Gemara

Question: How could someone transgress idolatry b'Shogeg without intention?

If he thought he was bowing to a Beis ha'Keneses, and it really was idolatry, he intended to serve Hash-m! (This is not idolatry.)

Answer #1: Rather, he bowed to a statue.

Rejection: If he accepted it to be his god, he was Mezid. If not, he did not serve idolatry!

Answer #2: Rather, he served idolatry due to love or fear [of a person].

Question: This is like Abaye, who obligates for serving due to love or fear. According to Rava, who exempts, how can we answer?

Sanhedrin 61b - Support (Abaye, for himself - Beraisa): "Lo Sishtachaveh Lahem" (to idols), but you may bow to a person;

Suggestion: Perhaps you may bow to a person that people serve [like idolatry], like Haman!

Rejection: "V'Lo Sa'avdem."

(Abaye): People served Haman because they feared Achashverosh, and the Torah considers this idolatry!

Rejection (Rava): No. The Torah forbids bowing to someone who resembles Haman in one respect, and not in all respects:

One may not bow to a person who is served, such as Haman. This is only if people truly intend to serve him, unlike Haman, who was served only out of fear.

Berachos 27b: R. Yirmeyah bar Aba prayed in back of Rav. Rav did not (return to his place, for he would have had to) interrupt between R. Yirmeyah and the wall.

Inference: A Talmid may pray in back of his Rebbi.

Question (Rav Yehudah): One may not pray in back of his Rebbi!

(Beraisa - R. Eliezer): One who prays in back of his Rebbi causes the Shechinah to depart from Yisrael.

Answer: R. Yirmeyah bar Aba was a Talmid Chaver of Rav (a peer of Rav's who had learned from him).

Rishonim

R. Yonah (Berachos 18b DH Al): One may not pray in back of his Rebbi, lest his Rebbi need to step back and he will not be able to, for the Talmid is still praying. If he distances four Amos in back, it is permitted, for this is like another Reshus.

Tosfos (27b DH v'Lo): Rashi says that one may not pray in back of his Rebbi due to haughtiness. Some say that it looks like he bows to his Rebbi.

Tosfos (72b DH Rava): The Beraisa says that one may bow to a person, but not to one who is served [due to love or fear], like Haman. This implies that one is liable even without accepting it for a god. Haman is contrasted to other people. The only difference is that Haman is served, but also he was not accepted for a god. Since Rava exempts for serving due to love or fear, how does he explain why Mordechai didn't bow to Haman? The Medrash says that Haman had two idols over his heart. Alternatively, Mordechai refused for Kidush Hash-m.

Poskim

Shulchan Aruch (OC 90:24): One may not pray in back of his Rebbi. Some say that this does not apply b'Tzibur, if this is where he normally sits. Even though it is good to be stringent, the custom is to be lenient. If he distanced four Amos, it is permitted. See YD 242 (brought below).

Mishnah Berurah (76): B'Tzibur, all know that this is his fixed place, so there is no concern for haughtiness or looking like he bows to him.

Mishnah Berurah (79): The Pri Megadim brings from the Pri Chodosh that one who prays in back should distance himself four Amos and three steps, so his Rebbi will be able to step back immediately.

Kaf ha'Chayim (141): According to Tosfos, the concern is for bowing, so it is permitted b'Tzibur. The Mechaber rules like R. Yonah (lest the Rebbi need to wait for the Talmid).

Levush (24): Some say that it looks like he bows to his Rebbi and makes him an idol, Chas v'Shalom. This is not a problem outside of four Amos.

Levush (25): Regarding a Talmid Chaver, we are not concerned lest it looks like he bows to his Rebbi.

Eliyahu Rabah (26): We need not forbid directly in back of one's Rebbi. This is always forbidden, due to a Chatzitzah (between the Talmid and the wall)! Rather, he is to the side, in back. This is why Rashi did not say that the problem is that it looks like he bows to him.

Shulchan Aruch (102:1): One may not sit within four Amos of someone praying, not in front or to the side. If he is engaged in matters of Tefilah, he need not distance. Some permit one who is engaged in Torah. Some forbid directly in front as far as one can see, even if he is engaged in Keri'as Shema.

Mishnah Berurah (8): In front is forbidden for it looks like he bows to him. If so, it is forbidden only to sit, but he may stand, even within four Amos. Perhaps one may not even stand, for this disturbs his Kavanah.

Mishnah Berurah (9): The Pri Chodosh rules like the first opinion. The other Acharonim say that it is good to be stringent. I say that surely one need not be stringent to stand outside of four Amos, and perhaps even within four Amos.

Eliyahu Rabah (4): We said that outside of four Amos is not a problem. That refers to a Talmid in back of his Rebbi. We must say that when the one in front sits, it is worse, even if the one in front is not his Rebbi, even past four Amos.

Eliyahu Rabah (5): Normally, Reuven cannot forbid a place that was permitted to Shimon, e.g. if Shimon was sitting and Reuven begins to pray next to him, Shimon need not rise. However, if Shimon is in front, perhaps he must rise, for it looks like Reuven bows to him.

Aruch ha'Shulchan (5): Tosfos, the Rosh, R. Yonah, the Mordechai, Semag and the Rashba all wrote in the name of Ge'onim that one engaged in Tefilah [and Torah] may sit. If it is forbidden in front, why did they omit this, and cause people to stumble? The Beis Yosef brought this in the name of Ohel Mo'ed. Seemingly, it is a lone opinion. The Levush explains 'it looks like he bows to a person.' I think he means that if he is directly in front, it is repulsive for this reason. He did not need to explain this.

Bach (131:1): The Tur brings from R. Natrunai Ga'on that one who falls on his face [in Nefilas Apayim] must suspend his head above the ground, lest it look like he bows to the one in front of him. Some texts of the Tur do not say 'lest it look like he bows to the one in front of him.' They say just 'he must suspend his head above the ground.' If his face would be flush to the ground, there would be concern for bowing on a stone floor, even if he bows to honor Hash-m.

Shulchan Aruch (150:5): The Zekenim sit in the Beis ha'Keneses facing the Tzibur. Everyone else faces the Kodesh and the faces of the Zekenim.

Levush (5, brought in Taz 2): There should not be any place in the Beis ha'Keneses between the Bimah and the Aron Kodesh. It is disgraceful and forbidden to face the Bimah with his back to the Aron. Also, he interrupts between those who [get Aliyos and] bless on the Sefer Torah. It looks like they bow to him when they bow to bless.

Magen Avraham (139:4): The Bach says those who bow in Birkas ha'Torah err, for we bow only where Chachamim enacted to bow. The Shach brings from the Roke'ach that it is an ancient custom. This is because people intend merely for Kevod ha'Torah.

Chayei Adam (1:17:19): The custom is that some people sit between the Bimah and Aron. We are not concerned that it looks like people bow to him when they bless on the Sefer Torah, since they bow merely to honor the Torah.

Mishnah Berurah (14): One may sit between the Bimah and the Aron if he is to the side [so it does not look like those who bless bow to him].

Kaf ha'Chayim (46): Mishbetzos Zahav says that since the people between the Bimah and Aron have their backs to the Bimah, it does not look like the Olim bow to them.

Shulchan Aruch (YD 242:16): One may not pray in back of his Rebbi. He should distance himself. He should not be directly in back of him. Rather, he should tilt to the side.