THE MILITARY TALKS Egypt and Israel opened Thursday, and the political talks they and the United States will open Monday, are the forums in which aspirations for peace will be translated - perhaps - into reality. That the peace process has moved this far in so short a time is as marvelous as it is mind-boggling. But, as Egyptian President Anwar Sadat's new expression of discouragement in October magazine unmistakably indicates, diplomacy cannot live on psychological breakthroughs alone. Events are at the point where further progress will strain the political equilibrium of Israel and Egypt alike.

In Israel it's already happening. Menahem Begin's closest crony went over the side the other day, refusing to support the prime minister's offer to return the Sinai and to grant Wast Bank Palestinians self-rule. The government had to fight hard to keep its right wing from forcing through a more extreme Sinai settlements policy than was adopted, and the Labor opposing stands ready if Mr. Begin flags to turn from sniping to frontal assault. As for Mr. Sadat, Arab "rejectionists" count on his failing to get more than a flimsy separate peace from Israel, if that, to allow them to redouble their attempts to destroy them.

These pressures are not necessarily fatal. Mr. Sadat and Mr. Begin don't live in vacuums. The only forward steps worth their taking are those supported by their constituences, who must either be neutralized or brought along. Such pressures do, however, produce reactions, commonly in the direction of rigidity and nationalistic defiance, and these can shake the negotiations hard. The parties must come to live with this erratic political rhythm, and the rest of us need to as well.

The media's contribution to the process is becoming understood. In the first, open stage, the media provided the means by which the leverage of popular yearning for peace was applied. In the current and inevitably more closed stage, the media are a source of jostling and potential upset. Too often now the game for journalists is to trap one actor in an indiscretion that can be played back off another. Thus on Thursday Jimmy Carter was asked whether the Israelis must withdraw from all Sinai and West Bank settlements before there can be peace. He pretty much sidestepped the invitation to stage a public brawl with the Israelis, like the others, must be worked out by Arab-Israeli negotiation and not American say-so, and 2) the essence of negotiations is to seek positions or processes that allow seemingly unavoidable conflicts to be eased and not exacerbated. If reporters can't stop trying to pick fights, then it's up to the parties not to be baited. In this current stage, while Egypt and Israel labor to widen the political breathing space for negotiation, this is critical.