הלכה על ביצה 8:13

And the truth is that the matter today is only a custom - [and] not [from] any other obligation. As we do not make that day because of a doubt, since all of Israel are now experts in the setting of the months and know the exact day of the appointed time according to the traditional calculation that is in their hand, as I wrote above in the Order of Bo el Pharaoh in Commandment 4 (Sefer HaChinukh 4). And the custom was set because at the beginning when there were ordained men in the Land, they would set the month according to sighting, which is the commandment of the Torah - as we have written there. And therefore all the places of Israel (Jewish settlement) far from the chosen place in which it was fixed there, that messengers could not reach to inform them of the day of the fixing, were in doubt about which day was fixed as the [first of the] month - whether the thirtieth [of the previous month] or the thirty-first. And [so] they would make the appointed time two days from this doubt. However they were never in doubt about more than one day, as they would always fix the new moon on the thirtieth or the thirty-first - whether with witnesses or without witnesses. As the thing is well-known and clear that the new moon never delays more [than this]. And therefore whether witnesses came or did not come, they would set the new month [no later than] the thirty-first. And because of this doubt that there is for those far from Jerusalem, they fixed for them at first to make two days of the holiday (Beitzah 4b). And the Sages, may their memory be blessed, ordained (Pesachim 52a) also now for those far from the Land to make two days like the law that they would do at that time - even though all of Israel have become experts in the fixing of the month, as we said. But it is not fitting for those close and - all the more so - those living in the Land itself that they should do anything but one day, like the custom of the people of the place always. And so have they practiced, according to that which we have heard.

And from the reason that we said - that the thing is an ordinance of the sages, not a doubt - some of the commentators said that we do not say now on the two days of the exiles, what was born on this one (the first day) is permitted on that one (the second day). As it comes in the Gemara (Beitzah 4b) that at the time that the thing was a doubt, they would say this. But now since it is from an ordinance of the Sages and not at all from the status of a doubt, we should not say this. Rather their law is like one [unit of] holiness. And there were some that said the Sages, may their memory be blessed, ordained it due to the first doubt, and we should not be more stringent about them than at first. And also since when, "what is born on this one is permitted on that one," was said in the Gemara, the fixing according to sighting [had] already ceased, according to what appears. And so have they practiced today. And all that they said is specifically about the two days of holiday of the appointed times of the year except for Rosh Hashanah - as with Rosh Hashanah, it is like one [unit of] holiness. And what is born on this one is forbidden on that one, because also in the house of council they would sometimes make it two days of holiday not from the status of a doubt - for example, if the witnesses came from the [time of] mincha (afternoon) and onward - such that they would treat today as holy and the next day as holy. And nonetheless even on Rosh Hashanah it is [only on account of] the ordinance of the Sages today to do two days in every place, since we are experts in the fixing of the new month (Mishneh Torah, Sanctification of the New Month 5:12).

The commandment is practiced by males and females in the Land of Israel by Torah writ, as it is stated, "when you eat from the bread of the land," but specifically at the time that all of [the people of] Israel are there, meaning to say their majority. [This is], as it is stated, "when you come" - and the explanation came upon this (Ketubot 20a) [to mean] all of you, and not when some of you come. On a rabbinic level [we are obligated] to separate challah [even] outside of Israel, so that the concept of challah not be forgotten by Israel (Mishneh Torah, Laws of First Fruits and other Gifts to Priests Outside the Sanctuary 5:7). And because the obligation is so that it not be forgotten by Israel, we are accustomed to be lenient with it, such that we only separate a kazayit from a large dough, and throw it into the fire. And it is not given to any priest - child or adult. And I have heard that in some places they are accustomed to separate large challah according to the measurement that the Sages gave us for it, and they give it to a minor priest boy, that impurity does not come to him out of his body or to a minor priest girl who has not yet menstruated. And they even give it to an adult priest who has immersed [to purify himself from genital flows]. And even though he is impure due to contact with the dead, they give him to eat it in these places. It also seems that another leniency outside of Israel is that one may deliberately cancel it out by a majority [of permissible matter], as it [is found] in Tractate Yevamot (it should read, Bekhorot 27a) and in other places in the Gemara. And as far as I know, the same does not apply to any other prohibition in the Torah, with the exception of [branches] that fell into the oven on a festival which can have other [prepared] wood added to it to cancel those, as they said (Beitzah 4b), "a person may add wood to them and permit them." And they said that the reason of the thing is because the prohibited matter burns constantly, meaning to say it is something consumed by the fire, and we can therefore be lenient.