Gemara

4b (Mishnah - R. Meir): One may eat Chametz until the end of the fifth hour.

R. Yehudah permits until the end of four hours.

Question: All forbid Chametz from six hours on Erev Pesach. What is the source of this?

5a - Answer (Rava): "Lo Sishchat Al Chametz Dam Zivchi" (do not slaughter Pesach while you still have Chametz) forbids Chametz on Erev Pesach.

Surely, it is [the same for everyone,] the [earliest] time to slaughter Pesach.

61a (Mishnah): If Pesach was slaughtered before midday it is Pasul, for it says "Bein ha'Arbayim."

11b (Mishnah - R. Meir): If Reuven testifies that an event occurred in the third hour of the day, and David says that it was in the fifth, their testimony is disqualified.

R. Yehudah says, it is valid.

12a (Rava): R. Meir holds that a person errs two hours. R. Yehudah holds that a person errs up to three hours.

12b - Question: If so, R. Meir and R. Yehudah should forbid Chametz from the beginning of the fifth and fourth hour, respectively!

Answer: In the fourth and fifth hour the sun is in the east, and in the seventh it is in the west. People do not confuse them.

Question: If so, R. Meir he should permit eating also in the sixth hour!

Answer (Rav Ada bar Ahavah): In the sixth hour the sun is virtually in the middle of the sky [like in the seventh. These could be confused.]

Question: R. Yehudah should permit eating also in the fifth hour!

Answer (Rava): He decrees due to a cloudy day.

Question: If so, also at four hours we should not eat!

Answer (Rav Papa): Most people normally eat at four hours of the day. (People know when this is.)

Megilah 20b (Mishnah): If any of these [daytime Mitzvos] was done after dawn, it is Kosher.

(R. Zeira): We learn from "we work... from dawn until Tzeis ha'Kochavim" and "we watched at night, and worked by day."

Rishonim

Rambam (Perush ha'Mishnayos Berachos 1:2): All the hours mentioned in the Mishnayos are relative hours. I.e. there are 12 hours during the day. Three hours are a quarter of the day.

Terumas ha'Deshen (121): In a leap year when the day is long in our lands (Austria), at the end of four hours, about three hours remain before midday. One may eat Chametz until two hours before midday. Even though Rava explains that R. Yehudah decrees due to a cloudy day, and everyone eats at four hours, we can say that even on long days, people finish eating at the end of four hours. There is reason to decree due to a cloudy day. However, since the first answer holds that a person errs two hours, we need not forbid more than two hours before midday. (Note: Rava said that R. Meir holds that people err up to two hours. However, the Halachah follows R. Meir regarding testimony.) We conclude with another answer, but we do not retract from decreeing only two hours before midday. R. Yehudah said "one may eat all four hours." He did not say that it depends on the time before midday, for on average days the fourth hour is two hours before midday. One who is lenient does not lose.

Tosfos (Pesachim 2a DH v'Ha): The Ri says that it was obvious to the Gemara that until Tzeis ha'Kochavim is day, for in Megilah we conclude that day is from dawn until Tzeis ha'Kochavim.

Tosfos (Pesachim 11b DH Echad): The beginning of the second hour of the day is before sunrise. One walks 40 Mil in a day, and five Mil from dawn until sunrise (Pesachim 93b), i.e. there are one and a half hours from dawn to sunrise.

Poskim

Shulchan Aruch (OC 443:1): Chametz is Asur b'Hana'ah after six hours on Erev Pesach. Two hours beforehand, i.e. from the start of the fifth hour, one may benefit from it, but not eat it.

Rema: In a leap year when the day is long, the four hours are based on the length of the day. One may eat Chametz until a third of the day.

Beis Yosef (431 DH u'Mah she'Chasav Ela): Based on Perush ha'Mishnayos, one may eat Chametz until four hours, i.e. a third of the day, whether in a regular year when the day is short, or in a leap year when the day is long. Also Terumas ha'Deshen says so.

Rebuttal (Bach DH Kasav): The Terumas ha'Deshen always permits until two standard (60-minute) hours before midday. This is more than a third of the day! The Rema brought both opinions (see also below). We are stringent not to permit past a third of the day. Also Maharil (Hilchos Erev Pesach 2) says so. The hours begin from dawn. This is clear from Tosfos 2a and 11b. The verse "we work..." connotes like this.

Bach (2): It is an excessive stringency to forbid in the fifth hour due to a cloudy day. Chachamim forbade only eating. However, even if it is not cloudy people could confuse the sixth and seventh hours, so Chachamim made the sixth hour like the seventh, and forbade even Hana'ah.

Magen Avraham (3): The Bach counts the hours from dawn until Tzeis ha'Kochavim. The Levush counts from sunrise to sunset. The difference between them is small. If one forgot to sell Chametz, he may rely on the latter opinion [in the Rema below] to sell until an hour before midday.

