Gemara

Rami bar Tamri was from Pumbadisa. He came to Sura on Erev Yom Kipur, and saw everyone discarding udders. He ate them.

Rav Chisda: Why did you do so?

Rami bar Tamri: I come from Rav Yehudah's area, where we eat udder.

Rav Chisda: One must observe the stringencies of his origin and of his new locale!

Rami: I ate them outside the Techum (more than 2000 Amos from the city).

Pesachim 51a (Abaye): A traveler must adopt the stringencies of his origin and his current locale, i.e. within Bavel, or within Eretz Yisrael, or from Eretz Yisrael to Bavel.

(Beraisa): Two brothers may bathe together. In Kavul (a certain place), they do not.

Once, two sons of R. Gamliel, Hillel and Yehudah, bathed together there. The whole region was in an uproar. Hillel went to the outer room. He did not want to tell them that it is permitted.

51b (Mishnah): One who goes from a place (where people work on Erev Pesach...or vice-versa... he may not deviate...)

Question: Granted, if they work in his origin but not in the new place, he must be stringent like the new place; and he may not deviate due to strife, so he works;

However, if they did not work in his origin and in the new place they do, since he may not deviate, he must work. However, he must follow the stringencies of both places!

Answer #1 (Abaye): 'He may not deviate' refers only to the Reisha (in his origin, they work).

Answer #2 (Rava): It applies to the Seifa. Deviating through not working will not cause strife. People who see him will not say that he forbids working. Rather, they will that he is like many other idle people.

52a - Question (Rav Safra): In our place, we find out which day was Rosh Chodesh (via messengers of Beis Din, before Yom Tov). In settled areas, we may not do Melachah on the day that we know is Chol, due to strife.

May one do Melachah in a Midbar (wilderness)?

Answer (R. Aba citing Rav Ami): It is forbidden in a settled area, it is permitted in a Midbar.

Version #1: R. Noson bar Asya left his Techum and went to Pumbedisa on Yom Tov Sheni. Rav Yosef excommunicated him, for this is more stringent than lashes.

Version #2: Rav Yosef lashed him. Rav and Shmuel say to excommunicate. Rav Yosef holds that this is for regular people. We are more lenient for a Talmid.

Rishonim

Rambam (Hilchos Nedarim 9:16): If one vowed not to enter a city, he may enter the Techum, but he may not enter Iburo (within 71 Amos of it).

Radvaz: We learn that the Ibur of a city is like the city from "va'Yhi bi'Heyos Yehoshua bi'Yricho". We learn that the Techum is not like the city from "u'Madosem mi'Chutz la'Ir Alpayim b'Amah."

Ran (Pesachim 17b DH v'Rabah): Why was Rav Safra forbidden to do Melachah on Yom Tov Sheni? He intended to return! Melachah is different, for it becomes known. Also, perhaps his Melachah was in public and he could not do it in private. We could have answered similarly for Rami bar Tamri. The Gemara preferred to give an answer that applies even if he does not intend to return.

Mordechai (711): We learn from Rami bar Tamri that one must accept the local stringencies only within the Techum, e.g. when they enact to forbid something and decree Cherem on one who transgresses. Hagahos Maimoniyos in Hilchos Nedarim says that one who vowed not to enter a city may enter the Techum. This requires investigation.

Yam Shel Shlomo (8:53): This is not found in our texts of Hagahos Maimoniyos. I say that we cannot learn from there. Surely, one who vows intends only for the city itself. Regarding Isur, the Techum follows the city, for people of the city may go there even on Shabbos. Therefore, any decree or stringent custom of the city applies also to the Techum, including one who happens to enter the Techum. Those who enact do not intend for those outside the Techum. Orchos Chayim forbids a Ben Yisrael in Chutz la'Aretz to do Melachah on Yom Tov Sheni in a Yishuv, even if he intends to return. Before reaching a Yishuv he is permitted, even if he does not intend to return, for he was not yet fixed to be like them. However, if he reached a Yishuv, and he intends to settle, he becomes like them and he is forbidden in a Midbar and in a Yishuv. Whenever one is outside the Techum, we do not impose on him the local stringencies.

