To what Extent Were the Bombs Dropped on Hiroshima and Nagasaki Necessary to End World War II?

In the analysis on the decision to drop 'the Bomb' on Japan at the end of World War II, historians will usually either tend to one of two schools of thought. The orthodox school stress that the atomic bombs dropped on Hiroshima and Nagasaki were necessary to end the war. The revisionist school argues that the atomic bomb was quite unnecessary. To what extent were the bombs dropped on Hiroshima and Nagasaki necessary to end WWII?
The orthodox theory relies heavily on the argument that Japan had no intention to surrender, and that the Japanese government by silently ignoring the Potsdam declaration expressed a clear refusal of the Allied terms1. The only other options open to Truman were a blockade or invasion. The bomb was conveniently promoted as a legitimate weapon of war and should be used to bring the Japanese to an quick and unconditional surrender2.…