Twelve days ago Andrei Sakharov, the nuclear physicist who has come to personify the most trenchant and uninhibited drive for human rights in the Soviet Union, began an indefinite hunger strike. He took the desperate step to press the government to allow a young woman to emigrate to the United States to join the man to whom she was married by proxy.

The Kremlin, generally extremely reluctant to yield under public pressure, previously has rejected attempts by the woman, Liza Alexeyevna, 26, to join Alexei Semenov, who is Sakharov's stepson. Sakharov, on the other hand, has asserted that the only possibility of ending his protest would be if the government changed its mind.

The confrontation is without precedent and so is the war of nerves between the two sides. The Kremlin has maintained public silence on the issue. For all practical purposes, Soviet officialdom silenced Sakharov almost two years ago by banishing him to Gorki, an industrial city 250 miles east of here that is closed to foreigners.

But if there is one man in this country whose accomplishments, intelligence and strength of character would permit such a brazen challenge with some dim hope of success, it is the 60-year-old Sakharov.

He is one of the country's foremost theoretical physicists and was instrumental in developing the Soviet hydrogen bomb. Over the years he has received more honors and awards than most of the Soviet leaders. He was the recipient of the 1975 Nobel Peace Prize.

The last thing the Kremlin would want at a time when it is courting Western public opinion is to have a man like Sakharov die, particularly while protesting an issue such as the exit visa.

It is precisely his preeminent standing in Soviet science that has made Sakharov's dissent such a complicated issue for the authorities. He is still a member of the Academy of Sciences and it is believed that the government thus far has been unable to secure a two-thirds majority of votes in the required secret ballot to expel him from that body.

Nor could the authorities resort to the "Solzhenitsyn solution" and expel Sakharov the way they did Nobel laureate and author Alexander Solzhenitsyn. As a friend of the physicist said, "Sakharov has been told that even if he does not know any secrets anymore, he still has his head on his shoulders. So they would never let him go."

Hence, the authorities seem to have been deliberately calculating their moves to shift Sakharov's attentions away from broad moral and political issues toward a relatively minor question of an exit visa for the wife by proxy of his stepson.

Semenov is the son of Sakharov's wife, Yelena Bonner. Bonner, 58, has also joined Sakharov in the hunger strike.

The official approach appears to have been designed to discredit Sakharov before Soviet audiences by suggesting that he was taking "extreme steps" for the benefit of a relative.

The legal aspects of the case are complicated. Semenov, was allowed to emigrate to the United States four years ago. He was married at the time to Olga Luvshchina and they have a 6-year-old child. Luvshchina and the child emigrated to the United States 18 months ago. They subsequently divorced in the United States and Semenov, a graduate student at Brandeis University, married Alexeyevna in a proxy ceremony in Montana last summer. In a proxy ceremony, a third party stands in for the absent bride or groom with the consent of the absentee.

Though the Soviets do not recognize such marriages, the proxy wedding could be used to try to buttress Alexeyevna's case for emigration with Soviet authorities, who recognize the right to emigrate on grounds of family reunification.

Alexeyevna's parents, however, have refused to sign an affidavit required for an exit visa. Both her father, who is a retired Soviet Army lieutenant colonel, and her mother do not want her to leave the country.

But what counts at this critical point more than the merits of the case is the serious threat to Sakharov's life. Knowledgeable sources said that because of his age, Sakharov's condition is likely to become critical in the next few days. He has stopped taking medications for his heart condition, which is described as a circulation problem. Sakharov and Bonner are taking only mineral water during their protest.

There have been no telegrams from Gorki since Tuesday, when Alexeyevna received the following cable: "Little Liza, we are okay. We are holding on cheerfully. We are following our regime on December four. Send a telegram to Tanya and Reme from us. They have their eleventh anniversary. How is the health of Georgy Nikolayevich? Kisses."

The reference to Tanya and Reme was to Bonner's daughter and son-in-law who are in the United States. Georgy Nikolayevich Vadimov is a Soviet writer who is a friend of Sakharov. He is currently in the hospital.

"I am very afraid for him," said Alexeyevna as she led visitors into a sparsely furnished room that was once Sakharov's bedroom, study and place to receive guests.

"He has a bad heart and this is very bad for him. But, you know, I cannot interfere with what he regards as necessary." She said she and Bonner had opposed his drastic protest. Alexeyevna quit her job as a computer technician 19 months ago and has been practically adopted by the Sakharovs.

Since his marriage to Bonner after being widowed in 1969, Sakharov's relations with his three children have cooled considerably, according to family sources. The walls of his Moscow apartment are decorated with a few icons, a lot of books on painting and pictures of Bonner children and grandchildren. Sakharov and Bonner met in 1970. She had been an active dissident for some time.

Sakharov himself was virtually unknown to the Soviet public until 1968, since he had spent most of his working life employed in secret laboratories. He fell from favor in that year for an essay in which he rejected censorship, intellectual restraints and Soviet pressure against the liberal communist government in Czechoslovakia.

In a statement issued in Gorki, Sakharov said that Alexeyevna was "the only" reliable source of news about his situation.

Both Alexeyevna and another Sakharov friend, Natalia V. Gesse of Leningrad, insisted that the hunger strike was "a logical step to remove certain problems" and that "this action is, in a broad sense, a struggle for human rights and legality."

Over the years Sakharov has attacked "an illusory detente that is not accompanied by an increase in trust and democratization." He has accused Soviet authorities of systematically violating human rights, and condemned the Soviet invasion of Afghanistan.

It is unclear whether the impact of the banishment to Gorki is affecting the physicist. He is living in a four-room apartment at the city's edge and is under constant police surveillance. There are only two persons from Gorki who are allowed to visit with him. One of them is a scientist but it was made clear that he was not an adequate conversation partner.

Gesse, who visited Sakharov last summer, has said that he was engaged in scientific work and that he was dealing with the problem of the open universe. The Soviet physicist was trying to disprove Einstein's theory of a closed universe.

Gesse said that Sakharov explained his new theory to her. "I felt like I was sitting on the sharp edge of the knife on both sides of which lay ignorance. I asked him if he saw his theory in a practical context and he said, 'Why, of course I see it that way.' "

Sakharov's friends insist his decision to stage a hunger strike was "carefully thought out." But his latest pronouncements smuggled out of Gorki suggest that he felt betrayed by his colleagues and surrounded, as he put it, by "lack of understanding, indifference and passivity."

He had appealed three times to President Leonid Brezhnev and the president of the Soviet Academy of Sciences, A. P. Alexandrov, in an effort to obtain an exit visa for Alexeyevna. He received no reply.

Sakharov also has written to his colleagues, the most illustrious physicists in the country with whom he was associated for a long time, including the dean of Soviet sciences, Pyotr Kapitza. He received no answers and he said he was "deeply disappointed not only on the personal level but also with the escape from responsibility" on the part of his colleagues.

"There is no talk about any contacts with my Soviet colleagues," Sakharov said in a letter, no talk of "any scientific work with them, as long as the tragedy of people close to me continues."