Yom tov sheni shel galuyot "the second festival day in the Diaspora" refers to the observance of an extra day of Jewish festivals outside of the land of Israel. Yom tov sheni was established as a gezera (rabbinic decree) by the rabbis of the Sanhedrin in the Second Temple period, approximately 2,000 years ago. The need for a second festival day arises from problems encountered by Jews living in the Diaspora following the Babylonian exile. The Jewish calendar, is a lunar system with months of 29 or 30 days. In Temple times, the length of the month depended on witnesses who had seen the new moon coming to the Temple in Jerusalem. Following confirmation of their evidence, a new Jewish month would be proclaimed. News of this proclamation was subsequently sent out to all Jewish communities. If no witnesses arrived, the new month was proclaimed the following day. Those communities who didn't receive word of the precise date of the beginning of the new month by the time of a festival, would keep the festival for two days, to account for the eventuality the new month wasn't proclaimed only the following day.
דתנן בראשונה היו משיאין משואות משקלקלו הכותים התקינו שיהו שלוחין יוצאין ואילו בטלו כותים עבדינן חד יומא והיכא דמטו שלוחין עבדינן חד יומא והשתא דידעינן בקביעא דירחא מאי טעמא עבדינן תרי יומי משום דשלחו מתם הזהרו במנהג אבותיכם בידיכם זמנין דגזרו המלכות גזרה ואתי לאקלקולי
As it is taught [in a Mishnah]: 'In the beginning, they would light torches [to announce the sighting of the new moon]. Since the confusion of the Samaritans [who would disrupt the torches], they decreed that there would be messengers who went out [and declared the sighting of the new moon].' And if the Samaritans were removed, then we would do one day [of Yom Tov], and in a case where the messengers arrive, we would do one day [of Yom Tov]." But now, since we know the fixing of the months, what's the reason that we do two days? Because they sent a message from there [Israel]: "Take care to maintain the custom of your ancestors, lest the government someday forbid you from studying Torah and you forget how to determine the calendar and come to denigrate the festival [by celebrating the wrong date]."
(כד) שני ימים טובים אלו של גליות שתי קדושות הן ואינן כיום אחד לפיכך דבר שהיה מוקצה ביום טוב ראשון או שנולד בראשון אם הכין אותו לשני הרי זה מותר. כיצד ביצה שנולדה בראשון תאכל בשני. חיה ועוף שניצודו בראשון יאכלו בשני. דבר המחובר לקרקע שנעקר בראשון יאכל בשני. וכן מותר לכחול את העין ביום טוב שני ואע"פ שאין שם חולי. במה דברים אמורים בשני ימים טובים של גליות אבל שני ימים של ראש השנה קדושה אחת הן וכיום אחד הן חשובים לכל אלו הדברים אלא לענין המת בלבד. אבל ביצה שנולדה בראשון של ראש השנה אסורה בשני וכן כל כיוצא בזה. שבת הסמוכה ליום טוב ונולדה ביצה באחד מהן אסורה בשני וכן כל כיוצא בזה. ואפילו נולדה ביום שני לא תאכל בשבת הסמוכה לו
(יד) כל הדברים האלו שאמרנו היו בזמן שהיו בית דין של ארץ ישראל מקדשין על פי הראיה והיו בני הגליות עושין שני ימים כדי להסתלק מן הספק לפי שלא היו יודעין יום שקדשו בני ארץ ישראל. אבל היום שבני ארץ ישראל סומכין על החשבון ומקדשין עליו אין יום טוב שני להסתלק מן הספק אלא מנהג בלבד.
R. Chaim: contradiction in the Rambam. He poskens like Rav that noldah bzeh muteret bzeh. but here he says that the tenai was only practiced in the time when the second day of yontof was observed out of safek, but nowadays when everyone relies on the calculation the essence of yom tov sheni is not to be removed from safek but rather is a minhag/takanah alone. So question is, if we hold that nowadays, as a result of minhag, we no longer view one day of a two day yontof as chol and the other as kodesh, but rather both as kodesh to some degree, how can the rambam posken that an egg born on the first day can be mutar on the second day, when this should not apply because both days are kodesh - and just like an egg born on yontof is not permitted on the shabbos immediately following, so too here it should not be permitted.
His answer - that yes the rambam holds that nowadays the two days of yontof are observed due to minhag and not due to safek, but the nature of this minhag is b'torat sfeika as opposed to b'torat vadai. looking at the first day of yontof, this is vadai yontof. However, looking at dinim that relate to the two days of yontof together, those dinim are in torat sfeika
so - din of noldah b'zeh muteret b'zeh - inherently involves the two days as a combined entity, which is in the torat sfeika and therefore makes sense to posken like rav. Rambam alludes to this reasoning when he says that the two days are two kedushos. This is the concept that, because of the origin of the two day observance out of safek, the minhag is to understand the two days as a seesaw of kedusha - when one day is kodesh, the other is chol; when one day is chol, the other day is kodesh. this applies, however, only when we deal with dinim - like nolad - that deal with both days together as a single entity.