I am so glad that my comment has triggered reactions! People cling to myth tenaciously. The Bomb in swathed in myths.
Hitler decided against major funding for the atomic bomb project when his troops were winning and this air force ruled Europe's skies. He did not see the need for such a weapon which won't be ready before the war was over. Then, when the tide turned, it was too late.
I posed the question regarding the Pacific Theater: but I did not answer it. Maybe it won't have shortened the war significantly, but it would not have prolonged it.
If you insist on believing that Nagasaki was the straw that broke the camel's back, fine. But the record of the Emperor's intervention in the war council on August 9th says otherwise. The Emperor was running down a long list of the ways the military had failed to deliver on key promises. Hiroshima was not near the top of the list. When news of Nagasaki arrive DURING THE MEETING, it was briefly noted and then attention turned back to other concerns.
Russia joining the fight on August 7th meant that Manchuria and all their conquered lands were lost. It boiled down to picking who to surrender to; they wisely chose the US and Britain.