Egypt sailed into the uncharted waters of peace tonight with scense of joy and scenes of indifference, but without a single reported act of significant protest.

Reports from the Mediterranean prot city of Alexandria told of wild jubilation, with ships in the harbor sounding sirens and motorists blowing horns as the signing ceremony was shown live on Egyptian television. Fireworks went off in the streets as the horns beeped out the rhythm of "Sadat, Sadat."

Here in Cairo the seene was much different. Although many shops closed early as their workers went home to watch the ceremony and the streets were much less crowded than usual, there was no official celebration and little sign of public excitement.

It was hard to tell, in a tour of downtown Cairo, that an event was unfolding that formally ends 30 years of debilitating struggle and affects the way an entire nation sees itself, its palce in history and its ties to its neighbors.

In the cafes of Cairo's working-class neighborhoods, some young men cheered for President Anwar Sadat and clustered around television sets to watch him, Prime Minister Menachem Begin and President Carter at the White House ceremony. But others never looked up from their backgammon boards or water pipes.

Even among Egyptians who support the treaty, there were groans ove Begin's speech and his reference to Jerusalem as "one city" -- a point the Egyptians still want to negotiate -- and there has been some grumbling that Begin's visit here next Monday is premature. But most Egyptians seemed more concerned with the possibility tha peace will bring prosperity than with the politics of Jerusalem.

Today was not a holiday here. Shops, schools and government offices were open as usual, and the government did nothing to organize popular reaction one way or the other. Big popular celebrations are planned for Sadat when he returns from the United States and for the day the Egyptians regain control of E1 Arish, the town on the north coast of the Sinai Peninsula that is to be evacuated by Israel within two months.

In the meantime, however, the treaty is not yet officially in effect, since it still must be ratified by the Eghptian parliament and the government has been stressing the difficult negotiations that lie ahead on the Palestian question.

In its calm acceptance of an event that will irreversibly alter the history of the Middle East and require a psychological reconstruction of the entire nation, it was as if Egypt were the eye of a hurricane -- going its own way, untroubled by the rain of criticism being poured down by its Arab neighbors.

Despite considerable popular anxiety about what is going to happen next and unease about the split with the other Arabs, there is little real opposition to the peace treaty. The government strengthened security arrangements over the weekend, stationing riot police at key intersections and installations and reactivating unused checkpoints on the highways, but there were no reported incidents.

The National Union of Students, a nationwide council of university students dominated by sympathizers of the ultraorthodox Moslem Brotherhood, distributed leaflets attacking the treaty on religious grounds.

The leaflets denounced Israel as a "usurper" state, which intended to reestablish the Jewish "kingdom" extending from the Nile to the Euphrates. The Koran, they said, "imposes on every Moslem the duty to arise and struggle to regain every square meter" of Arab land.

Last week, Egypt's minuscule leftist party distributed the same statement, word for word. But so far there has been little visible impact. The Egyptians have accepted the reality of peace with Israel ever since Sadat went to Jerusalem 16 months ago, and the popularity of his policy has withstood many tests.

Egyptians who watched the ceremonies tonight winced as Begin went through what they saw as an excessive and ill-timed reminiscence about the Holocaust. They also criticized his remarks about Jerusalem and his failure to offer anything new on the Palestinian question.

They noted that Sadat, by contrast, omitted remarks in his prepared text warning the Middle East peace could not be complete until the Palestinian question is settled. Sadat has been emphasizing that in his view the more difficult phase of the peace negotiations is to begin a month from now, on the nature and scope of Palestinian autonomy. But the view here seemed to be that today's ceremonies were not the forum for pressing the point.