller amounts. Halakha follows the view that this constitutes a Torah prohibition (Rambam, Hilkhot Ma’akhalot Asurot 1:13; Shulchan Arukh, Y.D. 80:6). As we discussed, the Gemara explains this rule as predicated on the factor of “chazi le-itzterufei” – the possibility that after eating a half-quantity of forbidden food, the individual may then eat another portion and thus be liable to punishment.
A number of Acharonim understood the Gemara’s comment to mean that the rule of chatzi shiur does not apply in situations where there is no such possibility. Meaning, if one is incapable of completing the entire minimum quantity, then there is no Torah prohibition forbidding smaller quantities.
One example of this perspective is a discussion by Rav Yechezkel Landau (author of Noda Bi-yehuda) in his Tzelach commentary to Masekhet Pesachim (47a), regarding the prohibition against eating chametz on Pesach. The Rambam, in Hilkhot Chametz U-matza (1:7), cites a Biblical source for the rule prohibiting the consumption of even a slight quantity of chametz on Pesach. Many later writers raised the question of why a special inference is necessary in light of the general principle of chatzi shiur. The Tzelach suggests that the inference was needed to instruct that eating less than a ke-zayit of chametz is forbidden on Pesach even when the factor of “chazi le-itzterufei” is inapplicable, and thus the rule of chatzi shiur does not apply. The case envisioned by the Tzelach is one where one eats less than a ke-zayit of chametz at the final moment of Pesach. As chametz becomes permissible the next moment, there is no possibility of completing the entire quantity of a ke-zayit in this situation. As such, the law of chatzi shiur does not apply. The Rambam therefore points to a specific Biblical source establishing that chametz is forbidden for consumption in any amount, to instruct that this is true even in the final moments of Pesach, when the principle of chatzi shiur does not apply.
Another example is Rabbi Akiva Eiger’s discussion in one of his responsa (154) regarding a person who took a vow not to eat a certain item, and part of that item later was destroyed, leaving behind only a small portion. Rabbi Akiva Eiger ruled that eating the remaining portion would not be forbidden on the level of Torah law, since there is no possibility of the individual eating more of the prohibited product to complete the entire quantity that he forbade upon himself.
This perspective can be seen as well in the Sha’agat Aryeh (81; see also his Gevurat Ari commentary to Masekhet Yoma), who addresses the case of somebody who carries an object on Shabbat through a public domain. The prohibition against carrying in a public domain on Shabbat is defined as carrying a distance of four amot, and nowhere do we find any mention of a Torah prohibition against carrying shorter distances on the grounds of chatzi shiur. The reason, the Sha’agat Aryeh suggests, is because the factor of “chazi le-itzterufei” does not apply to this prohibition. One of the conditions that must be met for one to transgress the prohibition of carrying on Shabbat is intent at the time the item is picked to carry it the prohibited distance. It thus turns out that once a person takes hold of an item in a public domain with the intent to carry it only two amot, for example, he no longer has any possibility of violating the prohibition against carrying. His two-amot of carrying cannot combine with another two-amot of carrying, and therefore, the rule of chatzi shiur is not applicable. Hence, there is no Torah prohibition against carrying something a distance of less than four amot on Shabbat.
(Taken from Rav Asher Weiss’ essay on the topic)