Tosfos 9b "Hasam" write that from sotah we only can be metaher b'reshus harabim if it is possible, as the case of sotah is possible, but if it is impossible (e.g. there are 2 people and we know one of them is tamei) we can't use sotah to be metaher both of them. Yet using chezkas kashrus, we can be metaher them both even if it's impossible. But why - the drasha from sotah must conform to the case of sotah, which was possible and not impossible. SO shouldn't the din of chazaka have to conform to the source of chasaka as well? THe gemara proves chazaka from negai batim, and there it is possible (in fact, quite likely) that the nega stayed its size before the kohen left. If so, we should only be able to rely on chazaka if it's possible, just like we say by sotah. Why, then, can we be metaher both people based on chazaka, even though it's impossible?
Yaron Barach, Brooklyn NY
Baruch she'Kivanta again! Your question is asked by the Achronim!
(1)
(a) Shev Shmaitata 7:2 (written by the author of Ketzot HaChoshen) explains that there is a basic difference between Sotah and Chazaka. In the case of the lady who had been warned by her husband not to be alone with such-and-such but did not listen and got caught alone with the man, she is given a Din as if she certainly had beeyah with him, even though we do not know for sure if it actually happened (See Sotah end 28a that even though there is only a doubt whether she was actually unfaithful to her husband, nevertheless the Torah considers this as if she certainly was). In contrast when something is placed on a chazaka this does not mean we are saying for certain that the situation is really the way the chazaka decides it is, but rather because we do not know for sure, we leave the situation like it was before i.e. we leave it on the original chazaka. Shev Shmaitata expresses this by writing that cahzaka is not a "Hora'ah Vadait" - not a ruling made out of certainty.
(b)So if there are 2 paths, and underneath one of them a corpse is buried but we do not know under which one, and 1 person walks on each of the paths, we say that both of them are tahor even though this is impossible, because chazaka tells us to leave the situation like it was before, namely that they were both tahor. The limud of sotah is different because it tells us how things really happened,and therefore we can only use it if it is possible, whilst the limud of chazaka does not tell us necessarily how it was, but rather what we learn out from Nigei Batim is that we behave as if the nega was still in the house just like it always was, even though we do not know for sure if this true. So we can be metaher both people even though this is impossible, because the idea of chazaka was never in the first place intended to be a certainty, but we are merely behaving as if things never changed.
(c) It seems to me that the above idea is hinted at in Tosfos Nazir 57a Dh b'Omer who writes that safek tuma in Reshut Harabim is not derived from Sotah but rather each case is placed on its chazaka. Tosfos writes that this is derived from a verse in Chulin 10b - that we should place everything on its chazaka of being tahor even though one of the people is surely tamei, since we do not know which is the tamei one. One sees from Tosfos that this is what we actually derive from Nigei Batim - that even though it is impossible, nevertheless we are metaher each one by placing it on its chazaka.
(2) See another answer to your question in the commentary of Rav Shlomo Zalman Auerbach zatsal to Shev Shmaitata 1:17, note 79.
KOL TUV
Dovid Bloom