To answer or not to answer...

And now for something entirely different.

Did it ever happen that you were davening somewhere, and the person davening next to you was obviously vocally challenged; he is unable to whisper. So he is davening shemona esrai and you can clearly hear every word that he is saying. This has happened to me, and I was wondering, should I answer amen to his brochos or not? (Obviously, after I finished shemona esrai.)

The consensus of the opinions that I was able to find was that one should not answer amen to such brachos. The reasons, however, were not all identical.

R. Yosef Shalom Elyashiv (Moriah Vol. 11-12 - kislev 5764, page 48) rules, that:

One who hears his friend davening the quiet shemona esrai, is forbidden from answering amen on the brachos of his friend, because [there is a rule that] we do not answer amen on a bracha that is shelo k'din, and brachos of the quiet shemona esrai that are said audibly are shelo k'din and thus amen should not be said.

R. Shlomo Zalmen Aurbach (Halichos Shelomo, 8:32) rules that:

One who hears the quite shemona esrai of his friend, even though he (i.e. the one who hears) is no longer davening, should not answer amen.

In the footnotes (#45) this ruling is explained as follows:

Since they were instituted to be said quietly, and he is acting shelo k'din when he says them audibly, it would make sense not to answer amen.

R. Hershel Schachter (Mepininai HaRav, pg. 35) writes the following:

Our teacher (R. Yoshe Ber Soloveitchik) was careful to audibly speak each word (so that he could hear what he was saying), even of the quiet shemona esrai. And once, one of the students asked our teacher, if he [the student] should answer amen when he hears the brachos of our teacher's quiet shemona esrai. After some thought, our teacher answered that it would seem that one should not answer amen because these brachos should be said [according to the halacha] quietly, and they were never meant to be heard by others, and as such, amen was never instituted for them.

A practical distinction between the two lines of reasoning (RYSE and RSZA who are of the opinion that we don't answer amen because the bracha is shlo k'din and RYBS who held that we don't answer amen because chazal were never misaken amen on these brachos) would be in a case where the person is allowed to daven audibly. For example, a person who is davening alone and can be michaven better if he davens aloud, according to the first opinion (RYSE and RSZA) since he not acting shelo k'din, amen should be said, however, the second opinion (RYBS) would still not answer amen because the brachos of shemona esrai were not included in the takana of answering amen.

I found that the Elef Hamagen on the Mateh Efraim (582:43) rules that on Rosh Hashana or Yom Kippur, since it is permitted to daven shemona esrai audibly, if one hears his friends brachos he may answer amen.