Why Sakharov begins fast

Andrei Sakharov, the world-renowned Soviet physicist and dissident, and his wife have begun a hunger strike to try to overcome Soviet opposition to the reuniting of two of their family members.

In a letter, a copy of which was obtained by this newspaper, Mr. Sakharov explained that he and his wife, Elena Bonner, ''despaired of breaking through'' by other means what he described as a ''wall'' of resistance built by the Soviet secret police, the KGB (Committee for State Security).

Sakharov and his wife, who now live in ''internal exile'' near the Soviet city of Gorki, began their hunger strike on Nov. 22. In a letter to ''foreign colleagues'' dated Oct. 9, Sakharov explained that his stepson Alyosha had been forced to emigrate from the Soviet Union to the United States 31/2 years ago. Alyosha's fianccf11ee at that time, Liza, had to remain behind. In June 1981, Alyosha and Liza were married by proxy in the state of Montana.

In his letter, Sakharov charged that Soviet authorities have not only refused to allow Liza to join her husband, but are ''persecuting her, threatening her with arrest, and attempting to deprive her of hope and drive her to despair.''

Although Soviet authorities do not acknowledge the validity of the marriage by proxy of Alyosha and Liza, Sakharov argues that it does affirm the deep desire of the couple to be together.

''According to the Helsinki accords and other international documents signed by the USSR, such a desire is sufficient grounds for Liza to receive permission to emigrate,'' said Sakharov, whose criticisms of the Soviet regime have brought him into disfavor. Sakharov, an atomic physicist and one of the fathers of the Soviet ''H'' bomb, remains a member of the Soviet Academy of Sciences.

The Sakharov International Committee, a group of intellectuals, scientists, and members of the US Congress, has sent telegrams concerning the Sakharovs' hunger strike to presidents Brezhnev and Reagan. The telegrams, which urge help in obtaining a Soviet exit visa for Liza, carry the signatures of 30 leading American scientists, 20 of them Nobel laureates. One of those laureates, Linus Pauling, is also the holder of a Lenin peace prize.