How did Truman's decision to use the atomic bomb forever change the nature of international relations?
Truman's decision to use the atomic bomb against Japan changed the future of international relations in a number of ways. First, in the short term, this move led to further distrust between the United States and the Soviet Union. The Soviet Union knew about the American Manhattan Project but was hurt that this new technology was not made available. The Soviet Union subsequently stepped up its own nuclear research and, by the end of the decade, would test nuclear weapons secretly on its own. The atomic bomb led to Japan's immediate surrender to the United States and made the United States the primary occupier of the island. The United States then remade the Japanese Constitution and the future of the country was far different than that of occupied Europe.
In the long term, the decision to use the atomic bomb created an arms race between the Soviet Union and the United States. After the Soviet Union developed its own bomb, both nations developed new weapon delivery systems and even larger bombs than the ones dropped on Hiroshima and Nagasaki. Under Eisenhower, the United States spent more on its nuclear arsenal in the hopes of not letting the Soviet Union get ahead. The whole idea was that a nuclear strike between the two powers would lead to the total destruction of both nations, thus making warfare quite costly and impractical. The United States developed a strategy called "mutual assured destruction" with the appropriate acronym MAD to describe its new Soviet strategy. While spending on nuclear capacity would rise and fall over the years, throughout the Cold War both the United States and Soviet Union focused on the delivery capabilities of these new terrible weapons. This nuclear stalemate was one of the key factors which led to no direct warfare between the two powers; instead a series of proxy wars was conducted throughout the developing world.
The development of the atomic bomb did more to change the nature of international relations than Truman’s decision. If Truman had not used the bomb then, it would eventually have been used and things would have changed at that point. So, it is the existence of atomic bombs/nuclear weapons that matters more than Truman’s decision.
The existence of nuclear weapons changed international relations forever because it, in essence, made all-out war against a nuclear power unthinkable. Before the development of nuclear weapons, it was possible to contemplate a war that might lead to the destruction of another country. Hitler clearly contemplated just such a result when he invaded the Soviet Union. He could launch that invasion, rationally expecting to be able to win. After nuclear weapons were developed, such thinking was impossible. There is no rational way to launch a major war against a nuclear power. It is clear that if you get to the point where you are seriously threatening that power’s existence, it will attack you with nuclear weapons. A unilateral nuclear attack destroys much or all of your country. A nuclear exchange can destroy all of both countries. This sort of thing is too horrible to contemplate.
Thus, the development of nuclear weapons, in a way, removed war between major powers as a possible instrument of international relations.