Again, this is a very difficult question to answer as it involves a question of ethics, not military necessity.
We knew that the Japanese government was sending inquiries to the Soviet government asking them to relay those inquires to the United States (since, as far as Japan knew, Russia was still neutral with Japan - see secret agreements during the Yalta Conference) inquiring about what surrender terms the United States might demand. We knew this because we had broken the Japanese code earlier in the war and understood their coded messages. Let me repeat - we knew of these Japanese inquires BEFORE we dropped either bomb. I believe personally that if we had promised to Japan that they could keep their emperor as a figurehead, (which we eventually allowed), Japan might have agreed to a surrender without the atom bomb. Whether the Japanese military would have staged a coup and continued the war effort is another (and so far unanswerable) question.
If the only alternative to ending the war was an invasion of the Japanese mainland, scheduled for the summer of 1946, then it could be logically argued that the atom-bomb did end the war early and saved, perhaps, hundreds of thousands of lives. Even hundreds of thousands of Japanese lives.
It has been argued that the real reason we dropped the atom-bomb was to intimidate the Soviet Union in the post-war years. We showed them that we had a nuclear bomb as well as the ability to deliver it. (Of course, through their own spy network, they already knew that.) This is a highly controversial theory but one that I, personally, feel holds some validity.
In my personal opinion, the answer to this is an emphatic no. While it can be argued that dropping the bomb ended the war more quickly thus preventing the loss of American lives, that cannot be prov en. There is a great deal of evidence to suggest that Japan was ready to end the war before the bomb was dropped.
Among thos Americans who felt that dropping the bomb was, essentially, overkill was Dwight D. Eisenhower. Eisenhower initially supported the idea, but then revised his opinion stating:
I was one of those who felt that there were a number of cogent reasons to question the wisdom of such an act. ...the Secretary, upon giving me the news of the successful bomb test in New Mexico, and of the plan for using it, asked for my reaction, apparently expecting a vigorous assent. "During his recitation of the relevant facts, I had been conscious of a feeling of depression and so I voiced to him my grave misgivings, first on the basis of my belief that Japan was already defeated and that dropping the bomb was completely unnecessary, and secondly because I thought that our country should avoid shocking world opinion by the use of a weapon whose employment was, I thought, no longer mandatory as a measure to save American lives. It was my belief that Japan was, at that very moment, seeking some way to surrender with a minimum loss of 'face'. The Secretary was deeply perturbed by my attitude...
Herbert Hoover, too, was revolted by the use of a weapon that killed so many innocent people in a war that was ready to be ended through diplomacy:
I am convinced that if you, as President, will make a shortwave broadcast to the people of Japan - tell them they can have their Emperor if they surrender, that it will not mean unconditional surrender except for the militarists - you'll get a peace in Japan - you'll have both wars over
There are many other well-respected Americans, military and political figures who were well versed in the situation, who echoed these sentiments. Military attacks that are directed at civilian targets should be a last resort, if and only if all efforts at diplomacy have failed and show o signs of doing anything more than continuing to fail in the future. This was clearly not the case in this situation. Could the war have ended diplomatically and without the bomb - it is my belief that it could have, but we will never know because the choice was made and the rest is history.
The debate on this question seems to be endless. There are many conditions that help to determine an individual's answer. Given the blurred lens of the time period in terms of what was justified and needed, as well as how groundbreaking it was to use the atomic bomb, it becomes more difficult to determine what was right and what was not. There is evidence to indicate that the Japanese were already losing, yet there is equal evidence to indicate the Japanese were not going to abandon the fight. There is evidence to indicate that a trial could have been held that would have convinced the Japanese to desist military operations, while there is as much evidence to indicate that the loss of critical uranium needed to build the bomb might have been a reality with excessive test trials. There is analysis to suggest that the bomb's dropping helped to save American military personnel, yet the results of dropping it cannot be denied and explained away. Both sides of the argument are equally compelling and perhaps the only way out of this is that one fully concede the authenticity of the other side in their own belief system.