A system that would allow our nuclear submarines to keep in touch with headquarters without being exposed to prying Soviet eyes has been determinedly deep-sixed by President Carter because of a campaign pledge he made to Michigan voters four years ago.

It will shock the American public to learn what the Russians discovered long ago: Our submarine missile force could not now effectively communicate with the White House in a national emergency from the safety of the ocean's depths.

Like Hansel and Gretel leaving a trail of bread crumbs, a sub that needs to send or receive signals from Washington must use a wire antenna towed either on the surface of the ocean or attached to a buoy just below the surface. Either technique makes the sub a sitting duck for enemy ships or aircraft.

The best way a submarine can protect itself is to run silent and deep -- but at the cost of not knowing what is going on in the world and what the commander-in-chief wants to do. To keep in touch, it must now bob up to periscope depth.

What makes the situation truly shocking, though, is that the Navy found a way out of this dilemma 11 years ago. It is a system known as ELF -- for extremely low frequency. It originally called for 2,400 miles of antenna to be buried in northern Wisconsin and the Upper Peninsula of Michigan. The superantenna would beam messages to subs deep under water.

Why wasn't ELF constructed? Fourteen secret and confidential White House, Pentagon and congressional documents, seen by my reporters Dale Van Atta and Gloria Danziger, trace ELF's scuttling to Oct. 25, 1976.

On that day, candidate Carter, wooing the votes of environmentalists and Michiganders worried about possible dangers in the underground antenna system, promised that ELF "will not be built in the Upper Peninsula of Michigan against the wishes of its citizens."

As president, Carter was persuaded -- briefly -- by his military experts that ELF was too vital to be put off. He asked Congress for $20 million in research and development funds. Military leaders, including Defense Secretary Harold Brown, were unanimous in their view that the need for ELF was both "real and urgent."

But Carter soon began to waffle. On Feb. 16, 1978, in a letter to Brown, the president said he had reservations about ELF, "primarily because of public opposition and the inevitable inconvenience to private landowners as well as its excessive cost." He conceded, however, that his staff could find no alternative to ELF if the nuclear submarine force was to be protected with "a resonable period of time." He recommended a scaled-down version.

Brown kept pushing. Carter kept stalling. One reason appears to have been timely prodding by Sen. Carl Levin (D-Mich.). On Jan. 10, 1979, he warned Carter that if he broke his promise on ELF it would "test the credibility of your administration."

Even more pointedly, Levin wrote the president last May 12 that approval of ELF "would focus the attention of the entire state and nation on [the] issue as a test of your credibility just before the general election."

Footnote: Both the Navy and the National Academy of Sciences conducted studies and concluded there was no cause for concern about environmental hazards.