I've been having rather heated arguments over the bombings of Hiroshima and Nagasaki recently. One idea that I see consistently is that the bombings were unnecessary and that other options should have been pursued. I'm asking what other options were available and why weren't they pursued?
From my understanding it was either the use of nuclear weapons, Operation Olympic (that no one really wanted), or waiting out the Japanese and letting a continued conventional air campaign or starvation take their toll.
In terms of "alternatives" available at the time, I've listed a number of the ones that were considered here. We could summarize them briefly as:
Demonstrate or use the atomic bomb first in a way that would not kill as many civilians, but would make clear how powerful it was
Wait to see what the Japanese did after the Soviet declaration of war against them, which the US was expecting to happen in mid-August
Modify the unconditional surrender requirement so that it would be more likely to be acceptable to the Japanese high command
For Nagasaki, just wait a few more days to see if, after assessing Hiroshima, they changed their mind about the war (the second bombing mission began only 50 hours after the US announced that Hiroshima was an atomic bomb — that's not enough time for the government to verify that it was an atomic bomb and then have a meeting about it)
(Note that Olympic was not scheduled to start until November 1945. So there was still some time for all of this.)
Now whether any of those would have resulted in a better outcome is a speculative venture. But I think it's important to note that 1) there were alternatives and choices made (though not necessarily by Truman personally; some of the above was, some of the above wasn't), 2) that "bomb or invade" was never how it was framed (it was always "bomb and invade"), and 3) this entire question presumes that the goal of the US was to reduce Japanese casualties, and that was not what they were trying to do. That is just not how it was framed; they'd didn't sit around and ask, "gosh, which of these options will kill the least of our enemy?"
They saw the atomic bomb as an additional tool for fighting both the war at hand, and they also saw that it would have huge future impacts (including on relations with the USSR, but also global impacts), and the people in charge saw very many good reasons to use the bombs on cities, and very few reasons not to. Which is not to say that the choices they made were in any way inevitable, but they weren't informed by the sensibilities that the people arguing about this question (on either side) tend to have in posing it.
So the framing of "either bombs or invasion" is a narrative that was invented after the war, to retroactively justify the bombings. In August of 1945, the allies were blockading Japanese ports, conducting conventional fire-bombing raids of Japanese cities, and preparing for a land invasion, while the Soviet Union was also planning to invade Japanese-held territory in Manchuria. I've written before about American and allied efforts in the Pacific.
There's plenty more on the atomic bombings in this section of our FAQ. One thing that it's important to note is that there's a fair amount of reasonable disagreement about what exactly led to the Japanese surrender -- a lot of things were happening around the same time. It's also worth pointing out that the conventional narrative, the idea that Truman had a choice of either dropping the bombs or invading, is incorrect for a couple of reasons. The first is that Truman never made a positive decision to use the bombs -- he just went along with the generals, and it's not clear he even realized Hiroshima was a city. He made a positive decision to stop the bombings after Nagasaki, which he also did not explicitly authorize -- he was clearly uneasy about civilian casualties. The second is that there was never an either/or, it was a both/and -- keep bombing along with an invasion, use bombs on the invasion beaches if necessary, etc.