No 500.000 American lives were lost, an invasion never took place, it's purely speculation. After Japans ally Germany was defeated, (now speculating as you did) Japan could have reached an agreement and cease fire, stopping hostility towards the US.
A "show-off" of the bomb (or two, three, four of them) could have been enough, or not. Fact is that Japan was severely hindered at the time they were bombed, as what I know, they lost almost their hole fleet beforehand, how would they be an immediate menace for the US, without having anything to attack with?
#1. the japanese were not Iraqi's, shock and awe would not have impressed them. I give the Japanese full credit, they were amazing warriors many of whom lived by the bushido code of death before dishonor and they truly meant it.
the japanese were close to building their own atomic bomb. there is even some evidence they detonated a atomic bomb in korea. what is clear is that the germans and Japanese were aware of nuclear fussion and realized that chain reactions could be produced...the fact is America was not the only country aware of and working on atomic weapons.
had we not bombed japan and left them alone thinking they were defenseless and have nothing to attack us with would have been a dramatic error with potentially catastrophic results.
if you think that saying the Japanese or germans would have used atomic weapons against us if they had developed them first is speculaton, then I speculate on your sanity.
What I know from history at school was heavily influenced by the regime, as I'm born in east Germany. Could it be that even you are indoctrinated by biased history?
To my understanding, Japan was economically destroyed at the time of the bomb. They endured famine and a complete blockade by sea and were on the brink of surrender, correct me if I'm wrong.
I may have to read about it again, but nah, not that interesting for me.
If others would have used the bomb against civilians, if they could? Speculative, but could be.