Yam Shel Shlomo: Orchos Chayim ruled properly. Heaven forbid to be lenient to act like a Yom Chol where many consider it Kodesh. There is no greater audacity and Apikorsus. He should be excommunicated for disgracing Yom Tov. Those who see him will come to be lenient and say that it is totally Chol and it is a mere custom of their ancestors. They will desecrate it in private.

Tosfos (52a DH b'Yishuv): In the Yishuv, one may not do Melachah even in private, even if he intends to return. This is because Melachah cannot be done in private like other things can.

Ran (Pesachim 17a DH Tanya): If people in a place have a custom to forbid something that they know is permitted, for a fence from Aveirah, a traveler gets the stringencies of both places. If people err and believe that something is forbidden due to letter of the law, one may not permit it in front of ignoramuses, for they will extrapolate (and permit what is really forbidden). A Chacham in that city may be lenient in private. The same applies if people were stringent for a fence, and their children think that letter of the law it is forbidden, we do not tell them that it is only a fence. This was the case with Hillel and Yehudah.

Ba'al ha'Ma'or (Pesachim 17a): People who come (to Chutz la'Aretz) from Eretz Yisrael may not do Melachah on Yom Tov Sheni in a Yishuv. Even though regarding other things, one who intends to return may do in private, here , since it is a great custom that spread throughout all of the Galus, one should not breach the fence.

Milchamos Hash-m: Outside the Techum is considered a Midbar.

Poskim

Shulchan Aruch (OC 496:3): A Ben Eretz Yisrael who came to Chutz la'Aretz may not do Melachah on Yom Tov Sheni in a Yishuv (settled area), even if he intends to return. He is permitted until he reaches a Yishuv, even if he does not intend to return, for he was not yet fixed to be like them.

Beis Yosef (DH Kasav): This is from Orchos Chayim. He says that some Poskim hold that he does not conduct the leniencies of his origin as long as he intends to return.

Ha'aros in Tur ha'Shalem: The text inww Orchos Chayim is 'some hold that he does not conduct the leniencies of his origin if he intends to return only later.'

Taz (2): The Isur is lest this cause strife. Therefore, it is permitted in private. The Maharshal says that he should not be lenient in front of us. The Mechaber should have explained this. He relied on what he wrote in 468:4 (below).

Magen Avraham (4): Tosfos (52a) forbids Melachah, for one cannot do it in private. Also Keneses ha'Gedolah says so in the name of Radvaz, Ra'anach and Rashdam, unlike the Mabit.

Magen Avraham (5): This refers only to Yishuv of Yisrael.

Shulchan Aruch (ibid.): However, if he reached a Yishuv, and he does not intend to return, he becomes like them and he is forbidden both in a Midbar and in a Yishuv. Whenever one is outside the Techum, we do not impose on him stringencies of the place he came to.

Magen Avraham (6): This is even in a Yishuv of Nochrim, since he does not intend to return.

Magen Avraham (7): If he intends to return, he is permitted outside the Techum. If he does not intend to return, he was not yet fixed to be like them. If Bnei Yisrael came to Chutz la'Aretz and did Melachah, we do not excommunicate them (Mabit 2:149). They pray a weekday Shemoneh Esre, like in their origin, When Yom Tov Sheni is on Erev Shabbos, they cook for Shabbos without an Eruv Tavshilin. If one moves with his wife from Eretz Yisrael to Chutz la'Aretz, even if he intends to return, it is as if he intends to settle. If one intends to settle, even if his wife remained there, it is as if he intends to settle. Mishpat Tzedek wrote other reasonings; one should not deviate from the Beis Yosef's ruling. See 574:2. (If one goes from a place where they are not fasting to a place where they are fasting, even if he intends to return he must fast with them, unless he goes outside the Techum.)