Rebuttal (Gra DH Shelish): This is like Ula, but he was refuted. We hold like R. Yehudah (94a). See what I wrote in 261:2 (that R. Yehudah holds that Bein ha'Shemashos lasts the time to walk 3/4 quarters of a Mil. According to the Magen Avraham, the time to walk a Mil) is 3/8 [of an hour, i.e. 22.5 minutes], a 40th of an hour (1.5 minutes) less than 2/5 of an hour (24 minutes). This is not precise. See Tosfos 11b [who says that one walks 5 Mil in 90 minutes] and YD 69:6 [which says that one must let meat salt for the time to walk a Mil, about a third of an hour. Granted, if the time is 18 minutes, the Mechaber was stringently imprecise. According to the Magen Avraham, he was leniently imprecise! This is difficult - Damesek Eliezer.]

Gra (DH uvi'Shnas): The Rambam says that all hours of the Mishnah are relative. Pesachim 4b forbids Chametz after six hours. This is midday (Rashi 5a DH Ach, and Rava 5a). The Agur brought a proof from Avodah Zarah 25a (when the sun stood still for Yehoshua. The Gemara discusses how much was added to the 12 hours of daylight, even though it was in summer.)

Note: The Agur says that the day ends at Tzeis ha'Kochavim.

Mishnah Berurah (7): In countries where Erev Pesach is less than 12 hours, one may eat Chametz only a third of the day.

Mishnah Berurah (8): Many Acharonim calculate from dawn to Tzeis ha'Kochavim. Some calculate from sunrise to sunset, including the Gra. L'Chatchilah one should be stringent like the first opinion.

Rema (ibid.): Some permit until two hours before midday.

Taz (3): The Rema is astounding. Terumas ha'Deshen connotes that he discusses two of our hours, i.e. each is a 24th of an entire day. Surely, eating until four hours is not our hours. The Torah does not mention hours! It depends on when one may slaughter Pesach, i.e. from midday. We call this six hours. Surely, people eat at four relative hours of the day. People can err by two relative hours. The Terumas ha'Deshen is astounding. He says that the Isur depends on our hours. Surely, all the hours are relative. One may not eat after a third of the day from dawn. Also the Bach says that one may not rely on the latter opinion.

Gra (DH v'Yesh Omrim): This is like Tosfos says in many places, that the conclusion is not a retraction. The answers do not argue with each other.

Mishnah Berurah (9): One may rely on the latter opinion to avoid a big loss if he did not sell his Chametz beforehand.

Bi'ur Halachah (DH v'Yesh): The Terumas ha'Deshen is stringent in countries [in the southern hemisphere] where Erev Pesach is a short day. He permits eating until two hours before midday. The first opinion allows a third of the day, which is later. Nehar Shalom and Mor u'Ktzi'ah say so.

Note: According to the Magen Avraham, every day is more than 12 (60-minute) hours in the entire inhabited southern hemisphere. Even according to the Gra, the shortest possible Erev Pesach is when it falls on April 23. Then, the Terumas ha'Deshen's stringency is 11 minutes before a third of the day in Beunos Aires, and 7 minutes before in Johannesburg and less at lower latitudes. In an average non-leap year, the stringency is less than half of this.

Bi'ur Halachah: I say that the Terumas ha'Deshen comes only to be more lenient than the first opinion. The Gemara answered that people do not err more than two hours, and the fourth hour is when people eat. The Terumas ha'Deshen says that these answers do not argue. We do not forbid within two hours, lest he eat after midday, for all eat in the fourth hour. Presumably, on short days people eat at four relative hours, even though it is within two hours of midday. One does not err about meal-time. In any case one may rely on the first opinion, since many say that it is primary.

Kaf ha'Chayim (21): The Levush, Lechem Chamudos, Rama (in Alfasi Zuta) and others calculate based on 12 hours from sunrise to sunset. The Bach brings from Tosfos that we count from dawn, and so say the Terumas ha'Deshen, Taz, Pri Chodosh, Eliyahu Rabah and others. The custom is like them due to the stringency of Chametz.

Note: The Terumas ha'Deshen, Beis Yosef and Rema discuss eating Chametz until four relative hours "in a leap year." In a regular year, Erev Pesach can be as early as March 25 (e.g. 5773). This is close to Tekufas Nisan (the equinox, March 22), so relative hours are close to standard hours. If we measure from sunrise to sunset, the excess of four relative hours over four standard hours is only about seven minutes in Eretz Yisrael (or similar latitudes), nine in Vienna (central Europe), and more in higher latitudes. This is not so significant, especially if one does not have super accurate clocks that allow eating until the last minute. In a leap year, Erev Pesach is between April 14 (e.g. 5774) and April 23 (e.g. 5765), so the excess is between 20 and 25 minutes in Eretz Yisrael, and 31-42 in Vienna. We can understand why the Terumas ha'Deshen, Beis Yosef and Rema discuss a leap year. However, if we measure from dawn to Tzeis ha'Kochavim, the excess is always significant (more than 30 minutes) even in Eretz Yisrael. There would be no reason to specify a leap year!