(paraphrasing Capt. Kirk: Does God need a starship?)
On an email list, a member noted that in some shuls, people face the back for the last verse of Lecha Dodi, even when there's no door there.
What they are actually doing? Turning away from the Torah to greet an abstraction.
Is there perhaps a greater problem in turning one's back on the Torah? R' Riskin once reprimanded a founding member of his shul who, following his personal (I had been told German, but other correspondents say not) custom, turned completely away from the Kohanim during duchening, thereby also turning his back on the Aron, containing the Torahs. Said member thereafter turned away, but not completely around.
And also, what are we doing in turning for L'cha Dodi?
- turning to the door to greet the Queen?
- turning away from the Aron, if the queen approaches the Aron?
- turning to the West, since the sun sets in the west, which signals the beginning of Shabbat?
Moshe Hallamish, in his recent "Kabbalistic Practices on Shabbat", considers the question on pp. 228-230.
It seems to have started with the Tzfat group, with the terse notation "they go out to the field to greet the Shabbat, facing west." Later, that seems to have glommed onto just the last stanza of Lecha Dodi.
By 17th-century Galicia, a source notes "they turn towards the western door". Other late teshuvot note "turning towards the door" or "turning to the west, because the Shechina is in the west".
The Mishna Brura (turn to the west to greet the shechina which is in the west) and the Aruch haShulchan (turn to the door) (both c. 1900) differ. R' B. Zilber (Oz Nidberu) tries to reconcile them, in terms of synagogue construction. He brings a third opinion explaining the "turn to the west" as non-literal, rather practical, to signal the mourners who are sitting in the western doorway that they can come in. He notes that shuls in the North of Israel, which should turn from South to North, actually turn to the West. So the reason must be to greet the Queen, Extra Soul, etc. from the kabbalistic reasons.
(MB and AhS deal with this in ch. 262).
The Yad Beit HaLevi notes that Sefardim in Tzfat would go out to the courtyard and turn to the West; in Galut this doesn't happen, but they still turn to the West, so it's clear that the whole thing is symbolic.
R' Zilber notes that since the Torahs are more than 10 tefachim above the ground (I know shuls where they are not), and turning away is only prohibited to greet a friend, because it's like bowing to the friend (and away from the Torahs) it is not a problem to turn away from the Torahs for this (citing Levush 150; this Levush is also cited by R' Ezriel Hildesheimer, OH #22).
Hallamish concludes with a passage from the siddur Tikun Shabbat by R' Moshe b. Gershom of Zalshin, 1827, saying that one should say the last verse with great joy, facing west from which one gets the Extra Soul, and the Sabbath Queen, adornment of Her husband. This implies that the Shechinah/Sabbath Queen nourishes us with the Extra Soul.
(note: also posted to Mail-Jewish)