Britain's troubles in the Falklands today could be America's troubles on a much larger scale tomorrow.

Britain's difficulties derive from a contradiction between two aspects of basic strategic policy.

When Britain withdrew from most of its overseas empire, it retained defense commitments requiring an ability to quickly mass enough sea power to forestall adventuristic neighbors.

Instead, Britain elected to try to maintain a fiction of world power by putting scarce naval appropriations into ballistic missile submarines, useless anywhere that Britain might have to act alone and redundant in any confrontation with the Russians.

The upshot is that Britain's usable forces are stretched to the breaking point in defense of commitments that it was unwilling to relinquish or to properly defend.

Although Defense Secretary Caspar Weinberger talks about "intellectual reform" of strategy, the fact of the matter is that our armed forces are stretched every bit as thin in relation to their commitments as are Britain's.

We cannot apply adequate conventional forces at any point of our commitments in time to prevent defeat by our major adversary without recourse to nuclear weapons; hence Secretary of State Alexander Haig's impassioned defense of the right of "first use."

Gen. Maxwell D. Taylor, former chairman of the Joint Chiefs of Staff, has called for a reexamination of our strategy to identify our true "vital" interests and then to design a military strategy to defend those interests.

One of our problems is that nowhere in the U.S. government is there an officially accepted definition of "vital interests." Left to our own devices, a reasonable definition would seem to be, "That which pertains to the survival of the United States and our free institutions."

Beginning with Thomas Jefferson, our statesmen have believed that the massing of Europe's resources under a single "sovereign" would pose a mortal threat to the United States. That led us to oppose German dominance in two world wars.

We took the same view of an industrialized Asia, and that led to war with Japan.

American conviction that Russian domination of the entire Eurasian land mass would be a mortal threat is a logical progression from the earlier asessments.

But what of the Persian Gulf and the Middle East generally?

We have a moral commitment to Israel that compels us, in Henry Kissinger's words, to protect "Israel, but not Israeli conquests." We have a self-proclaimed "vital interest" in the Persian Gulf which, on examination, proves to be a European and a Japanese vital interest in maintaining oil supplies. But there are few European and no Japanese forces in sight to help defend those interests.

As a result of this accumulation of real and perceived vital interests, we are every bit as overcommitted as Britain.

The initial response of the Reagan administration to this dilemma was to raise the defense budget to a level commensurate with our commitments. The result was to drive the country into an economic crisis. Does that not also impinge on a "vital interest."

Britain has been able to get away with its strategic fantasies this long because, in effect, we were picking up the bill long before we formally announced support in the Falklands confrontation. We are also underwriting Britain's largely emotional military involvement in Ireland, since Britain would not dare divert such forces from the Army of the Rhine if it thought that would mean turning the defense of Europe over to the Germans.

By similar means, we are financing what even liberally inclined American reporters call "bloated" European social services while more and more of our own people are being turned out into the streets.

Few challenge the idea that we have a genuine vital interest in maintaining a free Europe. But does that mean maintaining an American army there when the Europeans have all the manpower and money they need to replace it?

If the logic supporting a European vital interest is valid, we have a true vital interest in maintaining Japan as a democratically run country free of either Soviet or Chinese control. Quite rightly, we are asking the Japanese to devote greater resources to maintaining this mutual interest, but the main responsibility for control of the Pacific sea lanes will continue to be ours.

Whatever our real interests may be in the Persian Gulf, we must face up to the fact that they are virtually indefensible. We have no real friends in that region other than Israel and Turkey. Israel is too small and Turkey too exposed and poor to be of much help. We must find a way, then, to so threaten Soviet interests in an area in which we are strong and the Soviets are weak that they dare not employ their overwhelming geographic advantages in the Persian Gulf and the Middle East generally. That obvious area of Soviet vulnerability is the North Pacific.

The shadow of the Falklands episode falls as much on Washington as on London. If we do not soon rethink and re- size our strategic commitments along the lines Gen. Taylor has suggested, we are apt to find ourselves in a situation far more desperate than anything the British are likely to encounter.