IN HIS SPEECH last Wednesday night, President Reagan urged American scientists "to turn their great talents to the cause of mankind and world peace: to give us the means of rendering...nuclear weapons impotent and obsolete."

The world would surely rejoice if such a feat were possible. Unfortunately, it is not. Following the president's proposed course would only create false hopes and, in all likelihood, intensify nuclear dangers rather than diminish them.

There are, to begin with, serious doubts about the technical feasibility of developing a defense against ballistic missiles and the Soviets could not easily counter -- doubts that were aired widely in the late '60s and early '70s.

Our nation has overcome many technical challenges in the past, of course, and we certainly should not shrink from another if it would end or seriously reduce the threat of nuclear war. But the president's approach has problems that go far beyond technology. Consider just five:

1. Defending against bombers and cruise missiles. Ballistic missiles are only part of the nuclear threat we face. For example, low-flying bombers and terrain-hagging cruise missiles could pass unaffected through a defense such as the president proposes.

In fact, as unlikely as it may seem, defending against nuclear-armed bombers and cruise missiles is an ever greater technical challenge than defending against ballistic missiles. And if the defense against the bombers and cruise missles were not perfect, the weapons that "leak through" could destroy the ground-based components of the ABM system itself. Unless a defense can keep out all types of weapons, it is useless in a nuclear war.

2. Our allies. President Reagan said that our defense should destroy Soviet missiles before they reach "our own soil or that of our allies." But the Soviets have many ways to launch nuclear weapons against our allies in Europe that would be unaffected by an ABM defense. They could use aircraft, nuclear artillery or even armored vehicles carrying "atomic demolition munitions" with an invading force. It is inconceivable that an effective nuclear defense could be developed for Europe.

3. Treaty commitments. The president says he will carry out his program consistent with our obligations under the ABM treaty." But that treaty explicity prohibits not only the deployment but even the development of any system based in space -- the most likely candidate for the technological breaktrough the president seeks.

4. Destabilizing the nuclear balance. One can envision a world in which the nuclear powers have limited offensive capabilities and effective defenses. A small residual offensive nuclear force would still deter some wars, while the defense would eliminate threats from third countries and concerns about accidental attacks, and perhaps even the threat of massive destruction should war occur. But how do we get from where we are to this Nirvana?

Without a complete political reconciliation with the Soviet Union (which Reagan certainly does not anticipate), the initiation of large-scale ABM deployment by either side would be seen as an attempt by the other to enhance its capability to fight a nuclear war successfully.

The Soviets would understand this and undoubtedly respond with countermeasures to any ABM we deployed. The result would be a new escalation of the arms race, greatly exacerbated international tensions, and increased risk of nuclear war.

5. Cost. A full-scale AMB program, carried out in combination with the other necessary elements of such a posture (defense against bombers and cruise missiles, civil defense, defense of our allies, and a buildup of conventional weapons to offset the reduction in nuclear deterence) could easily double our current $250 billion-a-year defense budget.

The national could afford this if it had to -- defense would still be only about 12 percent of our Gross National Product. But it would call for an overwhelming national effort, requiring all elements of our society to be involved in active preparation for the possibility of war. It is inconceivable that the American public would support such an approach.

The president obviously is sincere in his concern about the risk of nuclear war and in his desire to marshall our scientific strength to reduce or eliminate this risk. But, unfortunately, some problems simply are not susceptible to easy techological solution.

There is no way we can turn the technological clock back on the overwhelming power of nuclear weapons. Our best hope is to negotiate effective arms control agreements that contain the risk and ultimately eliminate it. As we pursue negotiations, we must maintain strong and effective military programs that will deter Soviet aggression. But it is folly to pin our hopes on the chimera of a perfect or safe defense.