So the simplified history taught in schools is that the US scared Japan into surrender via nukes but it’s obviously more complicated than that. A historical apologist on Facebook was claiming that the US didn’t win either world war and that credit for victory in both conflicts was stolen by the US. When I pointed out how the US beat Japan fair and square they declared that the Soviet Union scared Japan more than America and its nukes. They claimed that it wasn’t Hiroshima or Nagasaki that persuaded the emperor and the high command to accept the Potsdam declaration but rather the soviets entering the war against them. How true is this? I mean I don’t deny that it played a part, that’s for sure. But I’m skeptical on that being more important than the US firebombing and nuking their cities at will and gearing up for an invasion of the home islands.
The way too short answer to this is that the atomic bombings and the Soviet invasion of Manchuria were both important, and reasonable people can disagree about which is most important in forcing Japan's hand in August 1945 -- there's plenty more in our FAQ about this. To borrow a list from this blog post by our own /u/restricteddata, many things happened in early August, including
The bombing of the city of Hiroshima
The Soviet declaration of war against the Japanese, and subsequent invasion of Manchuria
The bombing of the city of Nagasaki
Internal friction within the Japanese high command
An attempted coup by junior military officers
An offer of surrender that still maintained the status of the Emperor
A rejection of this offer by the Americans
An increase of American conventional bombing
An acceptance of unconditional surrender by the Emperor himself
and so forth.
I'll leave you to that link and the FAQ, but I would also just point out that the "The Soviets won the war and the US did nothing" narrative does rather a disservice to the massive scale of the American war effort, about which I've written before:
It was both: significantly, while Hirohito's surrender announcement to the people on August 15 spoke of the bombing, his rescript to the armed forces two days later instead singled out the Soviet intervention. On August 10 Truman's advisers were already discussing the need to soften peace terms to forestall a Soviet invasion of Japan itself.
It's worth recalling what the Soviet action in Manchuria entailed: this was no sideshow but an action involving over a million troops on each side, involving the fate of a territory of 45 million inhabitants which had been the base for Japan's invasion of China in the 1930s. And if Manchuria fell, Korea would follow along possibly with northern China proper, exposing the Japanese homeland to invasion from the west.
And politically, the Soviet declaration of war killed off Japanese hopes of negotiating a compromise peace through Moscow - the very reason given for Tokyo's conditional offer of August 10. For its part, US military intelligence was far from confident that more bombings would end the war any time soon, assistant C-of-S Bissell on August 12 reporting its view that "atomic bombs will not have a decisive effect in the next 30 days".
In the event, the war was ended by implicit US acceptance on August 11 of Hitohito's continuation as Emperor subject to Allied commands - less than Japan had asked for, but enough for Hirohito and his civilian advisers to override the war party. Until that point, neither the bombings nor Moscow's intervention had finished the job, but between them they forced the compromises that made peace possible.
