While there are many people who subscribe to your view, there are an equal number who believe that Japan would have surrendered within months/weeks with no ground invasion.

The allies had complete air and naval superiority and Russia had joined the the Japanese war theatre.

If you have read the ethics of atomic bombings in any detail you are already aware of the details, so I would refrain from linking to wikipedia. To push your POV that the bombing was entirely necessary and entirely morally right is immoral.

[Edit]

As requested below: here are the detail about the military unneccesity of the atomic bombings. http://en.wikipedia.org/wiki/Debate_over_the_atomic_bombings...

There are other debates around this, but this discusses only if Japan would have speedily surrendered without the Atomic bombing.

The purpose of the nuclear bomb was the same as the purpose of strategic bombing in general - to destroy buildings and infrastructure and kill people indiscriminately. The nuclear bomb was not fundamentally different in that aspect - strategic bombings had been going on for years and was highly destructive and deadly already. For example the firebombing of Tokyo with conventional bombs killed more people than the Hiroshima nuclear bomb. So the use of nuclear bomb did not require any special explanation or justification. It was natural extension of the strategy in use.

Of course it can be said that the purpose of the use of any weapon is to win and thereby end the was sooner, hence saving lives in the long run. In that case the purpose of any bomb, tank, landmine or gun is to save lives.

One can entertain the idea that the eventual outcome was ultimately better for all parties than the alternatives (though it's far from clear that's the case when the alternatives included "not playing hardball over unconditional surrender" and the scientists' favoured alternative of "demonstrate the bomb in a relatively benign manner") but the minutes of the meetings that made the decision quite explicitly discuss relative merits of targets in terms of the anticipated destructive effect on civilians, speaking favourably about wiping out Kyoto because of its high concentration of intellectuals before ultimately choosing Hiroshima over more obvious military targets because it "has the advantage of being such a size and with possible focusing from nearby mountains that a large fraction of the city may be destroyed" (and not really being militarily significant, it was largely undamaged). The notion that the surviving Japanese might ultimately be better off doesn't seem to have featured so highly in the decision-making calculus.

How many children was it worth killing to make sure Japan lost? What if the alternative to bombing Japan wasn't an invasion of Japan?

How about using those bombs on or over invading fleets of Japanese - if Japan ever actually planned to invade the US?

You have to look at these things in the context of the war that had been going on for years at the time. Imperial Japan had attacked, invaded, and occupied any neighbors who had resources they might need or who otherwise might oppose them. That occupation often came with brutality and oppression at a scale that would make the Nazis blush.

When the US entered the war, one of their first moves was unrestricted submarine warfare, meaning any Japanese ship is sunk on sight, regardless of who or what is onboard or where it is heading. It continued with sinking many naval fleets, re-invading many islands, generally resulting in the death of basically everyone in the Japanese garrison, as it was part of their code to kill themselves or carry out suicide attacks rather than surrender.

Continuing on, we have the unrestricted aerial bombing of basically every city in Japan. The only reason Hiroshima and Nagasaki were relatively untouched so late in the war was that they were exempted from conventional bombing for the purpose of evaluating the effectiveness of the atomic bombs when they were ready. Many of the conventional bombing raids caused greater death and destruction than the atomic bombings.

In light of all of this, suggesting a demonstration of the bomb seems kinda pointless. The Imperial Japanese administration would probably interpret such an act as saying that America didn't have the courage to carry out major attacks, thus encouraging them to hold out longer and requiring more destruction in the end to force a surrender. The bombings were terrible, but the real suffering was the war itself, and the only way to stop it was to force the surrender of Imperial Japan as quickly as possible. Against such an enemy, the best way to end the war with as much of Japanese society as possible still intact was to demonstrate total ruthlessness in doing anything in our power to destroy Japanese infrastructure and kill Japanese citizens as quickly as possible.

> It strikes me as pure evil that the very first use of nuclear energy was to drop a massive bomb over a bunch of fellow humans.

Atomic weapons are a natural evolutionary step up from conventional explosives, which are a natural evolutionary step up from clubs and rocks. All this talk about atomic weapons being qualitatively different (as opposed to quantitatively different) is mostly hyperbole, with one exception -- only wealthy industrial powers can create them ... so far.

> Surely the force of nuclear weapons could have been demonstrated without actually dropping it on a concentration of living, healthy people.

The people in charge decided that a demonstration wouldn't stop the war or the need to use the new weapons, and later events proved them right. Contrary to what many Americans believe, the Japanese didn't surrender because of the atomic bombings, but because Russia invaded Manchuria, a development the Japanese saw as much more dangerous than atomic bombs.