Mishnah Berurah (9): One may not do Melachah even in private, like we say in 468:4.

Kaf ha'Chayim (33): The Mabit and Taz permit in private. Many forbid.

Kaf ha'Chayim (34): If one sees one doing Melachah, even in private, he may hit him to stop him. One who tells him to do Melachah transgresses "v'Lifnei Iver Lo Siten Michshol."

Kaf ha'Chayim (36): On Motza'ei Yom Tov Rishon, he says Havdalah in private. On Shemini Atzeres he may not do Hakafos with the Sefer Torah.

Kaf ha'Chayim (37): On the second night of Pesach, if he intends to return to Eretz Yisrael, he does not the extra Berachos at the Seder, e.g. Kidush, Go'al Yisrael, Al Achilas Matzah, Al Achilas Maror and Hallel. He reads the Hagadah like one reading the Torah. If he is alone, he does not do a Seder at all.

Mishnah Berurah (11): When he intends to settle, he is forbidden even when he reaches a Yishuv of Nochrim. Some permit until he reaches a Yishuv of Yisrael

Mishnah Berurah (12): Once he reaches a Yishuv he is forbidden, even if later he goes to the Midbar.

Mishnah Berurah (13): Poskim exempt a Ben Eretz Yisrael from Eruv Tavshilin, for this is in private, since he intends to return. Therefore, he prays a weekday Shemoneh Esre on Yom Tov Sheni, and puts on Tefilin. He must wear Yom Tov clothing, for this is an open matter.

Birkei Yosef (3): The Taz relied on Ba'al ha'Ma'or to permit Melachah in private. The Ba'al ha'Ma'or explicitly forbids!

Avkas Rochel (26): If one went from Chutz la'Aretz to Eretz Yisrael and intends to return, he conducts like his origin, even to be lenient, just not in front of the residents, like the Rosh says. Rabah did not need to conceal that he was eating Chelev De'aisra, since he ate in private, like the Ran says. Anyone who intends to return is like one who is still in his origin in every way, but only in private, to avoid strife. Tefilah is in private, so surely he prays like in his origin.

Ha'aros on Birkei Yosef (1): In Tov Ayin (17), the Birkei Yosef says that it sounds like Avkas Rochel permits in private, but in the Shulchan Aruch he connotes that it is forbidden. Nowadays this does not apply so much, for all know that Bnei Eretz Yisrael do only one day of Yom Tov, for there is a great settlement in Eretz Yisrael, and many people from Chutz la'Aretz come to Eretz Yisrael. Rabbeinu wrote for his generation.

Shulchan Aruch (468:4): If one goes from a place where people do Melachah (on Erev Pesach) to a place where they do not, he may not do Melachah in the Yishuv, due to strife. He may do in the Midbar. One should never deviate, due to strife. Similarly, one who intends to return to his org is lenient or stringent people of his org, but he should not show this to people where he is now, due to strife.

Gra (DH Lo): This is unlike Tosfos (52a).

Gra (DH v'Af): 'One should never deviate, due to strife', i.e. to show that he is idle due to Isur. The Shulchan Aruch rules like Rava's answer. Doing in front of them causes strife, so it is forbidden.

Magen Avraham (12): In private, everything is permitted (like one's origin) except for Melachah, which cannot be done in private. Therefore, it is permitted only in a Midbar.

Mishnah Berurah (14): If one goes from a place where they are lenient about a matter to a place where they are stringent, if he does not intend to settle there, letter of the law he may be stringent. We permit in private in his house, but not in public, due to strife. What cannot be done so covertly, e.g. Melachah, he should not do even in private in the city. He may be lenient in a field outside the Techum. If he intends to settle there, he gets all local stringencies the moment he reaches the Techum. Afterwards, he may not be lenient outside the Techum.

Mishnah Berurah (18): 'Midbar' is a field outside the city where people of the city do not often go.